Methods

TOPSIS ranks alternatives by how far they sit from two hypothetical points built out of the best and worst value on every criterion: the alternative closest to the ideal and furthest from the worst comes out on top.

VIKOR ranks alternatives by weighing their total distance from the ideal together with their distance on the single worst criterion; it looks for a compromise solution that "everyone can accept."

SAW equalises the scale of every criterion, multiplies it by its weight, and sums directly; it is the oldest and plainest member of the multiple-criteria decision methods. The alternative with the highest weighted sum comes out first.

A method that ranks alternatives not by their position relative to the ideal, but by their position relative to the set's own average: an alternative that sits markedly above the average and falls only slightly below it comes out ahead.

A method that ranks alternatives by combining the ratio of the weighted sum of benefit criteria to the weighted sum of cost criteria, and gives a benefit degree expressed as a percentage of the best alternative.

A method that ranks alternatives by comparing each one to both an ideal (best possible) and an anti-ideal (worst possible) reference point, then combines these two ratios into a single utility function.

CODAS ranks alternatives by comparing them against a single worst reference point using two different distance measures. It looks first at straight-line, Euclidean, distance; if alternatives come out very close to one another, it also brings in horizontal-and-vertical, that is city-block, distance.

TODIM carries into multi-criteria ranking a behavioural decision theory in which the decision-maker is assumed to be cautious about gains and disproportionately sensitive to losses. It weighs alternatives pairwise, treating "winning" and "losing" separately.

WASPAS combines two different aggregation logics, the weighted sum and the weighted product, into a single result; it is a ranking method that offsets the weakness of one with the strength of the other.

ARAS measures each alternative by the ratio of benefit it delivers relative to a hypothetical "best" alternative derived from the same table, converting that ratio into a directly interpretable percentage degree of utility.

MABAC ranks alternatives not against an ideal or an average, but against their distance from a hypothetical "border area" built for every criterion. Sitting above the border strengthens an alternative; sitting below it weakens one.

One of the lightest ranking methods to compute, MOORA ranks alternatives by scaling each criterion value against that criterion's total magnitude, then subtracting the sum of the harmful ratios from the sum of the beneficial ratios.

GRA ranks alternatives by a "grey relational grade": how closely each one tracks a hypothetical "reference" alternative that holds the best performance on every criterion.

A method that evaluates alternatives with both an additive and a multiplicative measure of performance, then ranks them by combining these two measures through three different compromise strategies.

A method that ranks alternatives separately from three distinct viewpoints, ratio, distance from the worst case, and full multiplication, then combines those three rankings into a single order through dominance theory.

WPM raises each alternative's ratio on every criterion to a power equal to that criterion's weight, multiplies these together into a single unit-free score, and ranks alternatives on that score.

ELECTRE II does not settle for ELECTRE I's core-set output. It runs the same outranking logic in two directions at once, from the best alternative downward and from the worst upward, and places every alternative in a full order. Where the two directions disagree, it prefers to say "incomparable" rather than force a verdict.

SPOTIS ranks alternatives by their distance to a fixed ideal point. That point is not built from the other alternatives in a given analysis but from "best possible / worst possible" bounds fixed before the analysis begins. The method thereby aims to prevent the ranking from shifting as the alternative set changes, that is, to prevent rank reversal.

AROMAN does not rely on a single form of normalisation. It blends two different normalisations with a mixing coefficient, then combines the benefit and cost totals with a balance parameter to rank the alternatives.

DNMA does not rely on a single aggregation logic (sum alone, or product alone). It scores the same data by three different methods (weighted sum, weighted product, closeness to the ideal), then produces a single combined score by rewarding the consistency of both the scores and the ranks.

MAUT first converts the value on each criterion into its own "utility" scale, then sums these utilities with weights. The result is a single figure for how much total utility an alternative delivers to the decision-maker.

PSI asks for no external criterion weights. It derives them itself from how much the alternatives differ on each criterion, then ranks the alternatives using those weights.

