Methods that work with Fuzzy data

Every method that works with this data type has a page of its own. Those with an academy card are explained here through their philosophy, how to read their output and worked cases; the rest open on their formula page in the library.

101 academy cards · 17 only in the library · 108 methods in the catalogue

Methods with an academy card

101 cards

RankingFuzzy Information AxiomThe Fuzzy Information Axiom looks at how far each alternative's triangular fuzzy performance range overlaps with the desired design range; the greater the overlap, the less uncertainty the alternative carries, and the better it is judged to be.Open the card →
OutrankingHF-QUALIFLEXWhen experts cannot agree on a single value for a criterion and report several plausible values instead, HF-QUALIFLEX tries out every possible ranking of the alternatives one by one and picks the one most consistent with the criteria.Open the card →
Subjective weightingB-WENSLOB-WENSLO converts the linguistic scores experts assign to criteria into triangular fuzzy numbers, then measures the disagreement among experts and derives criterion weight from that disagreement.Open the card →
Subjective weightingFUCOM-FFUCOM-F is a criterion-weighting method, carrying uncertainty right to the end, in which the expert ranks the criteria and then states the importance ratio between successive criteria as a triangular fuzzy number.Open the card →
Subjective weightingFuzzy SIWECFuzzy SIWEC asks experts for no ranking or pairwise comparison at all; each expert scores every criterion on its own with a linguistic term, and the method looks at which expert distinguishes between criteria most clearly and gives that expert's opinion more weight.Open the card →
Objective weightingFCILOSFCILOS carries CILOS's idea of "the cost of missing out on being best in a criterion" into decisions given with triangular fuzzy numbers, keeping uncertainty in the calculation right to the end.Open the card →
Objective weightingFuzzy IDOCRIWFuzzy IDOCRIW carries classical IDOCRIW's "both spread and opportunity cost" logic into fuzzy data by running it separately on the lower, middle and upper end of the triangular fuzzy number and averaging the three results.Open the card →
Objective weightingFuzzy LOPCOWFuzzy LOPCOW carries classical LOPCOW's idea, the logarithmic ratio between a criterion's average magnitude and its spread, into fuzzy data by running it separately on the lower, middle and upper end of the triangular fuzzy number and averaging the three results.Open the card →
Objective weightingFuzzy PCAWhen criteria are given as triangular fuzzy numbers (TFNs), this objective profile runs principal component analysis separately on the lower bound, the most likely value and the upper bound, and produces weights by averaging the three results.Open the card →
Objective weightingFuzzy Standard DeviationWhen criteria are given as triangular fuzzy numbers (TFNs), this objective profile runs standard-deviation-based weighting separately on the lower bound, the most likely value and the upper bound, and produces weights by averaging the three results.Open the card →
Objective weightingFuzzy SPCWhen criteria are given as triangular fuzzy numbers (TFNs), this objective profile runs weighting based on each criterion's symmetry point separately on the lower bound, the most likely value and the upper bound, and produces weights by averaging the three results.Open the card →
Objective weightingScenario-Based Fuzzy CILOSScenario-Based Fuzzy CILOS is a straightforward way of adapting classical CILOS to triangular fuzzy input: it treats the lower, middle and upper corner of the triangle as three separate crisp tables, runs classical CILOS three times, then averages the three results.Open the card →
DefuzzificationAlpha-Cut DefuzzificationAlpha-cut defuzzification first reduces a fuzzy number to an interval at the desired confidence level, then converts that interval into a single number according to the decision-maker's attitude.Open the card →
DefuzzificationBisector DefuzzificationThe bisector finds the vertical line that splits the area under a fuzzy number exactly in half, and reports the point where that line falls as the single crisp number.Open the card →
DefuzzificationCentroid DefuzzificationCentroid finds the centre of gravity of the area beneath a fuzzy number and reports that point as a single crisp figure; this makes it the defuzzification rule most often used in fuzzy control and fuzzy decision methods.Open the card →
DefuzzificationGaussian Centroid DefuzzificationThis method finds the centre of mass of a fuzzy number whose membership degree is defined as a bell curve (a Gaussian curve); if the curve is symmetric this centre falls directly on the curve's peak, and if it spreads differently to the two sides the centre departs from the peak.Open the card →
DefuzzificationMean of Maxima DefuzzificationMOM finds the point at which a fuzzy number's degree of membership is highest (or, where the peak is flat, the midpoint of that plateau) and reports that point as a single crisp figure; it never looks at the fuzzy number's tails.Open the card →
DefuzzificationType Reduction DefuzzificationType reduction first collapses a Type-2 fuzzy number, defined by an upper and a lower bound, into an interval, then reduces that interval's midpoint to a single crisp figure; the width of the interval also shows the size of the uncertainty the number carries.Open the card →
TOPSIS extensionsFuzzy TOPSISThis 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.Open the card →
TOPSIS extensionsFuzzy TOPSIS (Chen 2000)This 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.Open the card →
TOPSIS extensionsComplex Fuzzy TOPSISThe 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.Open the card →
TOPSIS extensionsFermatean Fuzzy TOPSISThis 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.Open the card →
TOPSIS extensionsInterval-valued intuitionistic fuzzy TOPSISThe 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.Open the card →
VIKOR extensionsFuzzy VIKORThis 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.Open the card →
VIKOR extensionsComplex Fuzzy VIKORThe 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.Open the card →
VIKOR extensionsCubic fuzzy VIKORThis 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.Open the card →
VIKOR extensionsFermatean Fuzzy VIKORThis 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.Open the card →
VIKOR extensionsInterval-valued intuitionistic fuzzy VIKORThe 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.Open the card →
VIKOR extensionsInterval-valued intuitionistic fuzzy VIKORThis 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.Open the card →
SAW extensionsFuzzy SAWFuzzy 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.Open the card →
SAW extensionsFermatean Fuzzy SAWThis 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.Open the card →
SAW extensionsInterval-valued intuitionistic fuzzy SAWThe 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.Open the card →
AHP extensionsFuzzy AHPFuzzy 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.Open the card →
BWM extensionsFuzzy BWMFuzzy 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.Open the card →
SWARA extensionsFuzzy SWARAFuzzy 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.Open the card →
