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Extension cards

Forms of the base methods for different data types. Each card describes only the difference: cell format, scale alignment, distance or score, how to read the output; for philosophy and mechanics see the base method card, for the family see the data type card.

TOPSIS

Base method →

Fuzzy TOPSIS (Chen and Hwang, 1992)FuzzyThis is the earliest form of TOPSIS to express criterion values as a four-number trapezoidal fuzzy number. Each cell carries the lowest defensible value, the two ends of the plausible band, and the highest defensible value together. The method builds the ideal and anti-ideal point from the alternative set's own extremes, measures distance through the overlap of the fuzzy numbers, and ranks the result with a single closeness score.
Fuzzy TOPSIS (Chen 2000) (Chen, 2000)FuzzyThis is the form of TOPSIS that works with triangular fuzzy numbers for situations where expert scores are verbal or approximate, such as "good," "medium," "poor." It carries uncertainty through the calculation and still ranks the result by a closeness score.
Grey TOPSIS (Zavadskas, Turskis and Bagočius, 2015)GreyThis is the form of TOPSIS that works with grey interval numbers, for situations where a criterion's value is known only by its lower and upper bound. It carries the bounds separately through to the very last step, builds the ideal and anti-ideal point from those bounds, and ranks the result with a single closeness score.
Intuitionistic fuzzy TOPSIS (Boran, Genç, Kurt and Akay, 2009)IntuitionisticThis is the form of TOPSIS that expresses criterion assessment as a degree of support for, and a degree of rejection of, a judgement; this pair is called an intuitionistic fuzzy number. The method combines the views of several decision-makers and builds the ideal and anti-ideal points from these pairs. It measures distance through the degree of membership, the degree of non-membership and hesitancy, and ranks the result with a single closeness score.
Bipolar Neutrosophic TOPSIS (Akram, Shumaiza and Smarandache, 2018)NeutrosophicThis is the bipolar neutrosophic form of TOPSIS. It carries the positive and negative evidence behind a judgement in separate poles, and within each pole it keeps truth, indeterminacy and falsity apart. The method builds the ideal and anti-ideal point from these six components and ranks the result with a revised closeness measure.
Neutrosophic TOPSIS (Biswas, Pramanik & Giri, 2016)NeutrosophicThis is the single-valued neutrosophic form of TOPSIS. Criterion evaluation is given through degrees of truth, indeterminacy and falsity. The method builds the ideal and anti-ideal points from these three components, measures distance across all three, and ranks the result with a single closeness coefficient.
Pythagorean fuzzy TOPSIS (Zhang and Xu, 2014)PythagoreanThis is the Pythagorean fuzzy form of TOPSIS. The support and rejection degrees given to a judgement may sum to more than 1, provided the sum of their squares does not. The output is again a single closeness measure and a rank, built relative to the ideal and the anti-ideal.
Spherical fuzzy TOPSIS (Kutlu Gündoğdu and Kahraman, 2019)SphericalSpherical fuzzy TOPSIS is the form of TOPSIS used when criterion scores are given as three separate numbers stating a degree of support, rejection and hesitancy for a judgement. The calculation comes down to a single closure ratio; a small value in this ratio shows closeness to the ideal.
q-Rung orthopair TOPSIS (Pinar and Boran, 2020)q-Rung OrthopairThis is the form of TOPSIS for situations where an expert assigns a judgement both strong support and a strong reservation at once, and the sum of the two exceeds the intuitionistic or Pythagorean bound; it still ranks the result with a single closeness score.
Picture fuzzy TOPSIS (Sindhu, Rashid and Kashif, 2019)PicturePicture Fuzzy TOPSIS is the form of TOPSIS used when criterion scores come from a committee's or a survey's yes-abstain-no vote distribution. It runs the calculation directly on these three-degree votes and still ranks the result with a closeness score.
Hesitant fuzzy TOPSIS (Xu and Zhang, 2013)HesitantThis is the form of TOPSIS for situations where more than one plausible membership degree is held together for a single criterion. It carries these sets through the calculation and ranks the result, once again, with a single closeness score.
Plithogenic TOPSISPlithogenicThis is the form of TOPSIS for situations where criterion scores are given as a truth-indeterminacy-falsity triple and criteria carry a degree of contradiction relative to one another. Its output is again a closeness score and the ranking that follows from it.
Rough TOPSIS (Song, Ming & Wu, 2013)RoughThis is the form of TOPSIS that works with rough numbers for situations where criterion scores come from several experts' group assessment and the disagreement itself needs to be preserved. It carries the uncertainty as a lower and upper bound all the way to the final step, and still ranks the result with a closeness score.
Z-number TOPSIS (Gardashova, 2019)Z-NumberThis is the form of TOPSIS for situations where every criterion value is given together with how far that value can be trusted. The output is again a closeness score, and a rank drawn from that score.
2-tuple linguistic TOPSIS (Wei et al., 2010)LinguisticThis is the form of TOPSIS for situations where expert scores are chosen from a pre-declared term set, and where the aggregation result is preserved with its shift rather than rounded to a term.
Probabilistic linguistic TOPSIS (Lu et al., 2019)LinguisticThis is the form of TOPSIS for situations where an expert gives several terms together with their probabilities. It reduces every term distribution to a single expected value, then ranks the result with a closeness score as usual.
Bipolar fuzzy TOPSIS (Alghamdi, Alshehri & Akram, 2018)m-PolarThis is the form of TOPSIS for situations where each cell records, separately, a judgement's effect in the desired direction and its effect in the opposite direction. The two effects are reduced to a single score in the very first step, and the rest of the calculation follows the same path as crisp TOPSIS.
Complex Fuzzy TOPSISFuzzyThe form of TOPSIS for situations where the degree of support for, and rejection of, a judgement carry two components, amplitude and phase. It measures distance to the ideal and anti-ideal point through these two components and ranks the result with a closeness score.
Cubic intuitionistic fuzzy TOPSIS (Garg & Kaur, 2018)IntuitionisticThis is the form of TOPSIS for situations where a cell carries, together, both an interval-valued intuitionistic fuzzy pair AND a single-point intuitionistic fuzzy pair layered on top of it. It processes both layers and ranks alternatives with a single closeness coefficient.
D-number TOPSIS (Fei, Hu, Xiao, Chen & Deng, 2016)StochasticThis is the form of TOPSIS for situations where a criterion value is given not by complete, exact evidence but by a body of evidence that can remain incomplete or partial. It reduces every cell from this evidence to an expected value, and processes the rest exactly as crisp TOPSIS does.
Dual hesitant fuzzy TOPSIS (Wang, Li, Zhang and Han, 2020)HesitantThis is the form of TOPSIS for situations where a cell holds more than one possible degree of support and more than one possible degree of rejection, recorded separately and independently. It measures the distance to the ideal and anti-ideal point through these two sets, and ranks the result with a closeness coefficient.
Fermatean Fuzzy TOPSISFuzzyThis is the form of TOPSIS for situations where it is not the sum but the sum of the cubes of the support and rejection degrees given to a judgement that must not exceed 1. It accepts stronger support-rejection pairs than intuitionistic fuzzy allows, and processes the rest exactly as crisp TOPSIS does.
Interval-valued intuitionistic fuzzy TOPSIS (Jahanshahloo, Lotfi and Izadikhah, 2006)FuzzyThe form of TOPSIS for situations where criterion values are given with a lower and an upper bound, that is, as an interval. When only an interval is given, the rejection information is taken as zero, and the result is again ranked by a single closeness coefficient.
m-polar hesitant fuzzy TOPSIS (Akram, Adeel and Alcantud, 2019)HesitantThis is the form of TOPSIS for situations where a criterion is assessed from more than one independent viewpoint (pole), and each viewpoint itself is hesitant, that is, carries more than one plausible value.
m-Polar Hesitant TOPSIS (Akram, Adeel and Alcantud, 2019)m-PolarThis is the form of TOPSIS for situations where a criterion is assessed from several independent viewpoints (poles), and each viewpoint is itself hesitant, carrying more than one plausible value.
m-Polar Linguistic TOPSIS (Adeel, Akram and Koam, 2019)m-PolarThis is the form of TOPSIS for situations where a linguistic term is assessed from several independent viewpoints (poles) and built as a group decision from several decision-makers' shared opinion.
Probabilistic hesitant TOPSISHesitantThis is the form of TOPSIS for situations where more than one plausible value for a criterion is given together with its own probability of occurrence. Every cell is first reduced to its expected value, after which the remaining steps of classical TOPSIS are applied.
Simplified Neutrosophic Hesitant Fuzzy TOPSIS (Akram, Naz and Smarandache, 2019)HesitantThis is the form of TOPSIS for situations where a criterion's truth, indeterminacy and falsity degrees are each hesitant in their own right, that is, each carries more than one plausible value. Weights are not taken from outside; the method itself derives them from the disagreement in the data.

VIKOR

Base method →

Fuzzy VIKOR (Opricovic, 2011)FuzzyThis is the form of VIKOR in which criterion values are given as triangular fuzzy numbers. Uncertainty is carried corner by corner through the group-utility and individual-regret calculations, and is reduced to a single number only at the final ranking comparison.
Grey VIKOR (Chang, Liu and Wei, 2001)GreyThis is the form of VIKOR that works with grey numbers, for situations where criterion values are known only by a lower and upper bound. DecisionMind reduces these bounds to a single midpoint before the calculation begins, then runs crisp VIKOR's compromise procedure on those midpoints.
Intuitionistic fuzzy VIKOR (Devi, 2011)IntuitionisticThis is the judgement-based form of VIKOR. Criteria here are assessed with a degree of support (μ) and a degree of rejection (ν); on cost criteria it reverses direction by swapping support and rejection, and it calculates distance over these two degrees.
Neutrosophic VIKOR (Tooranloo & Ayatollah, 2024)NeutrosophicThis is the judgement-based form of VIKOR. Criteria here are evaluated through degrees of truth, indeterminacy and falsity; on cost criteria it swaps truth with falsity and complements indeterminacy, and computes distance across all three degrees.
Pythagorean fuzzy VIKORPythagoreanThis is the Pythagorean fuzzy form of VIKOR. The support and rejection degrees given to a judgement may sum to more than 1, provided the sum of their squares does not. The output is again group utility, individual regret, and a compromise index combining the two.
Spherical fuzzy VIKOR (Sharaf, 2021)SphericalSpherical fuzzy VIKOR is the form of VIKOR used when criterion scores are given as three separate numbers stating a degree of support, rejection and hesitancy for a judgement. Group utility and individual regret are carried through all three degrees, only scored at the very end, and combined with the same compromise logic.
q-Rung orthopair VIKOR (Erdebilli et al., 2023)q-Rung OrthopairThis is the form of VIKOR for situations where an expert assigns a judgement both strong support and a strong reservation at once. It is used when the sum of the two exceeds the intuitionistic or Pythagorean bound; it still gives its result as the same triad of group utility, individual regret and the compromise index.
Picture fuzzy VIKOR (Fan, Han and Wu, 2023)PicturePicture Fuzzy VIKOR is the form of VIKOR used when criterion scores come from a committee's or a survey's yes-abstain-no vote distribution. It computes group utility and individual regret directly on these three-degree votes.
Hesitant fuzzy VIKOR (Liao and Xu, 2013)HesitantThis is the form of VIKOR for situations where more than one plausible membership degree is held together for a single criterion. It computes group utility and individual regret using distances between sets, and ranks the result, once again, with a compromise index.
Plithogenic VIKORPlithogenicThis is the form of VIKOR for situations where criterion scores are given as a truth-indeterminacy-falsity triple and criteria carry a degree of contradiction relative to one another. Its output is again a group utility, an individual regret, and a compromise index combining the two.
Rough VIKOR (Zhu, Hu, Qi, Gu & Peng, 2015)RoughThis is the form of VIKOR that works with rough numbers for situations where criterion scores come from several experts' group assessment and the disagreement itself needs to be preserved. It carries group utility and individual regret as rough intervals, and still delivers the result as a compromise proposal.
Z-number VIKOR (Shen et al., 2018)Z-NumberThis is the form of VIKOR for situations where every criterion value is given together with how far that value can be trusted. The output is again group utility, individual regret, and a compromise index combining the two.
2-tuple linguistic VIKOR (Ju and Wang, 2013)LinguisticThis is the form of VIKOR for situations where expert scores are chosen from a pre-declared term set, and where the aggregation result is preserved with its shift rather than rounded to a term.
Probabilistic linguistic VIKOR (Li et al., 2021)LinguisticThis is the form of VIKOR for situations where an expert gives several terms together with their probabilities. It reduces every term distribution to a single expected value, then ranks the result with a compromise proposal as usual.
Bipolar fuzzy VIKOR (Alghamdi, Alshehri & Akram, 2018)m-PolarThis is the form of VIKOR for situations where each cell records, separately, a judgement's effect in the desired direction and its effect in the opposite direction. The two effects are reduced to a single score in the very first step, and the rest of the calculation follows the same path as crisp VIKOR.
Complex Fuzzy VIKORFuzzyThe form of VIKOR for situations where the degree of support for, and rejection of, a judgement each carry two components, amplitude AND phase. These four numbers first collapse into a distance, and the rest of the calculation runs exactly as crisp VIKOR does.
Cubic fuzzy VIKOR (Fahmi, Amin, Abdullah, Aslam & Ul Amin, 2019)FuzzyThis is the form of VIKOR for situations where a criterion assessment is given both as an interval and as a single point together. Every cell carries a fuzzy interval AND a fuzzy point together; the method combines the two into a single score and runs the rest of the calculation exactly as crisp VIKOR does.
Dual hesitant fuzzy VIKOR (An, Zhang, Liu and Zuo, 2025)HesitantThis is the form of VIKOR for situations where several decision-makers each give both a support and a rejection value for every criterion, and the weight of some criteria is not fully fixed in advance. It combines the decision-makers' votes, completes the missing weights with an optimisation, and ranks the result by a rule that is the exact opposite of classical VIKOR's: the HIGHEST Q counts as best.
Fermatean Fuzzy VIKOR (Gül, 2021)FuzzyThis is the form of VIKOR for situations where the cubes of the support and rejection degrees given to a judgement sum to no more than 1. This constraint lets the two degrees be high together over a region wider than Pythagorean fuzzy allows; the method reduces every cell to a distance straight away, and runs the rest exactly as crisp VIKOR does.
Interval-valued intuitionistic fuzzy VIKOR (aggregated, a DecisionMind derivation)FuzzyThe form of VIKOR for situations where a judgement's own degree of support and degree of rejection are given not as single numbers but as intervals. It computes distance over these four-number cells and again ranks the result by a compromise index.
Interval-valued intuitionistic fuzzy VIKOR (Park, Cho & Kwun, 2011)FuzzyThis is the form of VIKOR for situations where a judgement's degree of support and degree of rejection are themselves given as an interval rather than a single number. It computes distance over these four-number cells and genuinely tests classical VIKOR's two compromise conditions here as well.
Probabilistic hesitant VIKOR (Li, 2021)HesitantThis is the form of VIKOR for situations where a cell carries more than one possible degree, and it is also known how often, or with what probability, each of these degrees is observed. It reduces every cell to a probability-weighted expected value and builds the compromise index over these values.
VIKOR-SMAA (stochastic acceptability)StochasticThis is the form of VIKOR that runs when, about the criterion weights, only uncertainty information is available rather than a single number. Instead of a single compromise rank, it gives each alternative's probability of achieving each possible rank.