RAFSI maps alternatives onto a single scale interval against fixed ideal and anti-ideal points the decision-maker sets in advance, then ranks them. Because these points are fixed, the ranking does not break when an alternative is added or removed.

RAWEC measures every alternative, on a weighted basis, both by "how close to the best" and "how far from the worst" it sits, then combines these two perspectives into a single comparison index.

WISP scores each alternative through four separate comparison logics, based on both summing and multiplying, and averages these four results into a single ranking.

ARTASI places every criterion column into an "adaptive" interval that widens according to the column's own scale, then scores alternatives jointly on both closeness to the ideal and distance from the anti-ideal.

A method that assesses alternatives through two separate utility ratios, one for how close they sit to the ideal point and one for how far they sit from the worst point, and ranks them by the average of these two ratios.

Compares pairs of alternatives on a fuzzy scale of "how credibly does one outrank the other" and distils these credibility degrees in two directions to derive an order; some pairs may remain incomparable.

LMAW first standardises every cell in a way sensitive to both direction and magnitude, then passes it through a logarithmic transformation. It then sums these values through a weighted, bounded aggregation function to rank the alternatives. Its purpose is to stop extreme values from dragging the ranking to excess.

A method that separately sums the alternatives' relative shortfall on input (cost) criteria and their relative superiority on output (benefit) criteria, then combines the two at a common reference point to produce a ranking.

ROV ranks alternatives by the average of their best-case performance on benefit criteria and their worst-case performance on cost criteria.

SMART places each criterion's worst and best end directly onto a 0-to-1 scale, then sums these using importance weights supplied by the decision-maker; it is a simple multi-attribute rating method.

APLOCO compares alternatives two at a time: it sums how far each alternative leads its rival on each criterion, subtracts how far it trails, and ranks alternatives by the net score that remains.

COBRA ranks alternatives by combining their distance to four separate reference points (best, worst, above-average and below-average), rather than looking at a single ideal point from four different angles.

Before any decision is made, COMET shows the expert not the real alternatives but every possible combination of criterion levels, the "characteristic objects"; once the expert has scored these fictional profiles, the real alternatives are placed onto this ready-made preference map.

Compromise Programming ranks alternatives by how far they fall short of the best achievable value on each criterion; the alternative that falls short the least stands out as the best compromise.

Consensus Reaching treats every criterion in a decision table as a separate judge and measures how consistently an alternative holds its position across those judges.

Criteria Removal takes each criterion behind a ranking out of the table one at a time and checks how much the ranking shifts, revealing how dependent the ranking is on any single criterion.

Cross-Validation removes each alternative behind a ranking from the table in turn and checks whether the relative order of the remaining alternatives holds, measuring how dependent the ranking is on the presence of any single alternative.

ERVD judges every alternative not against an "ideal point" but against a reference (expectation) level the decision-maker has set in advance; it weighs losses below that reference more heavily than gains above it.

When some criteria are measured numerically and others are expressed only as a ranking (first, second, third), EVAMIX combines the two types in a single analysis without converting one into the other.

FDOSM takes each alternative's performance on each criterion directly as an "opinion score," ratios this score against the best value, and combines it with weights to rank the alternatives.

FMEA combines a product or process's possible failure modes into a single risk figure by multiplying scores for occurrence, severity and detectability; the failure with the highest figure is tackled first.

FUCA compares alternatives not by their raw figures but by their rank on every criterion; the alternative with the smallest weighted sum of criterion ranks comes out on top.

The 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.

Goal Programming first sets an attainable target level for every criterion, then compares alternatives by how far they fall short of that target; the alternative that approaches the targets with the least deviation comes out on top.

Grey Projection compares criterion values given as intervals (a lower and an upper bound rather than a single exact number) by projecting them onto the best and worst reference directions; the alternative with the larger projection onto the ideal and the smaller projection onto the worst comes out on top.