SWARA extensionsScenario fuzzy SWARAThis 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.Open the card →
Entropy Weighting extensionsFuzzy EntropyFuzzy 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.Open the card →
CRITIC extensionsFuzzy CRITICFuzzy 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.Open the card →
EDAS extensionsFuzzy EDASThis 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.Open the card →
EDAS extensionsComplex Fuzzy EDASThe 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.Open the card →
EDAS extensionsFermatean Fuzzy EDASThe 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.Open the card →
EDAS extensionsInterval-valued intuitionistic fuzzy EDASInterval-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.Open the card →
COPRAS extensionsFuzzy COPRASFuzzy 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.Open the card →
COPRAS extensionsFermatean Fuzzy COPRASThe 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.Open the card →
COPRAS extensionsInterval-valued intuitionistic fuzzy COPRASInterval-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.Open the card →
COPRAS extensionsInterval-valued intuitionistic fuzzy COPRASInterval-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.Open the card →
MARCOS extensionsFuzzy MARCOSThis 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.Open the card →
MARCOS extensionsComplex Fuzzy MARCOSThe 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.Open the card →
MARCOS extensionsFermatean Fuzzy MARCOSThe 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.Open the card →
MARCOS extensionsInterval-valued intuitionistic fuzzy MARCOSInterval-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.Open the card →
CODAS extensionsFuzzy CODASFuzzy 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.Open the card →
CODAS extensionsFermatean Fuzzy CODASFermatean 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.Open the card →
CODAS extensionsInterval CODASInterval 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.Open the card →
CODAS extensionsTriangular Intuitionistic Fuzzy CODASThis 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.Open the card →
PROMETHEE extensionsFuzzy PROMETHEEFuzzy 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.Open the card →
PROMETHEE extensionsFermatean Fuzzy PROMETHEEFermatean 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.Open the card →
TODIM extensionsFuzzy TODIMFuzzy 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.Open the card →
TODIM extensionsFermatean Fuzzy TODIMThis 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.Open the card →
TODIM extensionsInterval-valued intuitionistic fuzzy TODIMThe 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.Open the card →
TODIM extensionsInterval-valued intuitionistic fuzzy TODIMThis 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.Open the card →
WASPAS extensionsFuzzy WASPASThis 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.Open the card →
WASPAS extensionsCubic fuzzy WASPASThis 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.Open the card →
WASPAS extensionsFermatean Fuzzy WASPASThis 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.Open the card →
WASPAS extensionsInterval-valued intuitionistic fuzzy WASPASThe 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.Open the card →
ARAS extensionsFuzzy ARASFuzzy 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.Open the card →
ARAS extensionsFermatean fuzzy ARASFermatean 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.Open the card →
ARAS extensionsInterval-valued intuitionistic fuzzy ARASInterval-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.Open the card →
ARAS extensionsInterval-valued intuitionistic fuzzy ARASThe 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.Open the card →
ELECTRE extensionsFuzzy ELECTRE IFuzzy 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.Open the card →
ELECTRE extensionsFuzzy ELECTRE IIThis 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.Open the card →
ELECTRE extensionsFuzzy ELECTRE IIIThis 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.Open the card →
MABAC extensionsFuzzy MABACFuzzy 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.Open the card →
MABAC extensionsFermatean Fuzzy MABACFermatean 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.Open the card →
MABAC extensionsInterval-valued intuitionistic fuzzy MABACThis 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.Open the card →
MOORA extensionsFuzzy MOORAFuzzy 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.Open the card →
MOORA extensionsFermatean Fuzzy MOORAThe 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.Open the card →
MOORA extensionsInterval-valued intuitionistic fuzzy MOORAInterval-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.Open the card →
GRA extensionsFermatean Fuzzy GRAFermatean 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.Open the card →
GRA extensionsScenario fuzzy GRAThis 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.Open the card →
DEA extensionsFuzzy FMEA DEAThis 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.Open the card →
CoCoSo extensionsFuzzy CoCoSoFuzzy 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.Open the card →
CoCoSo extensionsFermatean fuzzy CoCoSoFermatean 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.Open the card →
MULTIMOORA extensionsFuzzy MULTIMOORAFuzzy 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.Open the card →
WPM extensionsFuzzy WPMFuzzy 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.Open the card →
WPM extensionsFermatean Fuzzy WPMFermatean 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.Open the card →
SPOTIS extensionsFuzzy SPOTISFuzzy 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.Open the card →
AROMAN extensionsFuzzy AROMANFuzzy 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.Open the card →
DNMA extensionsFuzzy DNMAFuzzy 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.Open the card →
MAUT extensionsFuzzy MAUTFuzzy 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.Open the card →
PSI extensionsFuzzy PSIFuzzy 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.Open the card →
RAFSI extensionsFuzzy RAFSIFuzzy 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.Open the card →
RAWEC extensionsFuzzy RAWECFuzzy 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.Open the card →
WISP extensionsFuzzy WISPFuzzy 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.Open the card →
DEMATEL extensionsFuzzy DEMATELFuzzy 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.Open the card →
DEMATEL extensionsScenario fuzzy DEMATELThis 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.Open the card →
LMAW extensionsFuzzy LMAWFuzzy 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.Open the card →
MEREC extensionsFuzzy MERECFuzzy 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.Open the card →
MEREC extensionsScenario fuzzy MERECThis 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.Open the card →
OCRA extensionsFuzzy OCRAFuzzy 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.Open the card →
ROV extensionsFuzzy ROVFuzzy 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.Open the card →
SMART extensionsFuzzy SMARTFuzzy 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.Open the card →