SAW

Base method →

Fuzzy SAW (Bonissone, 1982)FuzzyFuzzy SAW is the form of SAW that works with trapezoidal fuzzy numbers when criteria are given in words or as approximate judgements. It keeps the weighted sum in fuzzy form throughout the calculation, and only reduces the result to a single score, for ranking, at the very last step.
Grey SAWGreyGrey SAW is the form of SAW that works with grey numbers when criteria are known only by a lower and upper bound. It whitenises every cell, then applies crisp SAW's weighted sum.
Intuitionistic fuzzy SAW (Kaur and Kumar, 2013)IntuitionisticIF-SAW is the form of SAW that works with intuitionistic fuzzy numbers when criteria rest on a judgement (support/rejection). It runs the weighted aggregation on the support and rejection degrees separately, then reduces the result to a single score difference and ranks on it.
Plithogenic SAWPlithogenicThis is the form of SAW for when criteria are given as degrees of truth, indeterminacy and falsity, and a criterion's contradiction to a dominant one is also taken into account. It carries out the weighted combination on these three degrees, and again ranks the result with a single score.
Rough SAW (Stević, Pamučar, Zavadskas, Ćirović & Prentkovskis, 2017)RoughThis is the form of SAW in which every cell is given not as a single number but as a rough number interval, that is, a lower and an upper approximation. It computes the weighted sum over these intervals and reduces the result to a single score with the interval's midpoint.
2-tuple linguistic SAW (Cid-López et al., 2018)LinguisticThis is the form of SAW for situations where expert scores are chosen from a pre-declared term set, and where the aggregation result is preserved with its shift rather than rounded to a term.
Fermatean Fuzzy SAWFuzzyThis is the form of SAW for situations where the cubes of the support and rejection degrees given to a judgement sum to no more than 1. This constraint lets the two degrees be high together over a region wider than the Pythagorean fuzzy structure allows; the method carries this pair through the calculation and reduces it to a single number only at the final step.
Hesitant SAWHesitantThis is the form of SAW for situations where several plausible values on a criterion are held together. It carries these sets through the calculation and reduces the result to a single weighted score only at the last step.
Interval-valued intuitionistic fuzzy SAW (a DecisionMind derivation)FuzzyThe form of SAW for situations where a judgement's own degree of support and degree of rejection are given not as single numbers but as intervals. The support-rejection interval, combined by weight across the criteria, descends to a single score only at the final step.
Pythagorean fuzzy SAWPythagoreanThis is the Pythagorean fuzzy form of SAW. The support and rejection degrees given to a judgement may sum to more than 1, provided the sum of their squares does not. This pair is carried through the whole calculation, and comes down to a single weighted score only at the last step.
Picture fuzzy SAWPictureThis is the form of SAW for situations where criterion scores come from a board's or a survey's yes-abstain-no vote distribution. This triple is carried through the calculation, and comes down to a single weighted score only in the last step.
q-Rung orthopair SAWq-Rung OrthopairThis is the form of SAW for situations where an expert assigns a judgement both strong support and a strong reservation at once, and the sum of the two exceeds the intuitionistic or Pythagorean bound. It still ranks the result with a single score.
Spherical fuzzy SAW (Kutlu Gündoğdu and Yörükoğlu, 2021)SphericalSpherical fuzzy SAW is the form of SAW used when criterion scores are given as three separate numbers stating a judgement's degree of support, rejection and hesitancy. The calculation still comes down to a single weighted sum at the end; a larger value is better.

AHP

Base method →

Fuzzy AHP (Van Laarhoven & Pedrycz, 1983)FuzzyFuzzy AHP is the form of AHP that gives pairwise comparisons not as "how many times more important" but as "roughly how many times more important," using triangular fuzzy numbers. The output is again a weight vector, but this vector is obtained through a different route from crisp AHP's consistency ratio: through synthesis and defuzzification.
Z-Number AHP (Nuriyev, 2020)Z-NumberThis is the form of AHP that adds to pairwise comparisons not only "how many times more important" but also how much this judgement is trusted. The output is again a weight vector; but the reliability of every comparison is embedded into the weight.
Hesitant Fuzzy AHP (Zhu and Xu, 2014)HesitantHesitant Fuzzy AHP is the form of AHP for situations where a pairwise comparison rests not on a single ratio but on several defensible ratios at once. It converts these ratios directly into a weight vector through linear programming rather than an eigenvector.
Hesitant fuzzy linguistic AHP (Yavuz, Öztayşi, Çevik Onar and Kahraman, 2015)HesitantHesitant fuzzy linguistic AHP is the form of AHP for situations where criteria are compared pairwise and alternatives are scored on a seven-term verbal scale. Unlike crisp AHP, it does not generate weights alone; within the same exercise it also ranks the alternatives.

BWM

Base method →

Fuzzy BWM (Guo and Zhao, 2017)FuzzyFuzzy BWM is the form of BWM used when the expert's comparisons against the best and worst criterion are expressed not as crisp numbers but as triangular fuzzy numbers. Its output is not a ranking but a weight vector that carries the fuzziness through and is defuzzified only in the final step.
Z-number BWM (Aboutorab et al., 2018)Z-NumberThis is the form of BWM in which the comparisons given against the best and the worst criterion also carry how far that judgement is trusted. The output is still a weight vector; a comparison with low reliability enters the weight calculation more weakly.
Bayesian BWM (Mohammadi and Rezaei, 2020)ClassicalBayesian BWM is the form of BWM that combines the best-to-others and others-to-worst comparisons given by multiple decision-makers into a single hierarchical probability model and converts them into weights. The output is still a weight vector, but each weight now comes with a confidence interval and a probability table showing how certain the superiority between criteria actually is.
Z-number Game-Theoretic BWM (Adesina, Yazdi and Omidvar, 2022)Z-NumberThis extension combines BWM's best/worst-criterion weighting with a zero-sum game played over a payoff table of alternatives expressed as Z-numbers. Unlike every other BWM family member, the output is not a weight vector but a ranking of alternatives derived from the game's Nash equilibrium.

SWARA

Base method →

Fuzzy SWARA (Vrtagić et al., 2021)FuzzyFuzzy SWARA is the form of SWARA used when the successive importance differences that follow the ranking of criteria are given as triangular fuzzy numbers rather than crisp ones. Its output is not a ranking but a weight vector that carries the fuzziness and is defuzzified only at the last step.
Scenario fuzzy SWARAFuzzyThis is the form of SWARA for situations where criteria's successive importance differences are given as triangular fuzzy numbers. It applies crisp SWARA separately to the triangle's lower, middle and upper end and averages the three weight vectors; the output is not a ranking but a weight vector summing to 1.

Entropy Weighting

Base method →

Fuzzy EntropyFuzzyFuzzy Entropy Weighting is the form of Entropy Weighting used when the decision table's cells are given as a lowest-most likely-highest triple, that is, a triangular fuzzy number. It computes entropy separately on each of the three components and averages the result into a single weight vector.
Intuitionistic fuzzy Entropy (Hung & Chen, 2010)IntuitionisticIntuitionistic Fuzzy Entropy Weighting is the form of Entropy Weighting used when decision-table cells are given as a degree of support for and a degree of rejection of a judgement (an intuitionistic fuzzy pair). It produces weights by working directly on the support-rejection-indecision triple, without converting entropy into a probability.

CRITIC

Base method →

Fuzzy CRITICFuzzyFuzzy CRITIC is the form of CRITIC used when criterion values are given as triangular fuzzy numbers. It runs crisp CRITIC separately on each of the triangle's three corners and averages the three resulting weight vectors into a single fuzzy-derived weight vector.
Spherical Fuzzy Z-Number CRITIC (Niu, 2024)Z-NumberThis is the form of CRITIC for situations where criterion values are given as spherical fuzzy triples (support, rejection, hesitancy), and each of these three degrees is further accompanied by its own reliability. The output is again a weight vector.