The Hellwig method ranks units, without using any externally supplied weight, by their distance from a statistical "development pattern" that it builds out of their own data.

HF-DFT does not compare alternatives at a single instant; it simulates how preference accumulates over time and, at the end of a deliberation period, recommends the alternative that has accumulated the most preference.

HFGPE has every alternative judged not by one central authority but by all the other alternatives; it blends a generous and a strict viewpoint through a single adjustable parameter and ranks alternatives by their average peer score.

IF-DFT does not compare options at a single instant; using intuitionistic fuzzy assessments made up of degrees of support and rejection, it simulates how preference accumulates over time.

IV-PROJECTION ranks alternatives by how large a "projection" each one casts in the direction of the ideal alternative; that projection carries both how closely the alternative resembles the ideal and how large it is in that same direction.

KEMIRA splits the criteria into two meaningful groups, fits each group to the experts' priority rankings, and then ranks the alternatives by summing the two groups' scores.

Rather than asking you for criterion weights, LINMAP asks for your pairwise preferences between alternatives; it then works out for itself the ideal point and the weights most consistent with those preferences, and ranks the alternatives by their distance to that ideal.

LOCAL-OWA assesses alternatives within their own neighbourhoods rather than a single region; it works out which criterion is genuinely discriminating in each neighbourhood, and combines this with order weights that reflect the decision-maker's overall attitude to risk.

Local WLC accepts that the same criterion is not equally important in every region; it recalculates each neighbourhood's criterion weights against that neighbourhood's genuine range of variation, and scores the alternatives accordingly.

LoPM assigns each property its own limit, a floor, a ceiling or a target value, and scores alternatives by how well they meet that limit before summing the scores by weight.

Rather than relying on a single form of scale equalisation, MACONT blends three different normalisations, scores every alternative in two separate ways, one comparing it against an average rival and one looking at its best-worst extremes, then combines these two scores.

MAIRCA measures the gap between what each alternative "theoretically deserves" as a share and what it "actually delivers" in performance, and puts forward the alternative with the smallest gap.

MARA compares every alternative with a hypothetical "ideal alternative" and measures the gap as the area beneath a line segment; the smaller this area, the further ahead the alternative stands.

Rather than producing a single order from a single set of weights, Monte Carlo simulation tries thousands of possible weight sets and counts how often each alternative comes first, second and so on, to show how robust the ranking is.

MOOSRA divides each alternative's total weighted strength on the benefit criteria by its total weighted burden on the cost criteria, and brings forward the alternative with the largest such ratio.

NAIADE converts the gap between two alternatives, when compared, into fuzzy degrees such as "much better," "slightly better" and "no difference"; without asking for weights, it combines these comparisons across every pair to produce an order.

ORESTE is a method that compares alternatives and the importance of criteria not by exact figures but purely by their ranks, producing a single order.

OWA is an aggregation method that weights criterion values not by which criterion they came from but by the rank they occupy within each alternative, letting the decision-maker's optimistic or cautious attitude show up directly in the result.

PAM turns every alternative into a polygon with as many sides as there are criteria, and ranks alternatives by the area that polygon covers.

PHFS-EHVaR resolves the cases PHFS-HVaR cannot distinguish by computing, instead of just an alternative's worst-case boundary, the probability-weighted average of every scenario below that boundary.

PHFS-HVaR is a risk measure that, when an alternative's future is expressed through several possible values and their probability of occurring, finds the worst boundary that stays below a chosen confidence level.

PIV ranks alternatives solely by their distance from the best value attainable on each criterion; unlike TOPSIS, it does not take the worst point as a reference.

PROBID is a ranking method that judges alternatives not by distance to a single ideal point, but by distance to a whole series of hypothetical "rank" points running from best to worst, and to their average.

PROSA-C corrects the balanced score PROMETHEE II produces with a penalty that measures whether an alternative built that score from a single criterion or evenly across all of them; an alternative that shines on one criterion while staying weak on the rest is pulled back.