Other methods in the library

These methods do not yet have an academy card. Their formulae, steps and source citation live in the library; each link opens the method page directly.

BWM + Z-number + Zero-Sum Game - Best Worst Method weighting with Z-number payoff matrix and game-theoretic ranking2022 ↗
Cubic-EDAS - Cubic Pythagorean Fuzzy EDAS (CuP-EDAS)2023 ↗
Cubic-TOPSIS - Cubic extension of TOPSIS2018 ↗
DHF-COPRAS - Dual Hesitant Fuzzy extension of COPRAS2020 ↗
DHF-EDAS - Dual Hesitant Fuzzy extension of EDAS2023 ↗
DHF-TODIM - Dual Hesitant Fuzzy extension of TODIM2023 ↗
DHF-TOPSIS - Dual Hesitant Fuzzy extension of TOPSIS2020 ↗
DHF-VIKOR - Dual Hesitant Fuzzy extension of VIKOR2025 ↗
HFL-PROMETHEE - Hesitant Fuzzy Linguistic PROMETHEE (Liang-Wang-Zhang 2018)2018 ↗
L2T-EDAS - 2-Tuple Linguistic Neutrosophic EDAS2019 ↗
LPF-CRITIC-EDAS - Linguistic Pythagorean Fuzzy EDAS with CRITIC weighting (Akram-Ramzan-Deveci 2023)2023 ↗
PHF-COPRAS - Probabilistic Hesitant extension of COPRAS2021 ↗
PHF-EDAS - Extended Hesitant Fuzzy Linguistic EDAS (EHFL-EDAS)2018 ↗
PHF-TOPSIS - Probabilistic Hesitant extension of TOPSIS ↗
PHF-VIKOR - Probabilistic Hesitant extension of VIKOR2017 ↗
Rough-MABAC - Rough extension of MABAC2019 ↗
TIF-CODAS - Triangular Intuitionistic Fuzzy Group CODAS (TIFN-CODAS)2020 ↗