EDAS

Base method →

Fuzzy EDASFuzzyThis is the form of EDAS that works with triangular fuzzy numbers. It is used when criterion scores are verbal or approximate; it calculates the positive and negative deviation from the set's average separately in each of the fuzzy number's three components, then ranks the result with a single appraisal score.
Grey EDAS (Stanujkic, Zavadskas, Keshavarz Ghorabaee & Turskis, 2017)GreyThis is the form of EDAS that works with grey interval numbers. Criterion values are used here only when they are known by a lower and upper bound alone; the positive and negative distance from the set's average is computed across both ends of the interval, and the result is ranked by a single appraisal score.
Intuitionistic fuzzy EDAS (Yıldırım & Meydan, 2021)IntuitionisticIF-EDAS is the form of EDAS used when criterion values are given as a degree of support for and a degree of rejection of a judgement, working with intuitionistic fuzzy numbers. The method first reduces every cell to a single score, then computes the positive and negative distances from that score against the set's own average.
Neutrosophic EDAS (Stanujkić, Karabašević, Popović, Pamučar, Stević, Zavadskas & Smarandache, 2021)NeutrosophicN-EDAS is the form of EDAS that works with single-valued neutrosophic numbers, used when criterion assessments are given as degrees of truth, indeterminacy and falsity. The method computes the positive and negative deviation from the set's average through a three-component distance and a score function.
Pythagorean fuzzy EDASPythagoreanThis is the Pythagorean fuzzy form of EDAS. The sum of the support and rejection degrees given to a judgement may exceed 1, provided the sum of their squares does not. The output is again a single closure ratio built relative to the set's own average, and the ranking that follows from it.
Spherical fuzzy EDAS (Garg & Sharaf, 2022)SphericalSpherical fuzzy EDAS is the form of EDAS used when criterion scores are given as three separate numbers: a judgement's degree of support, rejection and hesitancy. Both the average solution and the deviations stay three-degree throughout; they drop to a single number only in the very last step.
q-Rung Orthopair EDAS (Li et al., 2019)q-Rung OrthopairThis is the form of EDAS for situations where an expert gives a judgement both strong support and a strong reservation. It is used when the sum of these two exceeds the intuitionistic or Pythagorean boundary; it still expresses the result as an assessment score based on distance from the average solution.
Picture fuzzy EDAS (Kamber, 2026)PicturePicture fuzzy EDAS is the form of EDAS used when criterion scores come from a board's or a survey's yes-abstain-no vote distribution. It measures every alternative's position relative to the set's average directly on these three-degree votes.
Hesitant Fuzzy EDAS (Kutlu Gündoğdu, Kahraman and Civan, 2018)HesitantThe form of EDAS in which every cell is given as a triangular fuzzy number and DecisionMind reduces this number to a single value at the very start of the calculation, comparing it against the set's average.
Plithogenic EDASPlithogenicThis is the form of EDAS for situations where criterion scores are given as a truth-indeterminacy-falsity triple and criteria carry a degree of contradiction relative to one another. Its output is again an assessment score relative to the set's own average, and the ranking that follows from it.
Rough EDAS (Paul, Chakraborty & Chakraborty, 2022)RoughThis is the form of EDAS that works with interval-valued rough numbers for situations where criterion scores must carry both an expert's own hesitation and the disagreement between experts at once. It carries the deviation from the average as two nested intervals, and still gives the result as a single appraisal score.
Z-number EDASZ-NumberThis is the form of EDAS for situations where every criterion value is given together with how far that value can be trusted. The output is again an assessment score, and a rank drawn from that score.
Probabilistic Linguistic EDAS (Wei, Wei and Guo, 2021)LinguisticThis is the form of EDAS for situations where expert scores are given not as a single word but as the probabilities of several linguistic terms. Every cell is first reduced to an expected linguistic value, and the ranking against the average runs on these values.
Bipolar fuzzy EDAS (Jana & Pal, 2021)m-PolarThis is the form of EDAS for situations where each cell records, separately, a judgement's effect in the desired direction and its effect in the opposite direction. Experts' judgements are combined with a bipolar fuzzy average, and alternatives are ranked by their distance from this average.
Complex Fuzzy EDASFuzzyThe form of EDAS for situations where the degree of support for, and rejection of, a judgement each carry two components, amplitude AND phase. These two components merge into a single score first, and the rest of the calculation runs exactly as crisp EDAS does.
Cubic Pythagorean fuzzy EDAS (Paul, Jana & Pal, 2023)PythagoreanThis is the form of EDAS for situations where a criterion assessment is given both as an interval and as a single point. Every cell carries a Pythagorean interval AND a Pythagorean point together; the method combines the two into a single score and ranks alternatives against the set's average.
Dual hesitant fuzzy EDAS (Ning, Lin, Wei and Chen, 2023)HesitantThis is the form of EDAS for situations where criterion evaluation carries more than one plausible value on both the supporting and the rejecting side, each value given with its own probability of occurrence. It merges several experts' matrices, builds weights from three sources, and still ranks the result with a single appraisal score.
Fermatean Fuzzy EDASFuzzyThe form of EDAS for situations where the sum of the cubes of a judgement's support and rejection degrees does not exceed 1. This constraint allows the two degrees to be simultaneously high over a region wider even than Pythagorean fuzzy data permit; the method reduces every cell to a score straightaway and runs the remainder exactly as in crisp EDAS.
Interval-valued intuitionistic fuzzy EDAS (DecisionMind derivation)FuzzyInterval-valued intuitionistic fuzzy EDAS is the form of EDAS for situations where the degree of support and rejection given to a judgement is itself not a single number but an interval. The method first reduces every cell to a single score, then measures positive and negative deviation from the set's average through that score.
2-tuple linguistic neutrosophic EDAS (Wang, Wang & Wei, 2019)Linguistic2-tuple linguistic neutrosophic EDAS is the form of EDAS for situations where criterion assessment is made in words chosen from a term set, with a degree of truth, indeterminacy and falsity attached to those words. The combined result is not rounded to a term; it is carried together with its term and translation value.
Linguistic Pythagorean fuzzy EDAS (CRITIC-weighted) (Akram, Ramzan and Deveci, 2023)LinguisticLinguistic Pythagorean fuzzy EDAS is the form of EDAS where criterion assessment is done with support and rejection degrees chosen from a term set, and criterion weights are derived not from an expert but from the data itself, by the CRITIC method.
Probabilistic hesitant EDAS (manifest name: extended hesitant linguistic EDAS)HesitantThis is the form of EDAS in which more than one plausible value for a criterion is carried in a single cell together with its probability of occurrence. Every cell is reduced to a probability-weighted expected value in the method's first step, and the rest of the calculation runs on that value.

COPRAS

Base method →

Fuzzy COPRASFuzzyFuzzy COPRAS is the form of COPRAS used when criterion values are given as triangular fuzzy numbers. The benefit/cost ratio logic is run separately on each of the three corners (lowest, most likely, highest) and finally descends to a single degree of utility.
Grey COPRAS (Zavadskas, Kaklauskas, Turskis and Tamošaitienė, 2009)GreyGrey COPRAS is the form of COPRAS used when criterion values are known only by a lower and an upper bound, that is, when they are grey. DecisionMind reduces every interval to its midpoint, that is, whitens it, and then runs COPRAS's benefit/cost ratio calculation on these single numbers exactly as usual.
Intuitionistic fuzzy COPRASIntuitionisticThis is the form of COPRAS used when criteria are assessed in intuitionistic fuzzy form, that is, through degrees of support for and rejection of a judgement. Every cell is first reduced to a Chen-Tan score difference (support minus rejection); COPRAS's benefit/cost ratio then works on these scores.
Neutrosophic COPRAS (Şahin, 2019)NeutrosophicThis is the form of COPRAS used when the degrees of truth, indeterminacy and falsity in criterion assessment are each given as a range, that is, interval-valued neutrosophic data; it was proposed by Şahin (2019). Benefit and cost sums are combined not by classical addition but by a Maclaurin symmetric mean operator, and reduced to a single number by a risk indicator.
Pythagorean fuzzy COPRASPythagoreanThis is the Pythagorean fuzzy form of COPRAS. The sum of the support and rejection degrees given to a judgement may exceed 1, provided the sum of their squares does not. The output is again a benefit degree expressed as a percentage relative to the best alternative.
Spherical fuzzy COPRASSphericalSpherical fuzzy COPRAS is the form of COPRAS used when criterion scores are given as three separate numbers: a judgement's degree of support, rejection and hesitancy. Every cell drops to a single score within its constraint in the first step; the benefit and cost totals are then built on these scores exactly as in crisp COPRAS.
q-Rung Orthopair COPRASq-Rung OrthopairThis is the form of COPRAS for situations where an expert gives a judgement both strong support and a strong reservation. It is used when the sum of these two exceeds the intuitionistic or Pythagorean boundary, and it still expresses the result as a benefit degree.
Picture fuzzy COPRAS (Lu, Zhang, Wu & Wei, 2021)PicturePicture fuzzy COPRAS is the form of COPRAS used when criterion scores come from a board's or a survey's yes-abstain-no vote distribution. It builds the benefit and cost sums directly on these three-degree votes, and still gives the result as a percentage relative to the best alternative.
Hesitant Fuzzy COPRAS (Mishra, Rani and Pardasani, 2018)HesitantThe form of COPRAS for situations where more than one plausible degree of membership on a criterion must be held together. It builds the benefit and cost totals through set aggregation, then ranks the result, once again, with a relative-significance value.
Plithogenic COPRASPlithogenicThis is the form of COPRAS for situations where criterion scores are given as a truth-indeterminacy-falsity triple and criteria carry a degree of contradiction relative to one another. Its output is again a percentage utility degree relative to the best alternative.
Rough COPRAS (Pamučar, Božanić, Lukovac & Komazec, 2018)RoughThis is the form of COPRAS that works with rough numbers for situations where criterion scores come from a group assessment by several experts and the disagreement between them needs to be preserved. It carries the benefit and cost sums as rough intervals, and still gives the result as a degree of utility, a percentage relative to the best.
Z-number COPRASZ-NumberThis is the form of COPRAS for situations where every criterion value is given together with how far that value can be trusted. The output is a relative-significance value that comes from combining the benefit and cost totals.
2-tuple linguistic COPRASLinguisticThis is the form of COPRAS for situations where criterion values are given in words chosen from a pre-declared term set, and the calculation is carried out without converting these terms into numbers, through a lossless representation. The output is again a percentage relative to the best alternative and a ranking based on that percentage.
Bipolar fuzzy COPRASm-PolarThis is the form of COPRAS for situations where each cell records, separately, a judgement's effect in the desired direction and its effect in the opposite direction. The two effects are reduced to a single score in the very first step, and the rest of the calculation follows the same path as crisp COPRAS.
Dual Hesitant Fuzzy COPRAS (Rani, Mishra and colleagues, 2020)HesitantThis is the form of COPRAS for situations where a cell records several possible degrees of both support and rejection separately. It builds the benefit and cost sums over these dual sets, and ranks the result by a relative-importance value.
Fermatean Fuzzy COPRASFuzzyThe form of COPRAS for situations where criterion assessment is given as a degree of support for a judgement and a degree of rejection of it, and these two degrees can be simultaneously high over a wider region than intuitionistic fuzzy data allow. It builds the benefit and cost totals from these support-rejection pairs.
Interval-valued intuitionistic fuzzy COPRAS (aggregative, DecisionMind derivation)FuzzyInterval-valued intuitionistic fuzzy COPRAS is the form of COPRAS for situations where the degree of support and rejection of a judgement is itself not a single number but an interval. It builds the benefit and cost sums from these four-number cells.
Interval-valued intuitionistic fuzzy COPRAS (Davoudabadi, Mousavi, Mohagheghi & Vahdani, 2019)FuzzyInterval-valued intuitionistic fuzzy COPRAS is the form of COPRAS for situations where a judgement's degree of support and degree of rejection are themselves given as intervals rather than single numbers. It sums the support and rejection intervals separately on the benefit and cost sides, and reduces them to a single number only in the very last step, through a balancing coefficient.
Probabilistic hesitant fuzzy COPRAS (Song and Chen, 2021)HesitantThis is the form of COPRAS for situations where a cell carries more than one possible degree, and it is also known how often, or with what probability, each of these degrees is observed. It builds the benefit and cost sums over expected values weighted by these probabilities.

MARCOS

Base method →

Fuzzy MARCOS (Stanković et al., 2020)FuzzyThis is the form of MARCOS that works with triangular fuzzy numbers when criterion scores are verbal or approximate. The proportional position to the ideal and the anti-ideal is carried as fuzzy throughout the calculation, and collapse into a single number happens only after the utility ratios have been built.
Grey MARCOS (Badi & Pamučar, 2020)GreyThis is the form of MARCOS that works with grey numbers when criterion values are known only by a lower and upper bound. The bounds are first whitenised to a single midpoint, and the remaining calculation then follows the same ideal/anti-ideal ratio as crisp MARCOS.
Intuitionistic fuzzy MARCOS (Ecer & Pamučar, 2021)IntuitionisticIF-MARCOS is the intuitionistic fuzzy form of MARCOS used when the support given to a judgement and its rejection are known separately. It reduces cells to a support-rejection score and aggregates them, then builds the ratio to the ideal and anti-ideal from this score.
Neutrosophic MARCOS (Martin et al., 2023)NeutrosophicN-MARCOS is the neutrosophic form of MARCOS used when the degrees of truth, indeterminacy and falsity of an assessment are known independently of one another. It reduces every cell to a single score, and continues the rest of the calculation with crisp MARCOS's ideal/anti-ideal ratio logic.
Pythagorean fuzzy MARCOSPythagoreanThis is the Pythagorean fuzzy form of MARCOS. The support and rejection degrees given to a judgement may sum to more than 1, provided the sum of their squares does not. The output is again a ratio built relative to the ideal and the anti-ideal, combined into a single utility degree.
Spherical fuzzy MARCOS (Kovač et al., 2021)SphericalSpherical fuzzy MARCOS is the form of MARCOS used when criterion scores are given as three separate numbers: a judgement's degree of support, rejection and hesitancy. Distance to the ideal and the anti-ideal is measured with an angular distance rather than a straight-line one.
q-Rung Orthopair MARCOSq-Rung OrthopairThis is the form of MARCOS for situations where an expert gives a judgement both strong support and a strong reservation. It is used when the sum of these two exceeds the intuitionistic or Pythagorean boundary, and it still expresses the result as a final utility degree.
Picture fuzzy MARCOS (Tatar & Ayvaz, 2024)PicturePicture fuzzy MARCOS is the form of MARCOS used when criterion scores come from a board's or a survey's yes-abstain-no vote distribution. It builds the utility ratio to the ideal and anti-ideal references directly on these three-degree votes.
Hesitant MARCOS (Li, Geng and Yuan, 2023)HesitantThis is the form of MARCOS for situations where several plausible membership degrees on a criterion are held together. It reduces the sets to a score first, then ranks them by comparing them against the ideal and anti-ideal references.
Plithogenic MARCOSPlithogenicThis is the form of MARCOS for situations where criterion scores are given as a truth-indeterminacy-falsity triple and criteria carry a degree of contradiction relative to one another. Its output is again a final utility degree measured against ideal and anti-ideal references.
Rough MARCOS (Matić, Marinković, Jovanović, Sremac & Stević, 2022)RoughThis is the form of MARCOS that works with rough numbers for situations where criterion scores come from a group assessment by several experts and the disagreement between them needs to be preserved. It carries the ideal and anti-ideal references as rough intervals, and still gives the result as a single final degree of utility.
Z-number MARCOS (Yazdani, Pamucar, Chatterjee & Torkayesh, 2021)Z-NumberThis is the form of MARCOS for situations where the decision-matrix cells are not crisp numbers but Z-numbers, carrying a value together with how far that value is trusted. The logic of the utility ratio relative to the ideal and the anti-ideal stays exactly the same; only the cells change.
Probabilistic Linguistic MARCOSLinguisticThis is the form of MARCOS for situations where expert scores are given not as a single word but as the probabilities of several linguistic terms. Every cell is first reduced to an expected linguistic value, and the utility ratio against the ideal and anti-ideal is built on these values.
Bipolar fuzzy MARCOSm-PolarThis is the form of MARCOS for situations where each cell records, separately, a judgement's effect in the desired direction and its effect in the opposite direction. The two effects are reduced to a single score in the very first step, and the rest of the calculation follows the same path as crisp MARCOS.
Complex Fuzzy MARCOSFuzzyThe form of MARCOS for situations where the degree of support for, and rejection of, a judgement each carry two components, amplitude AND phase. The output is still a final utility degree and a rank.
Complex Fuzzy Z-Number MARCOS (Shahid et al., 2026)Z-NumberThe form of MARCOS for situations where criterion values are given both as an amplitude-phase pair and as a reliability degree attached to that pair. The output is still a final utility degree and a rank.
Fermatean Fuzzy MARCOSFuzzyThe form of MARCOS for situations where the sum of the cubes of a judgement's support and rejection degrees does not exceed 1. This constraint allows the two degrees to be simultaneously high over a region wider even than Pythagorean fuzzy data permit; the ideal/anti-ideal utility-ratio logic remains exactly as it is.
Interval-valued intuitionistic fuzzy MARCOS (aggregated, a DecisionMind derivation)FuzzyInterval-valued intuitionistic fuzzy MARCOS is the form of MARCOS for situations where a judgement's own degree of support and degree of rejection are given not as single numbers but as intervals. The utility-ratio logic against the ideal and the anti-ideal runs on these intervals throughout.
Spherical Fuzzy Z-Number MARCOS (Niu, 2024)Z-NumberThis is the form of MARCOS for situations where criterion values are given as spherical fuzzy triples (support, rejection, hesitancy), and each of these three degrees is further accompanied by its own reliability. The output is again a final utility degree and a rank.