Proximity-Adjusted WLC does not hold each alternative's criterion weights fixed; instead it redistributes them according to the alternative's geographic location, so that alternatives close to a reference point see the criteria under one set of relative importance, and distant alternatives under another.

QUALIFLEX tries every possible ordering of the alternatives in turn and, by summing how well each criterion agrees with that ordering, selects the ordering with the highest total agreement.

RAM accumulates each alternative's total contribution on benefit and cost criteria separately, then collapses them into a single number by placing cost in a power exponent and benefit in a base value: a high cost shrinks the exponent, a high benefit grows the base.

Rank Reversal Analysis does not compute a ranking method's result once and stop there; it reruns the same method after adding a new candidate to the alternative set or removing one, and counts whether the remaining alternatives' order relative to one another breaks.

RAPS compares two alternatives directly, measures the size of the gap between them, and ranks every alternative by this "how much better" strength against all its rivals.

REGIME compares two alternatives not by the magnitude of their numbers but purely by who is better and who is worse on each criterion, then sums this simple superiority information with the criterion weights to build a ranking.

Rather than assuming "more is always better," RIM defines a target range for every criterion and ranks alternatives by how close they sit to that target range.

Rough-DRSA does not rank alternatives; it sorts them into "certainly good," "certainly bad" and "uncertain" classes using dominance rules learned from past examples, and it shows contradictory examples openly rather than hiding them.

SAPEVO-M aggregates the simple "which is better" judgements that several decision-makers give, for both criteria and alternatives, into a single common ranking.

SECA does not take criterion weights from outside; while ranking the alternatives, it derives the weights too, from the same calculation, out of its own data.

Sensitivity analysis does not rank alternatives itself; it measures how robust a ranking remains once criterion weights are perturbed a little.

SIMUS turns each criterion in turn into an "objective" and solves a linear programming problem; the shares it hands to the alternatives fall out of these repeated solutions.

SMAA does not ask the decision-maker for a single weight; it calculates, as a probability over every possible weight, which alternative comes out first with which weights.

SMAA-2 extends the point where SMAA looks only at "who comes first": it calculates how often each alternative lands in each rank (first, second, last…) and combines these into a single holistic score.

SOWA applies a different risk attitude, depending on the geographic zone alternatives sit in, when ranking them by criterion scores; the same table is assessed optimistically or pessimistically according to its zone.

SPROBID is a lighter-weight form of PROBID; it ranks alternatives not against every reference point in between, but only against the references in the best and worst quartile.

STOCHASTIC-UTA derives a consistent utility function from a reference ranking supplied by the decision-maker, and carries uncertainty in the criterion values through into the result by sampling.

TAXONOMY standardises alternatives on each criterion against their own mean and standard deviation, then converts their distance to a hypothetical "best" reference point into a single measure of development.

UTA observes how the decision-maker ranks a handful of reference alternatives and derives, by linear programming, an additive utility function consistent with that ranking.

UTASTAR takes a ranking the decision-maker has already given for a small group of alternatives, derives a utility function that reproduces that ranking with the least error, and applies that function to the whole list to rank every alternative.

WEBIRA computes two separate ratios for every alternative, how close it is to the ideal and how far it is from the worst case; it ranks alternatives by the weighted sum of the difference between these two ratios.

WEDBA ranks alternatives by their weighted Euclidean distance to two hypothetical points built from the best and worst value on every criterion; the alternative far from the worst and close to the best comes out on top.

Weight sensitivity analysis is a robustness test that computes how much the criterion weights behind a ranking can change, and at what point that change breaks the ranking.

Weighted voting turns the rankings given by several decision-makers or sources into a single shared ranking, using Borda scores weighted by each source's reliability.

WINGS measures, within a system built from components that influence one another, how central each component is and whether it stands mainly as an influencer or as something influenced.

WSM calculates each alternative's score by multiplying its criterion values by their weights and summing them; it is the oldest and simplest of the multi-criteria decision methods.