CODAS

Base method →

Fuzzy CODAS (Keshavarz Ghorabaee et al., 2017)FuzzyFuzzy CODAS is a form of CODAS, working with triangular fuzzy numbers, used when criterion scores are given approximately through expert judgement. It carries two distinct distance measures through the calculation in fuzzy form and still ranks the result with a single assessment score.
Intuitionistic fuzzy CODAS (Daami Remadi & Moalla Frikha, 2020)IntuitionisticTIF-CODAS is the form of CODAS used when criterion scores carry both linguistic approximation and a support/rejection judgement, and when more than one expert's opinion has to be combined. It works with triangular intuitionistic fuzzy numbers and directly supports group decisions.
Grey CODASGreyGrey CODAS is the form of CODAS that works with grey numbers when criterion values are known only by a lower and an upper bound. It computes two different distance measures over the bounds, and ranks the result, again, with a single assessment score.
Neutrosophic CODASNeutrosophicN-CODAS is the form of CODAS that works with single-valued neutrosophic numbers for situations where the degrees of truth, indeterminacy and falsity in criterion assessment are given separately. It computes two distinct distance measures through a score function and ranks the result with a single assessment score.
Fermatean Fuzzy CODASFuzzyFermatean fuzzy CODAS is the form of CODAS used when an expert states, together, how strongly a criterion is supported and how strongly it is rejected. This pair is admitted over a wider region than intuitionistic fuzzy data allow, and the result is again ranked by a single assessment score.
Hesitant Fuzzy CODASHesitantHesitant Fuzzy CODAS is the form of CODAS used when more than one plausible value on a criterion must be held together. It carries these sets through most of the calculation and still ranks the result with a single assessment score.
Hesitant fuzzy linguistic CODAS (Yalçın and Pehlivan, 2019)HesitantHesitant fuzzy linguistic CODAS is the form of CODAS used when a criterion is scored not with a single verbal term but with a comparative verbal expression such as "at least good" or "between medium and good." It converts this expression into a fuzzy envelope and carries it as such through most of the calculation.
Interval rough CODAS (Cherif and Frikha, 2021)RoughInterval rough CODAS is the form of CODAS used when several experts score the same criterion as an interval and the disagreement between them needs to be preserved. It directly supports a group decision and still ranks the result with a single assessment score.
Interval CODAS (Yeni and Özçelik, 2018)FuzzyInterval CODAS is the form of CODAS used when experts give both the degree of support and the degree of rejection for a criterion as intervals, and the opinions of several experts need to be combined. It directly supports a group decision and still ranks the result with a single assessment score.
2-tuple linguistic CODASLinguisticThis is the form of CODAS for situations where expert scores are chosen from a pre-declared term set, and the two distances to the negative-ideal are computed carrying the symbolic translation value rather than rounding to a single term.
Neutrosophic Spherical Set CODAS (Bhuvaneshwari & Sweety, 2024)NeutrosophicThis is the form of CODAS for situations where the degrees of truth, indeterminacy and falsity are given independently, but the sum of the squares of these three degrees is kept within a defined bound. The output is a single closeness ratio that shows proximity to the ideal rather than to the negative-ideal, and where a lower value is better.
Plithogenic CODASPlithogenicThis is the form of CODAS for situations where criterion evaluation is given as a truth-indeterminacy-falsity triple and criteria carry a degree of contradiction relative to one another. Its output is again an assessment score built from two distinct distance measures, and the ranking that follows from it.
Pythagorean fuzzy CODAS (Peng, 2021)PythagoreanThis is the Pythagorean fuzzy form of CODAS. The sum of the support and rejection degrees given to a judgement may exceed 1, provided the sum of their squares does not. The output is again an assessment score built from two different distance measures to the negative-ideal, and the ranking that follows from it.
Picture fuzzy CODAS (Simic, Karagoz, Deveci & Aydın, 2021)PictureThis is the form of CODAS for situations where criterion scores are given as a proportion of yes, abstention and no on a judgement; it still ranks the result with an assessment score.
q-Rung Orthopair CODASq-Rung OrthopairThis is the form of CODAS for situations where an expert gives a judgement both strong support and a strong reservation. It is used when the sum of these two exceeds the intuitionistic or Pythagorean boundary; it still ranks the result with an assessment score.
Spherical fuzzy CODAS (Karaşan, Boltürk & Kutlu Gündoğdu, 2021)SphericalThis is the form of CODAS for situations where criterion scores are given as three separate numbers: a judgement's degree of support, rejection and hesitancy; it still ranks the result with an assessment score.
Triangular Intuitionistic Fuzzy CODAS (Daami Remadi and Frikha, 2023)FuzzyThis is the form of CODAS for situations where criterion scores are given both as a triangular support and as a separate, wider triangular rejection region; it still ranks the result with an assessment score.

PROMETHEE

Base method →

Fuzzy PROMETHEE (Goumas & Lygerou, 2000)FuzzyFuzzy PROMETHEE is the form of PROMETHEE used when criterion scores are given as triangular fuzzy numbers. It first reduces the pairwise difference to a single real number, builds the preference function and the incoming/outgoing flows on this number, and ranks the result with a single net flow, as before.
Grey PROMETHEE (Kuang, Kilgour & Hipel, 2015)GreyGrey PROMETHEE is the form of PROMETHEE used when criterion scores are given only by a lower and upper bound. It reduces every pair of bounds to a single number by its midpoint (whitenisation), and derives the preference function's threshold automatically from that criterion's spread across the alternatives.
Intuitionistic fuzzy PROMETHEE (Liao and Xu, 2014)IntuitionisticIntuitionistic fuzzy PROMETHEE is the form of PROMETHEE used when criterion scores are given as a support-rejection pair (an intuitionistic fuzzy number). Each pair is first reduced to a score, and the preference function and flows are built on the difference between these scores. The method can also combine the assessments of more than one decision-maker.
Neutrosophic PROMETHEE (Xu, Wei, Ding & Bin, 2020)NeutrosophicNeutrosophic PROMETHEE is the form of PROMETHEE used when criterion scores are given as degrees of truth, indeterminacy and falsity (a single-valued neutrosophic number). Every triple is reduced to a score and a signed distance, and the preference function and the flows are built on these.
m-Polar Fuzzy PROMETHEE (Akram, Shumaiza and Alcantud, 2020)m-PolarThis is the form of PROMETHEE for situations where every cell is rated separately from several independent viewpoints. Every cell is first reduced to a single score, and the pairwise comparison and net-flow calculation then proceed on these scores exactly as in crisp PROMETHEE.
Fermatean Fuzzy PROMETHEE (Akram and Bibi, 2023)FuzzyFermatean fuzzy PROMETHEE is the form of PROMETHEE for situations where multiple decision-makers' judgements are expressed with a linguistic term and a shift, and where support and rejection are also stated separately. It combines the judgements into a single number, then ranks alternatives with crisp PROMETHEE's own preference function and flow logic.
Hesitant fuzzy linguistic PROMETHEE (Liang, Wang and Zhang, 2018)HesitantHesitant fuzzy linguistic PROMETHEE is the form of PROMETHEE for situations where a judgement is given not as a single verbal term but as more than one possible term (such as "between good and very good"). It reduces every cell to a closeness degree relative to the best term, then ranks alternatives with crisp PROMETHEE's same pairwise comparison and flow logic.
Plithogenic PROMETHEEPlithogenicThis is the form of PROMETHEE for situations where criterion scores are given as a truth-indeterminacy-falsity triple and criteria carry a degree of contradiction relative to one another. The output remains a net flow, built from an entering and a leaving flow, and a rank based on that flow.
Pythagorean fuzzy PROMETHEE (Zhang et al., 2019)PythagoreanThis is the form of PROMETHEE for situations where the support and rejection degrees given to a judgement may sum to more than 1, provided the sum of their squares does not. The output is again a net flow built from the incoming and outgoing flows, and a rank based on this flow.
PROMETHEE I (Brans, Vincke & Mareschal, 1986)ClassicalThis is the form within the PROMETHEE family that keeps the incoming and outgoing flows separate rather than merging them into a single net flow, and honestly leaves some pairs of alternatives "incomparable." Its output is not a complete ranking but a partial dominance relation.
PROMETHEE III (Brans, Vincke & Mareschal, 1986)ClassicalThis is the form within the PROMETHEE family that presents every alternative's net flow not as a single number but as a confidence interval. Two alternatives are ranked strictly only if their intervals do not overlap; if the intervals overlap, the two are treated as indifferent.
PROMETHEE V (Brans & Mareschal, 1992)ClassicalThis is the form of PROMETHEE that selects rather than ranks. Under a resource constraint, it finds the subset of alternatives that maximises the total net flow. The output is not a ranking; it is a selected-or-rejected decision for every alternative.
PROMETHEE VI (Brans & Mareschal, 1995)ClassicalThis is the form of PROMETHEE that turns the ranking into an interval for situations where the weights are not known exactly. Every alternative's net flow is not a single number but the lowest and highest value it can take while the weights vary within a plausible band.
q-Rung orthopair PROMETHEE (Akram and Shumaiza, 2021)q-Rung OrthopairThis is the form of PROMETHEE for situations where criterion scores are given as a pair of support and rejection degrees (μ, ν) for a judgement, and this pair does not fit the intuitionistic or Pythagorean constraint. Each pair is first reduced to a single score, and classical pairwise comparison then runs on these scores.
Spherical fuzzy PROMETHEE (Sharaf, 2021)SphericalThis is the form of PROMETHEE for situations where criterion scores are given as a degree of support, a degree of rejection and a degree of hesitancy, each supplied separately by the expert. Because no direct difference can be taken between two spherical fuzzy numbers, the comparison runs through an intermediate closeness ratio.
Z-number PROMETHEE (Nuriyev, 2020)Z-NumberThis is the form of PROMETHEE for situations where every criterion value is given together with how far that value can be trusted. The output is again a net flow and a rank; but a claim with low reliability does not enter the ranking with its full stated value.

TODIM

Base method →

Fuzzy TODIM (Krohling & de Souza, 2012)FuzzyFuzzy TODIM is the form of TODIM used when the values in the decision table are not crisp but triangular fuzzy numbers in "lowest, most likely, highest" form. It runs the same pairwise comparison logic carrying loss aversion, but over fuzzy inputs.
Grey TODIM (Sen, Datta & Mahapatra, 2015)GreyGrey TODIM is the form of TODIM used when the values in the decision table are known not as single numbers but only by a lower and upper bound (a grey number). It runs the same loss-aversion logic on values reduced to the midpoint of the bounds.
Intuitionistic fuzzy TODIM (Krohling, Pacheco and Siviero, 2013)IntuitionisticIF-TODIM is the form of TODIM used when the values in the decision table are not single numbers but the support and rejection degrees given to a judgement (an intuitionistic fuzzy pair). It runs the same loss-aversion logic through a distance and a score comparison between these pairs.
Neutrosophic TODIM (Ji, Zhang & Wang, 2018)NeutrosophicN-TODIM is the form of TODIM used when the values in the decision table are not single numbers but an independent (neutrosophic) triple of truth, indeterminacy and falsity degrees. It runs the same loss-aversion logic through a distance between these triples and a score-function comparison.
Dual hesitant fuzzy TODIM (Liu, Tariq, Khan and Abdullah, 2023)HesitantThis is the form of TODIM for situations where a cell holds more than one possible degree of both support and rejection, recorded separately. It runs the loss-aversion logic through a distance and a score comparison between these dual sets.
Fermatean Fuzzy TODIMFuzzyThis is the form of TODIM that operates where the support and rejection degrees given to a judgement can be high together, over a region wider than intuitionistic fuzzy allows. It carries the same loss-aversion logic through a distance and a score comparison between these support-rejection pairs.
Hesitant TODIM (Zhang and Xu, 2016)HesitantThis is the form of TODIM for situations where several plausible membership degrees on a criterion are held together. It runs the loss-aversion logic through a measurement function and a distance, without collapsing these sets early into a single number.
Interval-valued intuitionistic fuzzy TODIM (Mishra et al., 2020)FuzzyThe form of TODIM for situations where a judgement's own degree of support and degree of rejection are given not as single numbers but as intervals. It carries the loss-aversion logic through a divergence measure between these interval pairs and a score comparison.
Interval-valued intuitionistic fuzzy TODIM (Krohling & Pacheco, 2014)FuzzyThis is the form of TODIM for situations where a judgement's degree of support and degree of rejection are themselves given as an interval rather than a single number. It first brings the support–rejection intervals onto a common scale, then runs a score and distance comparison under loss-aversion logic.
2-tuple linguistic TODIM (Qi et al., 2021)LinguisticThis is the form of TODIM for situations where criterion scores are chosen from a pre-declared term set, and where the aggregation result is preserved with its shift rather than rounded to a term.
Plithogenic TODIMPlithogenicThis is the form of TODIM for situations where criterion scores are given as a truth-indeterminacy-falsity triple and criteria carry a degree of contradiction relative to one another. It runs the loss-aversion logic over these triples and reduces the result to a single global value.
Pythagorean fuzzy TODIM (Ren, Xu and Gou, 2016)PythagoreanThis is the Pythagorean fuzzy form of TODIM. The support and rejection degrees given to a judgement may sum to more than 1, provided the sum of their squares does not. The loss-aversion logic runs on these pairs and comes down to a single global value.
Picture fuzzy TODIM (Wei, 2018)PictureThis is the form of TODIM for situations where criterion scores come from a committee's or a survey's yes–abstain–no vote distribution. It runs the loss-aversion logic on these triples and descends to a single global value.
Probabilistic linguistic TODIM (Liu & Teng, 2017)LinguisticProbabilistic linguistic TODIM is the form of TODIM for situations where an expert judges a criterion not with a single word but with an opinion spread across several terms. It reduces the term distribution to an expected value and ranks alternatives with the same loss-aversion logic.
q-Rung orthopair TODIM (Tian, Niu, Zhang, Li and Herrera-Viedma, 2021)q-Rung Orthopairq-Rung orthopair TODIM is the form of TODIM for situations where an expert assigns a judgement both strong support and a strong reservation at once, and the sum of the two exceeds the intuitionistic or Pythagorean bound. It runs the same loss-aversion logic over these support-rejection pairs.
Rough TODIM (Tiwari, Khanna & Tandon, 2024)RoughRough TODIM is the form of TODIM for situations where every cell in the decision matrix is given as a lower and upper bound derived from disagreement within a group. It carries out the pairwise gain-loss comparison over these intervals.
Spherical fuzzy TODIM (Sharaf and Khalil, 2021)SphericalSpherical fuzzy TODIM is the form of TODIM for situations where criterion scores are given as three separate numbers stating a degree of support, rejection and hesitancy. It carries the same loss-aversion logic through a score and a distance built from these three degrees.

WASPAS

Base method →

Fuzzy WASPAS (Turskis, Zavadskas, Antuchevičienė and Kosareva, 2015)FuzzyThis is the form of WASPAS used when criterion scores are given as triangular fuzzy numbers rather than crisp measurements. It computes the sum and product components with triangular arithmetic, then reduces the result to a single number by its centroid.
Grey WASPASGreyGrey WASPAS is the form of WASPAS used when criterion values are known only by a lower and upper bound. It reduces the bounds to a single midpoint value, then computes the sum and product components on that midpoint exactly as crisp WASPAS does.
Intuitionistic fuzzy WASPASIntuitionisticIF-WASPAS is the form of WASPAS used when criterion assessments are given as a judgement's degree of support and degree of rejection. It replaces the sum with an optimistic aggregation and the product with a more cautious one, then reduces the two to a single score.
Neutrosophic WASPASNeutrosophicN-WASPAS is the form of WASPAS used when criterion assessments are given as degrees of truth, indeterminacy and falsity. It reduces every cell to a single score, then computes the sum and product components on these scores exactly as crisp WASPAS does.
Plithogenic WASPASPlithogenicThis is the form of WASPAS for when criteria are given as degrees of truth, indeterminacy and falsity, and a criterion's contradiction to a dominant one is also taken into account. It carries out the additive and multiplicative combination with these three degrees, blends the two with λ, and ranks the result with a single score.
Rough set WASPAS (Stojić, Stević, Antuchevičienė, Pamučar & Vasiljević, 2018)RoughThis is the form of WASPAS in which every cell is given as a rough-number interval rather than a single number. It computes the additive and multiplicative components over these intervals, then combines the two with a λ interval derived from the data itself, reducing them to a single score.
Z-number WASPAS (Jafarzadeh Ghoushchi et al., 2021)Z-NumberThis is the form of WASPAS for situations where the decision-matrix cells are not crisp numbers but Z-numbers, carrying a value together with how far that value is trusted. The logic of blending the sum with the product stays exactly the same; only the cells change.
Bipolar Fuzzy WASPASm-PolarThis is the form of WASPAS for situations where each cell records, separately, a judgement's effect in the desired direction and its effect in the opposite direction. The two poles are carried through with their own arithmetic from the first step, the sum and product components are built with this arithmetic, and only at the end does the result descend to a single score.
Complex fuzzy Z-number WASPAS (Shahid et al., 2026)Z-NumberThis is the form of WASPAS for situations where criterion values are given both as an amplitude-phase pair and as a separate reliability degree attached to that pair. The output remains a combined score and a rank.
Cubic fuzzy WASPAS (Jun, Kim & Yang, 2012)FuzzyThis is the form of WASPAS for situations where a criterion assessment is given both as an interval and as a single point together. Every cell carries an interval and an accompanying confidence degree together; the method reduces the two to a single score and blends the sum with the product.
Fermatean Fuzzy WASPAS (Senapati and Yager, 2020)FuzzyThis is the form of WASPAS for situations where the criterion evaluations are support and rejection degrees given to a judgement whose cubes sum to no more than 1. In place of the sum it uses an optimistic combination of these pairs, and in place of the product a cautious combination; it reduces the two to a single score with λ.
Hesitant fuzzy WASPAS (Mishra, Rani, Pardasani and Mardani, 2019)HesitantThis is the form of WASPAS for situations where more than one plausible membership degree is held together, in the criterion assessment, for the same criterion-alternative pair. The sum and product components are built on sets; the two are reduced to a single score with a coefficient.
Interval-valued intuitionistic fuzzy WASPAS (a DecisionMind derivation)FuzzyThe form of WASPAS for situations where the degrees of support and rejection given to a judgement are themselves intervals. The weighted-sum and weighted-product components are computed separately over these interval pairs, and only the final step reduces them to a single score.
Pythagorean fuzzy WASPAS (DecisionMind derivation)PythagoreanThis is the form of WASPAS for situations where the support and rejection degrees given to a judgement can together exceed 1, provided only that the sum of their squares does not exceed 1. The weighted-sum and weighted-product components are calculated separately over these support-rejection pairs, and only descend to a single score at the very last step.
Picture fuzzy WASPAS (Chowdhury, Chatterjee and Chakraborty, 2025)PictureThis is the form of WASPAS for situations where criterion scores come from a committee's or a survey's yes-abstain-no vote distribution. The weighted-sum and weighted-product components are computed separately on these triples, and only the final step reduces them to a single score.
q-Rung orthopair WASPAS (DecisionMind derivation)q-Rung OrthopairThis is the form of WASPAS that lets an exponent (q) set how large the support and rejection degrees given to a judgement can jointly be. The weighted-sum and weighted-product components are computed separately over these support-rejection pairs, and only the final step reduces them to a single score.
Spherical fuzzy WASPAS (Boltürk and Kutlu Gündoğdu, 2021)SphericalThis is the form of WASPAS used when criterion scores are given as three separate numbers stating a degree of support, rejection and hesitancy for a judgement. The weighted-sum and weighted-product components are calculated separately with these three degrees, and only come down to a single score at the very last step.

ARAS

Base method →

Fuzzy ARAS (Turskis and Zavadskas, 2010)FuzzyFuzzy ARAS is the form of ARAS used where criterion scores are given as triangular fuzzy numbers coming from a judgement or an estimate. It computes the additive utility ratio over the triangles, and ranks the result by a single defuzzified utility degree.
Grey ARAS (Turskis and Zavadskas, 2010)GreyGrey ARAS is the form of ARAS that works with grey numbers when criterion values are known only by a lower and an upper bound. It computes the additive utility ratio over the bounds, reduces the result to a single midpoint, and converts it into a degree of utility.
Intuitionistic fuzzy ARAS (Mishra, Sisodia, Pardasani and Sharma, 2020)IntuitionisticIntuitionistic fuzzy ARAS is the form of ARAS used when a criterion is assessed with a degree of support for, and a degree of rejection of, a judgement, and where more than one decision-maker's opinion can be combined. On cost criteria it reverses direction by swapping support and rejection, and calculates the ratio to the optimal alternative from these two degrees.
Neutrosophic ARAS (Adalı, Öztaş, Özçil, Öztaş and Tuş, 2023)NeutrosophicNeutrosophic ARAS is the form of ARAS used when a criterion's assessment is given as degrees of truth, indeterminacy and falsity. It first reduces every cell to a single score, then computes the utility degree by ratioing that score to the best score in its own criterion.
Fermatean fuzzy ARASFuzzyFermatean fuzzy ARAS is the form of ARAS for situations where criterion evaluation is given as both a degree of support and a degree of rejection for a judgement. These two degrees may be jointly high over a wider region than intuitionistic fuzzy allows; the method computes the ratio to the optimal alternative through these two degrees.
Hesitant Fuzzy ARAS (Mishra, Rani, Krishankumar, Ravichandran and Kar, 2021)HesitantHesitant Fuzzy ARAS is the form of ARAS for situations where an assessment on a criterion holds more than one plausible value at once. It weights these sets, reduces them to a single number by averaging, and computes the ratio to the optimal alternative.
Interval-valued intuitionistic fuzzy ARAS (aggregative, DecisionMind derivation)FuzzyInterval-valued intuitionistic fuzzy ARAS is the form of ARAS for situations where the degree of support and rejection of a judgement is itself not a single number but an interval. It aggregates the alternatives across criteria with weights, then computes the ratio to the optimal alternative.
Interval-valued intuitionistic fuzzy ARAS (Büyüközkan and Göçer, 2018)FuzzyThe form of ARAS used when a judgement's degree of support and degree of rejection are given as an interval rather than a single number. It computes the additive utility ratio over these four-number cells and reduces the result to a single degree of utility.
Plithogenic ARASPlithogenicPlithogenic ARAS is the form of ARAS used when criterion assessment is given as degrees of truth, indeterminacy and falsity, and how contradictory this assessment is in itself is also known. It factors the contradiction share into the calculation beforehand, then computes the additive utility ratio.
Pythagorean fuzzy ARASPythagoreanPythagorean fuzzy ARAS is the form of ARAS used when criterion assessments are given as a membership and non-membership degree pair, and the sum of these two degrees is permitted to exceed 1 provided the sum of their squares does not. It computes the additive utility ratio over these pairs, reducing the result to a single degree of utility.
Picture fuzzy ARAS (Chowdhury, Chatterjee and Chakraborty, 2025)PicturePicture fuzzy ARAS is the form of ARAS used when a criterion assessment is given as degrees of yes, abstain and no. It computes the additive utility ratio over these three-degree cells and the weights, and reduces the result to a single degree of utility.
Probabilistic ARASStochasticProbabilistic ARAS is the form of ARAS for situations where a criterion value comes from a probability distribution and this distribution is reduced to a single representative number (for instance, the expected value). The calculation itself is identical to crisp ARAS; only the source of the number that enters the cell changes.
q-Rung Orthopair ARAS (Mishra & Rani, 2023)q-Rung OrthopairThis is the form of ARAS for situations where criterion scores are given as a judgement's support and rejection degrees, and the sum of these two degrees exceeds the intuitionistic and Pythagorean boundary. It still expresses the utility degree as a percentage ratio against a hypothetical optimal alternative.
Rough ARAS (Daoud Ben Amor, Moalla Frikha & Martínez López, 2021)RoughThis is the form of ARAS that works with rough numbers for situations where criterion scores come from a group assessment by several experts and the disagreement between them needs to be preserved. It carries uncertainty as a lower and upper bound all the way to the final step, and still ranks alternatives by a single degree of utility.
Spherical fuzzy ARASSphericalThis is the form of ARAS for situations where criterion scores are given as three separate numbers: a degree of support for a judgement, a degree of rejection, and a degree of hesitancy. It produces a ratio against the optimal alternative, but this ratio has a particular quirk that means it cannot be read as a percentage the way crisp ARAS's can; this is explained below.

ELECTRE

Base method →

Fuzzy ELECTRE I (Hatami-Marbini & Tavana, 2011)FuzzyFuzzy ELECTRE I is the form of ELECTRE I in which several decision-makers' performance and weight judgements are collected as verbal or trapezoidal fuzzy numbers. The outranking relation is built directly on these fuzzy numbers, without defuzzification; the output remains a core set and an outranking graph.
Fuzzy ELECTRE II (Govindan, Grigore & Kannan, 2010)FuzzyThis is the ELECTRE II form used when performance scores are given verbally or as triangular fuzzy numbers. But this fuzziness is reduced to a single number right at the outset, and everything that follows runs exactly as in crisp ELECTRE II; the output remains a full ranking.
Fuzzy ELECTRE III (Montazer, Qahri Saremi & Ramezani, 2009)FuzzyThis is the ELECTRE III form used when fuzzy scores from an expert evaluation system are reduced to a single number right at the start. The remaining graded threshold logic, indifference, preference and veto, then runs exactly as in crisp ELECTRE III; the output remains close to a full ranking.
Bipolar neutrosophic ELECTRE I (Akram, Shumaiza & Smarandache, 2018)NeutrosophicThis is the form of ELECTRE I used when every cell holds a judgement's truth, indeterminacy and falsity in both a positive and a negative direction, that is, six separate numbers, as bipolar neutrosophic data. Concordance and discordance are built from a score and a distance derived from these six numbers; the thresholds are not chosen by the user but set from the data's own average.
m-Polar Fuzzy ELECTRE I (Akram, Waseem and Liu, 2019)m-PolarThis is the ELECTRE I member of the ELECTRE family for situations where every cell is rated separately from more than one independent viewpoint. Its output is not a ranking but the core set of alternatives that no other alternative outranks.
ELECTRE IV (Roy and Hugonnard, 1982)ClassicalThis is the member of the ELECTRE family that assigns no weight to criteria at all. It works with three thresholds per criterion (indifference, preference, veto), and its output is not a complete ranking but a partial pre-order that emerges from a two-way distillation.
Hesitant Fuzzy ELECTRE I (Chen, Xu and Xia, 2015)HesitantThis is the form of ELECTRE I for situations where performance scores are given as hesitant fuzzy sets, holding several plausible values together rather than one. These values are compared without first collapsing them to an average; the output remains a core set together with outranking relations.
m-Polar Fuzzy ELECTRE IV (Akram and Adeel, 2023)m-PolarThis is the member of the ELECTRE family that both assigns no weight to criteria at all and rates every cell from several independent viewpoints. Its output is not a complete ranking but a partial pre-order emerging from a two-way distillation.

MABAC

Base method →

Fuzzy MABACFuzzyFuzzy MABAC is the form of MABAC used when criterion scores rest on expert estimation and are too approximate to reduce to a single number. It computes the border approximation area, and each alternative's distance to that border, on fuzzy numbers, then ranks the result with a single score, just as the base method does.
Grey MABACGreyGrey MABAC is the form of MABAC that works with grey interval numbers. It is used when only the lower and upper bound of criterion values are known and no most-likely point in between can be given. It builds the border approximation area on the intervals, and again ranks the result with a single score.
Intuitionistic fuzzy MABAC (Li, 2021)IntuitionisticIF-MABAC is the intuitionistic fuzzy form of MABAC used when criteria are assessed through a degree of support for and a degree of rejection of a judgement. It derives criterion weights itself from disagreement among experts, and computes distance to the border through a behavioural weighting.
Neutrosophic MABAC (Peng & Dai, 2018)NeutrosophicN-MABAC adapts MABAC to work with single-valued neutrosophic numbers for situations where criteria are assessed independently by degrees of truth, indeterminacy and falsity. It builds the border approximation area from these three components and ranks the result once again with a single score.
Plithogenic MABACPlithogenicThis is the form of MABAC for situations where criteria are given as degrees of truth, indeterminacy and falsity, and a contradiction between one criterion and the dominant one is also taken into account. It builds the border approximation area from a single score derived from these three degrees, and ranks alternatives against this border.
Rough MABAC (Jia, Liu & Wang, 2019)RoughThis is the form of MABAC for situations where expert scores are not crisp numbers but intuitionistic fuzzy judgements. These judgements are opened out into a lower and an upper approximation from the disagreement within a group of experts. The border-region logic stays exactly the same; the cells change.
Fermatean Fuzzy MABACFuzzyFermatean fuzzy MABAC is the form of MABAC used when an expert states, together, how strongly a criterion is supported and how strongly it is rejected. This pair is admitted over a wider region than intuitionistic fuzzy data allow, and alternatives are again ranked by their distance to a hypothetical border approximation area.
Hesitant MABAC (Mishra, Saha, Rani, Pamučar, Dutta and Hezam, 2022)HesitantThis is the form of MABAC for situations where several plausible membership degrees on a criterion are held together. It builds the border approximation area from the sets themselves, and ranks alternatives by their distance to this border.
Hesitant fuzzy linguistic MABAC (Sun, Hu, Zhou and Chen, 2018)HesitantHesitant fuzzy linguistic MABAC is the form of MABAC used when a criterion is scored not with a single verbal term but with a comparative verbal expression such as "at least high" or "between medium and high." It converts this expression into a linguistic term set and calculates its signed distance to the border area.
Interval-valued intuitionistic fuzzy MABAC (Xue, You, Lai & Liu, 2016)FuzzyThis is the form of MABAC for situations where a judgement's degree of support and degree of rejection are themselves given as intervals. It builds the border approximation area from these four-number cells and ranks alternatives by a signed sum of distances.
Pythagorean fuzzy MABACPythagoreanThis is the form of MABAC for situations where criterion scores are given as support and rejection degrees for a judgement, and the sum of these two degrees may exceed 1. It builds the border approximation area on a score derived from these two degrees, and ranks the result, once again, with a single figure.
Probabilistic linguistic MABAC (Wei, Wei, Wu and Wang, 2019)LinguisticThis is the form of MABAC for situations where the expert gives several terms together with their probabilities. Every term distribution is reduced to a single expected value, and the result is still ranked by a score relative to the border approximation area.
q-Rung Orthopair MABAC (Wang, Wei, Wei & Wei, 2020)q-Rung OrthopairThis is the form of MABAC for situations where criterion scores are given as a judgement's support and rejection degrees, bounded by the sum of these two degrees' q-th powers. It builds the border approximation area with a signed distance derived from this degree, and still ranks the result with a single score.
Spherical fuzzy MABACSphericalThis is the form of MABAC used when criterion scores are given as three separate numbers: a judgement's degree of support, rejection and hesitancy. It builds the border approximation area on a score derived from these three degrees, and still ranks the result with a single score.

MOORA

Base method →

Fuzzy MOORAFuzzyFuzzy MOORA is the form of MOORA that works with triangular fuzzy numbers when criterion scores come from expert judgement and reducing them to a single number would create an artificial precision. It runs the ratio system across three components and only descends to a single net score at the end.
Grey MOORA (Stanujkić, Magdalinović, Jovanović & Stojanović, 2012)GreyGrey MOORA is the form of MOORA that works with grey (interval grey) numbers when criterion values are known only by a lower and upper bound. It whitenises the bounds and feeds them into the ratio system, again ranking the result by a single net score.
Intuitionistic fuzzy MOORAIntuitionisticIF-MOORA is the form of MOORA that works with intuitionistic fuzzy numbers when criteria are not a measured quantity but a judgement, and the support and rejection degrees of that judgement are known separately. It turns the support-rejection difference into a single number and feeds it into the ratio system.
Neutrosophic MOORANeutrosophicN-MOORA is the form of MOORA for situations where a criterion judgement arrives as independent degrees of truth, indeterminacy and falsity. The triple is reduced to a single score before entering the ratio system.
Fermatean Fuzzy MOORAFuzzyThe form of MOORA for situations where the sum of the cubes of a judgement's support and rejection degree does not exceed 1. It reduces every cell to a score straightaway and runs the remainder like crisp MOORA's own ratio system.
Hesitant MOORA (Li, 2014)HesitantThis is the form of MOORA for situations where criterion scores are given as several plausible values (a hesitant set) rather than a single number. It reduces every cell to a score and runs the rest exactly as crisp MOORA's ratio system.
Interval-valued intuitionistic fuzzy MOORAFuzzyInterval-valued intuitionistic fuzzy MOORA is the form of MOORA for situations where a judgement's own degree of support and degree of rejection are given not as single numbers but as intervals. It reduces every cell to a score straight away and runs the rest exactly as crisp MOORA's ratio system does.
Plithogenic MOORAPlithogenicThis is the form of MOORA for situations where criterion scores are given as a truth-indeterminacy-falsity triple and criteria carry a degree of contradiction relative to one another. It runs the ratio system on this triple and arrives at a single net score.
Pythagorean fuzzy MOORAPythagoreanThis is the Pythagorean fuzzy form of MOORA. The support and rejection degrees given to a judgement may sum to more than 1, provided the sum of their squares does not. The ratio system runs on this pair and comes down to a single net score.
Picture fuzzy MOORAPictureThis is the form of MOORA for situations where criterion scores come from a board's or a survey's yes-abstain-no vote distribution. It merges the beneficial and harmful criteria separately, then reduces their difference to a single net score.
q-Rung orthopair MOORAq-Rung OrthopairThis is the form of MOORA for situations where an expert assigns a judgement both strong support and a strong reservation at once, and the sum of the two exceeds the intuitionistic or Pythagorean bound. The ratio system runs on this pair and descends to a single net score.
Rough MOORARoughThis is the form of MOORA for situations where every cell in the decision matrix is given as a lower and upper bound derived from disagreement within a group of experts. It runs the ratio system over these intervals and still comes down to a single net score.
Spherical fuzzy MOORA (Aydın & Kutlu Gündoğdu, 2021)SphericalSpherical fuzzy MOORA is the form of MOORA's ratio system for situations where criterion scores are given as a support-rejection-hesitancy triple. Its output remains a single score and the rank that score produces.

GRA

Base method →

Grey relational analysis (interval grey)GreyGrey GRA is the form of GRA that works with grey numbers when criterion values are known only by a lower and upper bound rather than a single figure. The calculation runs from the midpoint of each cell's bounds, and the result is again ranked by a grey relational grade.
Intuitionistic fuzzy GRAIntuitionisticIF-GRA is the form of GRA that works with intuitionistic fuzzy numbers when criteria are assessed through degrees of support for and rejection of a judgement. It computes distance to the reference from these two degrees and ranks the result again by a grey relational grade.
Neutrosophic GRA (Biswas, Pramanik & Giri, 2014)NeutrosophicN-GRA is the form of GRA that works with neutrosophic triples for situations where criteria are assessed independently by degrees of truth, indeterminacy and falsity. It computes the distance to a reference from these three components, and ranks the result once again with a grey relational degree.
Fermatean Fuzzy GRAFuzzyFermatean fuzzy GRA is the form of GRA for situations where criterion scores are given as a degree of support for a judgement and a degree of rejection of it, and these two degrees can be simultaneously high over a region wider even than Pythagorean fuzzy data permit. It computes distance to the reference from these two degrees and ranks the result, again, by a grey relational degree.
Hesitant GRA (Li and Wei, 2014)HesitantHesitant GRA is the form of GRA that works for situations where several plausible values for one criterion — expert opinions, scenarios, repeated measurements — are preserved together rather than collapsed into a single number. It builds its reference from both the best and the worst end, and ranks the result with a closeness ratio.
Interval Number Grey Relational Analysis (Olson and Wu, 2008)ClassicalThis is the form of GRA for situations where criterion values are given not as a single number but as a known, exact lower and upper bound. It carries the bounds through without reducing them to a single number at any step; it computes the reference and the distance from the two bounds together.
Plithogenic GRAPlithogenicThis is the form of GRA for situations where criterion scores are given as a truth-indeterminacy-falsity triple and criteria carry a degree of contradiction relative to one another. Its output is again a grey relational degree and the ranking that follows from it.
Pythagorean fuzzy GRAPythagoreanThis is the form of GRA that works for situations where criterion scores are given as the degree to which a judgement is supported and rejected, and the sum of these two degrees can exceed 1. It computes the distance to the reference from these two degrees, and ranks the result again with a grey relational grade.
q-Rung Orthopair GRAq-Rung OrthopairThis is the form of GRA that works for situations where criterion scores are given as a judgement's degree of support and rejection, and how large these two degrees may be together is bounded by an exponent (q) chosen to fit the data. It still ranks the result with a grey relational grade.
Scenario fuzzy GRAFuzzyThis is the form of GRA for situations where criterion scores are given as triangular fuzzy numbers: it applies crisp GRA separately to the triangle's lower, middle and upper ends, then combines the results. Its output is again a score between 0 and 1 and a ranking based on that score.
Spherical fuzzy GRASphericalThis is the form of GRA used when criterion scores are given as three separate numbers: a judgement's degree of support, rejection and hesitancy. Its output remains a grey relational grade and the rank that grade produces.

DEA

Base method →

Data envelopment analysis BCC (variable returns to scale) (Banker, Charnes & Cooper, 1984)ClassicalThis is the form of DEA for situations where the units being compared differ in size and that size difference must not distort the efficiency comparison. The output remains an efficiency score, together with every unit's returns-to-scale classification (advantaged at small scale, or at large scale).
DEA cross-efficiency (Sexton, Silkman & Hogan, 1986)ClassicalThis is the form of DEA where every unit is evaluated not only by its own chosen weights but also by every other unit's chosen weights, with units scoring one another reciprocally. The output is a single cross-efficiency average for every unit, and this average places the units in a complete ranking.
Dynamic Network DEA (Fukuyama and Weber, 2013)ClassicalThis is the form of DEA that compares units across several consecutive periods rather than within a single year. It also accounts for an asset carried over between periods and an undesirable output that spills from one period into the next. Its output is a single combined efficiency score for each unit.
Environmental DEA (Färe, Grosskopf, Lovell and Pasurka, 1989)ClassicalThis is the form of DEA for situations where an undesirable output (such as a pollutant) cannot be disposed of freely, but can only be reduced proportionally alongside the inputs. Its output is again an environmental efficiency score between 0 and 1.
Two-Stage Network DEA (Fukuyama and Weber, 2010)ClassicalThis is the form of DEA for situations where a unit converts input into output not in one step, but across two consecutive stages through an intermediate product. It can also produce an undesirable output in the second stage. Its output is again a network efficiency score between 0 and 1.
Network SBM DEA (Tone and Tsutsui, 2009)ClassicalThis is the form of DEA that evaluates a multi-stage process with its own importance weight per stage. It measures input/output slack directly rather than proportionally, and can examine several periods together within a single window. Its output is again a network efficiency score between 0 and 1.
DEA Range-Adjusted Measure of Inefficiency (RAM) (Cooper, Park and Pastor, 1999)ClassicalRAM is a form of DEA that measures and sums, separately for each measure against its own value range, the input excess and output shortfall that a classical radial (percentage) score can overlook. The output is again an inefficiency score between 0 and 1, but this score captures not only the proportional contraction but also any remaining slack.
Slacks-Based Measure DEA (SBM) (Tone, 2001)ClassicalSBM is a form of DEA that, instead of a classical proportional contraction ratio, directly measures every input excess and output shortfall on its own scale. The result is again an efficiency score between 0 and 1, but this score rests not on a ratio but directly on the slack share.
Super-Efficiency DEA (Andersen and Petersen, 1993)ClassicalSuper-efficiency DEA is a form that allows units classical DEA rates as equally "efficient" (theta=1) to be ranked amongst themselves as well. Each unit is re-evaluated with its own data excluded from the reference set; this brings out a degree of superiority even among efficient units.
Fuzzy FMEA DEA (Adesina, Yazdi, Zarei and Pouyakian, 2022)FuzzyThis is a hybrid method in which experts score a failure mode's severity, occurrence and detectability verbally, derive the classical risk priority number (RPN) from these scores, and compare the cost-time efficiency of corrective actions with DEA. The output is both a risk magnitude and a DEA efficiency score.

CoCoSo

Base method →

Fuzzy CoCoSoFuzzyFuzzy CoCoSo is the form of CoCoSo used when criterion values are given as triangular fuzzy numbers. It equalises the scale separately on each of the three corners, then computes the additive and multiplicative measures from numbers already reduced to their centroid, before combining them with three compromise strategies.
Intuitionistic fuzzy CoCoSoIntuitionisticIF-CoCoSo is the intuitionistic fuzzy form of CoCoSo. Here criterion assessments are expressed through a degree of support for, and a degree of rejection of, a judgement (μ, ν). Every cell is first reduced to a single Chen-Tan score. The rest of the calculation, that is scale equalisation, the additive and multiplicative measures, and the three compromise strategies, runs exactly as in crisp CoCoSo.
Fermatean fuzzy CoCoSo (built on Senapati and Yager's 2020 foundation)FuzzyFermatean fuzzy CoCoSo is the form of CoCoSo used for situations where criterion evaluations are expressed as the support and rejection degree given to a judgement. The constraint here is not the sum of these two degrees but the sum of their CUBES, and this sum cannot exceed 1. Every cell is first reduced to a single Fermatean score; everything that follows runs exactly as in crisp CoCoSo.
Neutrosophic CoCoSo (Nabeeh & Sallam, 2024)NeutrosophicNeutrosophic CoCoSo is the form of CoCoSo for situations where criterion scores are given as three independent degrees: truth (T), indeterminacy (I) and falsity (F). Each cell is first reduced to a single score, and the additive and multiplicative measures are then computed directly from these scores.
Plithogenic CoCoSoPlithogenicThis is the form of CoCoSo for situations where criterion scores are given as a truth-indeterminacy-falsity triple and criteria carry a degree of contradiction relative to one another. Its output is again a combined compromise score and the ranking that follows from it.
Pythagorean fuzzy CoCoSoPythagoreanThis is the form of CoCoSo for situations where the sum of the support and rejection degrees given to a judgement may exceed 1, but the sum of their squares does not exceed 1. Its output is again a combined compromise score and the ranking that follows from it.
q-Rung Orthopair CoCoSo (Kuvvetli, 2023)q-Rung OrthopairThis is the form of CoCoSo for situations where an expert gives a judgement both strong support and a strong reservation, and the sum of the two exceeds the intuitionistic or Pythagorean boundary. Its output is again a combined compromise score and the ranking that score produces.
Spherical fuzzy CoCoSoSphericalThis is the form of CoCoSo for situations where criterion scores are given as three separate numbers: a judgement's degree of support, rejection and hesitancy. Its output remains a combined compromise score and the rank that score produces.

MULTIMOORA

Base method →

Fuzzy MULTIMOORAFuzzyFuzzy MULTIMOORA is the form of MULTIMOORA used when criterion values are given as a lowest-most likely-highest triple (a triangular fuzzy number). It computes the ratio system, the reference point and the full multiplicative form separately on these triples, then merges them into a single ranking with dominance theory.
Intuitionistic fuzzy MULTIMOORAIntuitionisticIntuitionistic Fuzzy MULTIMOORA is the form of MULTIMOORA used when criterion assessment is given as a degree of support for, and a degree of rejection of, a judgement (an intuitionistic fuzzy pair). It reduces the support-rejection difference to a single score for the ratio system and the reference point, while the full multiplicative form is computed keeping the support-rejection structure intact.
Neutrosophic MULTIMOORA (Stanujkic et al., 2017)NeutrosophicNeutrosophic MULTIMOORA is the form of MULTIMOORA used when a criterion evaluation is given as a truth-indeterminacy-falsity triple (a single-valued neutrosophic number). The ratio system, the reference point and the full multiplicative form each compute a score derived from this triple separately, and the result is merged into a single ranking by a two-out-of-three dominance rule.
Interval neutrosophic MULTIMOORA (Stanujkić et al., 2021)NeutrosophicInterval neutrosophic MULTIMOORA is the form of MULTIMOORA for situations where each component of a criterion assessment's truth-indeterminacy-falsity triple is given not as a single number but as an interval. The ratio system, the reference point and the full multiplicative form are each computed separately over these intervals; the result is then combined into a single ranking by the average-rank rule.
2-tuple linguistic MULTIMOORA (Baležentis and Baležentis, 2011)Linguistic2-tuple linguistic MULTIMOORA is the form of MULTIMOORA for situations where a criterion score is given as a term chosen from a pre-declared term set together with a shift away from that term. The ratio system, the reference point and the full multiplicative form are each computed on these terms separately, and the three sub-rankings are merged into a single order by dominance theory.
Plithogenic MULTIMOORAPlithogenicThis is the form of MULTIMOORA for situations where criterion scores are given as a truth-indeterminacy-falsity triple and criteria carry a degree of contradiction relative to one another. The ratio system, the reference point and the full multiplicative form are each computed separately on these triples, and the result is merged into a single rank by the average-rank rule.
Probabilistic linguistic MULTIMOORA (Wu et al., 2018)LinguisticProbabilistic linguistic MULTIMOORA is the form of MULTIMOORA for situations where a criterion assessment is split across several terms and the probabilities of those terms. The ratio system, the reference point and the full multiplicative form are all computed on the same expected value; the result is combined with an improved Borda score.
Triangular Neutrosophic MULTIMOORA (Stanujkić et al., 2021)NeutrosophicTriangular neutrosophic MULTIMOORA is the form of MULTIMOORA for situations where several experts' truth-indeterminacy-falsity judgements are gathered into a triangle that carries both consensus and disagreement together. The ratio system, the reference point and the full multiplicative form aggregate benefit and cost criteria separately; dominance theory reduces the three results to a single rank.

WPM

Base method →

Fuzzy WPM (Kahraman, Birgün and Yenen, 2008)FuzzyFuzzy WPM is the form of WPM used when criterion values and weights are given as triangular fuzzy numbers. It carries out weighted exponentiation and multiplication, corner by corner, on the raw, that is unscaled, fuzzy values. It defuzzifies the result to a single number only at the final step.
Intuitionistic fuzzy WPMIntuitionisticIF-WPM is the form of WPM used when criterion assessments are expressed as a judgement's degree of support and degree of rejection (μ, ν). On cost criteria the (μ, ν) pair is first converted to its complement, then all criteria are combined with the weighted geometric aggregation operator (IFWG), and only in the final step is this reduced to a single Chen-Tan score.
Neutrosophic WPM (Ye, 2014)NeutrosophicN-WPM is the form of WPM used when criterion assessments are expressed as degrees of truth (T), indeterminacy (I) and falsity (F). Criteria are combined with the neutrosophic weighted geometric aggregation operator (SVNWG), and reduced, at the very last step, to a single score that counts indeterminacy with double weight.
Fermatean Fuzzy WPM (based on Senapati and Yager's 2020 foundation)FuzzyFermatean fuzzy WPM is the form of WPM used where criterion evaluations are expressed through the support and rejection degrees given to a judgement. The constraint here is not on the sum of these two degrees but on the sum of their CUBES, and this sum must not exceed 1. The criteria are reduced to a single support-rejection pair by the weighted geometric aggregation operator (FFWG), and this pair is then resolved into a single score.
Plithogenic WPMPlithogenicPlithogenic WPM is the form of WPM used when criterion assessments are given as a truth-indeterminacy-falsity triple and criteria carry a degree of contradiction relative to one another. Once adjusted by this contradiction degree, criteria are combined through a weighted geometric aggregation operator (PNWG-like) and reduced to a single score.
Pythagorean fuzzy WPMPythagoreanPythagorean fuzzy WPM is the form of WPM used when criterion values are recorded as a support and rejection degree (μ, ν) given to a judgement. The sum of the squares of these two degrees does not exceed 1. Its output is a Pythagorean score for every alternative and the rank that follows from it.
q-Rung orthopair WPMq-Rung Orthopairq-Rung orthopair WPM is the form of WPM for situations where an expert assigns a judgement both strong support and a strong reservation at once. The sum of the two exceeds the intuitionistic or Pythagorean bound. Its output is still a single score and the rank that score gives.
Spherical fuzzy WPM (Kutlu Gündoğdu and Yörükoğlu, 2021)SphericalSpherical fuzzy WPM is the form of WPM used when criterion scores are given as three separate numbers stating a degree of support, rejection and hesitancy for a judgement. The calculation first reduces every cell to a single number, then multiplies these numbers together with weights.

ELECTRE II

Base method →

Hesitant Fuzzy ELECTRE II (Chen and Xu, 2015)HesitantThis is the form of ELECTRE II for situations where performance scores are given as hesitant fuzzy sets. The fuzziness is carried through to the very last step and is never collapsed early into a single average; the output remains a complete ranking.
m-Polar Fuzzy ELECTRE II (Akram and Adeel, 2023)m-PolarThis is the form of ELECTRE II for situations where performance scores are rated separately from several independent viewpoints. The viewpoints are preserved without being reduced to an average, and the output remains a complete ranking.
Pythagorean fuzzy ELECTRE II (Akram, Ilyas and Garg, 2021)PythagoreanThis is the form of ELECTRE II for situations where decision-makers give criterion scores as Pythagorean fuzzy pairs carrying both strong support and marked reservation, and several experts' opinions are assessed together. The output is again a ranking built from two directions.

SPOTIS

Base method →

Fuzzy SPOTIS (Shekhovtsov, Paradowski, Więckowski, Kizielewicz & Sałabun, 2022)FuzzyFuzzy SPOTIS is the form of SPOTIS used when criterion values and the fixed bounds are given by expert judgement as triangular fuzzy numbers. It calculates distance to the fixed ideal via the triangles' centroid, and ranks the result, again, by a single distance value.
Neutrosophic SPOTIS (Abdel-aziem, Mohamed & Abdelhafeez, 2023)NeutrosophicNeutrosophic SPOTIS is the form of SPOTIS that works when criterion values are given neutrosophically, as degrees of truth, indeterminacy and falsity. Every cell is first reduced to a single score, the distance to fixed bounds is computed on this score, and the result again ranks alternatives by a single distance value.
Balanced SPOTIS (Shekhovtsov, Dezert and Sałabun, 2025)ClassicalBalanced SPOTIS is the form of SPOTIS that, alongside the fixed ideal, also takes into account a "realistic target" point set by the decision-maker. It blends the distance to the two reference points with a single coefficient, and still ranks alternatives by one distance value.
Plithogenic SPOTISPlithogenicThis is the form of SPOTIS for situations where criterion scores are given as a truth-indeterminacy-falsity triple and criteria carry a degree of contradiction relative to one another. It reduces every cell to a single score and computes that score's scaled distance to the ideal.

AROMAN

Base method →

Fuzzy AROMANFuzzyFuzzy AROMAN is the form of AROMAN used when the values in the decision table are not crisp numbers but an approximation drawn from expert judgement or estimation. It carries the calculation through triangular fuzzy numbers and still ranks the result with a single score.
Neutrosophic AROMANNeutrosophicN-AROMAN is the form of AROMAN used when a criterion's assessment is given as degrees of truth, indeterminacy and falsity. These three degrees are called a single-valued neutrosophic triple. The method first reduces the triple to a single score, then applies AROMAN's two normalisations to this score, and ranks the result with a single number.
Plithogenic AROMANPlithogenicThis is the form of AROMAN for situations where criterion scores are given as a truth-indeterminacy-falsity triple and criteria carry a degree of contradiction relative to one another. DecisionMind's implementation applies the base AROMAN's two-normalisation and benefit-cost-balance idea in a simplified form; this is explained explicitly below.

DNMA

Base method →

Fuzzy DNMAFuzzyFuzzy DNMA is the form of DNMA used when the values in the decision table are an approximation drawn from expert judgement or estimation. It holds the decision matrix in triangular fuzzy numbers, computes three aggregation models over these triangles, and still ranks the result with a single score.
Neutrosophic DNMANeutrosophicN-DNMA is the form of DNMA used when criterion assessment is given by degrees of truth, indeterminacy and falsity. These three degrees are called a single-valued neutrosophic triple. The method first reduces every cell to a single score, then ranks alternatives with a single aggregation model that averages two normalisations of this score.
Plithogenic DNMAPlithogenicThis is the form of DNMA for situations where criterion scores are given as a truth-indeterminacy-falsity triple and criteria carry a degree of contradiction relative to one another. It combines three separate aggregation measures and again produces a single combined score.

MAUT

Base method →

Fuzzy MAUTFuzzyFuzzy MAUT is the form of MAUT that works with triangular fuzzy numbers when criterion values, or the bounds of the utility function, are given approximately through expert judgement. It computes each criterion's utility in fuzzy terms and still ranks the result with a single aggregate utility score.
Intuitionistic fuzzy MAUTIntuitionisticIF-MAUT is the form of MAUT that works with intuitionistic fuzzy numbers when criterion values are expressed as a degree of support for, and a degree of rejection of, a judgement. Rather than constructing a utility function, it combines the support-rejection pair directly by weighting, and ranks the result with a single score.
Plithogenic MAUTPlithogenicThis is the form of MAUT for situations where criterion values are given as a truth-indeterminacy-falsity triple and criteria carry a degree of contradiction relative to one another. Each criterion is converted to its own utility scale and summed with weights; the output remains a single aggregate utility score.

PSI

Base method →

Fuzzy PSIFuzzyFuzzy PSI is the form of PSI used when criterion scores are given as triangular fuzzy numbers. It derives the weight itself, and its output is a preference selection score.
Neutrosophic PSINeutrosophicNeutrosophic PSI is the form of PSI used when criterion scores are given as degrees of truth, indeterminacy and falsity, that is, as a T, I, F triple. It derives its own weights, and its output is a preference selection index.
Plithogenic PSIPlithogenicThis is the form of PSI for situations where criterion scores are given as a truth-indeterminacy-falsity triple and criteria carry a degree of contradiction relative to one another. It still derives its own weights, and its output remains a preference selection score.

RAFSI

Base method →

Fuzzy RAFSIFuzzyFuzzy RAFSI is the form of RAFSI used when criterion scores are given as triangular fuzzy numbers. It maps the alternatives onto a fixed-length scale interval and reduces them to a single score.
Neutrosophic RAFSINeutrosophicNeutrosophic RAFSI is the form of RAFSI used when criterion scores are given as degrees of truth, indeterminacy and falsity, that is, as a T, I, F triple. It maps the alternatives onto a fixed-length scale interval and reduces them to a single score.
Plithogenic RAFSIPlithogenicThis is the form of RAFSI for situations where criterion scores are given as a truth-indeterminacy-falsity triple and criteria carry a degree of contradiction relative to one another. It maps alternatives onto a fixed-length scale interval and reduces them to a single score.

RAWEC

Base method →

Fuzzy RAWEC (Katrancı, Kundakcı & Arman, 2026)FuzzyFuzzy RAWEC is the form of RAWEC used when criterion scores are given in words or as approximate judgements. It measures every alternative in terms of both its closeness to the good side and its distance from the bad side using triangular fuzzy numbers, and merges the two into a single index.
Neutrosophic RAWECNeutrosophicNeutrosophic RAWEC is the form of RAWEC used when criterion scores are given as degrees of truth, indeterminacy and falsity. It reduces every triple to a single score, then runs RAWEC's closeness-to-best and distance-from-worst logic on this score.
Plithogenic RAWECPlithogenicThis is the form of RAWEC for situations where criterion scores are given as a truth-indeterminacy-falsity triple and criteria carry a degree of contradiction relative to one another. Its output remains a ranking score built from the sum of weighted contributions.

WISP

Base method →

Fuzzy WISPFuzzyFuzzy WISP is the form of WISP used when the values in the decision table are an approximation drawn from expert judgement or estimation. It runs all four comparison logics over triangular fuzzy numbers and ranks the result with a single score.
Neutrosophic WISP (Stanujkić et al., 2022)NeutrosophicNeutrosophic WISP is the form of WISP used when the values in the decision table are given as degrees of truth, indeterminacy and falsity. It computes the four comparison logics by combining benefit and cost criteria in separate groups through neutrosophic summation and multiplication operations.
Plithogenic WISPPlithogenicPlithogenic WISP is the form of WISP used when the values in the decision table are given as a truth-indeterminacy-falsity triple and criteria carry a degree of contradiction. It computes the four comparison logics over scores adjusted by the criterion's contradiction degree.

ARTASI

Base method →

Picture fuzzy ARTASI (Kara, Yalçın, Kaygısız, Simić, Örnek and Pamučar, 2024)PictureThis is the form of ARTASI for situations where criterion scores come from a vote or a distribution of opinion, given as a yes-abstain-no degree. It keeps the adaptive-range and ideal/anti-ideal-benefit logic, but the cells first descend to a single number through a score function.

CIMAS

Base method →

Picture fuzzy CIMAS (Kara et al., 2024)PicturePicture fuzzy CIMAS is the form of CIMAS used when experts' importance judgements and criterion scores are given as degrees of yes, abstention and no. The output remains a weight vector: every judgement is reduced to a single crisp score in the first step of the calculation, and the rest of the computation runs exactly as in crisp CIMAS.
Picture fuzzy CIMAS-ARTASI (Kara et al., 2024)PictureThis hybrid method carries the criterion weights produced by picture fuzzy CIMAS directly into picture fuzzy ARTASI's ranking step. Two picture fuzzy stages run one after the other: first a weighting, then, using these weights, a ranking of alternatives.

CRADIS

Base method →

Spherical fuzzy Z-number CRADIS (Niu, 2024)Z-NumberThis is the form of CRADIS for situations where criterion values are given as a spherical fuzzy triple (support, rejection, hesitancy) and each of these three degrees is additionally accompanied by a reliability. The output is again a compromise score.
Z-fuzzy CRADIS (Puška et al., 2022)Z-NumberThis is the form of CRADIS for situations where a criterion value is carried as a triangular fuzzy number together with a separate Z-number component stating how far that value can be trusted, the two together reduced to a single fuzzy number. The output remains a compromise score.

DEMATEL

Base method →

Fuzzy DEMATELFuzzyFuzzy DEMATEL is the form of DEMATEL that aggregates cross-criterion influence with triangular fuzzy numbers when experts give that influence verbally or approximately. It converts the fuzzy influence matrix into a single crisp matrix at the very start of the calculation, and runs the rest exactly like crisp DEMATEL.
Scenario fuzzy DEMATELFuzzyThis is a form of DEMATEL for situations where the influence scores between criteria are given as triangular fuzzy numbers: it runs DEMATEL separately on each triangle vertex (lower, middle, upper) and averages the results. The output is an averaged criterion-weight vector.

ELECTRE III

Base method →

m-Polar Fuzzy ELECTRE III (Akram and Adeel, 2023)m-PolarThis is the form of ELECTRE III for situations where criteria are rated separately from several independent viewpoints. It derives weights from the data itself, and delivers the result as a single, clean outranking order that leaves no pair incomparable.

LMAW

Base method →

Fuzzy LMAW (Božanić, Pamučar, Milić, Marinković and Komazec, 2022)FuzzyFuzzy LMAW is the form of LMAW for situations where experts express the priority they give to criteria as a triangular fuzzy number rather than a crisp number. Its output is not a ranking but a criterion weight vector.
Z-fuzzy LMAW (Puška, Božanić, Nedeljković and Janošević, 2022)Z-NumberZ-fuzzy LMAW is the form of LMAW that carries the priority experts give to criteria not only as a fuzzy term, but together with a separate component stating how much that term is trusted. Its output is not a ranking but a criterion weight vector.

MEREC

Base method →

Fuzzy MEREC (Saidin, Lee, Marjugi, Ahmad & Seow, 2023)FuzzyFuzzy MEREC is the form of MEREC used when criterion scores are given as triangular fuzzy numbers. It produces a weight vector rather than a ranking; it measures how much removing a criterion would disturb the overall evaluation.
Scenario fuzzy MERECFuzzyThis is a form of MEREC for situations where criterion scores are given as triangular fuzzy numbers: it runs MEREC fully and separately on each triangle vertex (lower, middle, upper) and averages the three weight vectors. The output is an averaged criterion-weight vector; it does not produce a ranking.

OCRA

Base method →

Fuzzy OCRAFuzzyFuzzy OCRA is the form of OCRA used when input and output criteria are scored verbally or approximately. It measures an alternative's shortfall on the input side and its superiority on the output side with triangular fuzzy numbers, then merges the two into a single score at the end.
Plithogenic OCRAPlithogenicPlithogenic OCRA is the form of OCRA for situations where input and output criteria are given as a truth-indeterminacy-falsity triple and each criterion carries a degree of contradiction relative to a dominant criterion. It measures the shortfall on the input side and the superiority on the output side separately on these triples, and merges them into a single score at the end.

ROV

Base method →

Fuzzy ROVFuzzyFuzzy ROV is the form of ROV used when criterion values are given in words or as approximate judgements. It normalises benefit and cost criteria with triangular fuzzy numbers, computes the most optimistic and most pessimistic scores in fuzzy form, and averages them.
Plithogenic ROVPlithogenicThis is the form of ROV for situations where criterion scores are given as a truth-indeterminacy-falsity triple and criteria carry a degree of contradiction relative to one another. It ranks alternatives by a weighted sum score placed on a fixed [0,1] scale.

SMART

Base method →

Fuzzy SMARTFuzzyFuzzy SMART is the form of SMART used when the importance ratings a decision-maker gives to criteria are verbal or approximate. It takes these ratings as triangular fuzzy numbers and produces only the criterion weights.
SMART weighting (Edwards and Barron, 1994)ClassicalSMART weighting runs, on its own, the step of SMART that converts importance ratings into weights. Its input is not an alternative table but only the importance ratings given to criteria; its output is a weight vector that sums to 1.

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