PROMETHEE II does not compare alternatives one by one against an ideal. Instead it compares them pairwise against each other, grading "how much better" on every criterion with a preference function. Summing these grades into a net flow yields a complete ranking.

It does not rank alternatives; for every pair, it asks together "am I superior on enough criteria" (concordance) and "am I not very poor on any criterion" (discordance), and extracts a "kernel" of alternatives that no other alternative outranks.

PROMETHEE is a family of outranking methods that compare alternatives not against a hypothetical ideal but against each other. It grades "how much better" on every criterion with a preference function, comparing alternatives pairwise, and combines these comparisons into positive and negative flows to yield a partial or a full ranking.

Not a single method but a family of outranking methods. The family establishes the relation "which alternative clearly beats which" through concordance and discordance criteria. Members built on the same core logic produce a choice, a ranking or a sorting, depending on the purpose.

EXPROM I evaluates the difference between two alternatives on two levels, "somewhat better" and "much better, almost beyond dispute", and leaves pairs that cannot be clearly compared unranked rather than forcing them into an order.

EXPROM II evaluates the difference between two alternatives on two levels, "somewhat better" and "much better, almost beyond dispute". Unlike EXPROM I, it reduces every alternative to a single net-flow score and gives a complete ranking.

When 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.

PAMSSEM I compares alternatives pairwise and measures how far one outranks the other in each pair; in some pairs this comparison yields no clear result, and the two alternatives remain incomparable.

PAMSSEM II uses the same concordance and flow calculation as PAMSSEM I, but at the end places every alternative in order by its net flow; it leaves no incomparable pair, always producing a complete ranking.

SIR calculates separately how much each alternative outperforms the others and how much it falls behind them, then combines these two values into a single net score to rank the alternatives.

A subjective weighting method that sets criteria against one another through pairwise comparison, and from those comparisons derives both a weight vector and a consistency measure showing how far the underlying judgements conflict with one another.

A subjective weighting method that weights criteria through a non-linear model built from the comparisons an expert makes against only the most important and the least important criterion, and that asks for comparatively few judgements.

SWARA first orders the criteria by importance, then compares each criterion only with the one immediately above it; it is a subjective weighting method that produces a weight vector from the smallest possible number of judgements.

A subjective weighting method that converts the importance scores given by several experts into criterion weights, weighting each expert by their experience.

DEMATEL resolves the mutual influence between criteria from an influence matrix, separating how much influence each criterion gives from how much it receives, and so divides the criteria into a cause group and an effect group.

AHSPR derives a priority ranking from pairwise comparisons, but it does so not on one shared scale, but on a scale that bends to fit each decision-maker's own attitude to risk.

HFLPR-PRIORITY derives a priority order directly from pairwise comparisons decision-makers give in words ("somewhat good," "very good," and the like), without first trying to make those words consistent.

ANP models the relationship between criteria and alternatives not as a one-way hierarchy but as a network of mutual interactions, and produces weights from the point where that network settles into equilibrium.

B-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.

DANP first measures the mutual influence between criteria with DEMATEL, then carries this influence into ANP's network structure to weight criteria by their power to influence one another.

Delphi collects opinion from experts round by round, without them knowing one another's identity, and shows each round a summary of the previous one to track whether the views are converging on a consensus.

DIBR asks the expert to rank criteria by importance and to state only the share between each pair of consecutive criteria; it then derives the weights from these consecutive shares in a chain.

FUCOM asks the expert to rank the criteria by importance and to state only the importance ratio between successive criteria; it then finds the weights through a calculation that matches these ratios as consistently as possible.

FUCOM-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.

Fuzzy Delphi asks experts not for a single number but for a triangular range in the form "at least, most likely, at most"; it pools the opinion across experts by combining these triangles and reduces them to a single central value that becomes a weight.

Fuzzy 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.

LBWA asks the expert first to select the most important criterion, then to split the remaining criteria into a few levels of importance and give each a small influence score within its level; no pairwise comparison is made between criteria.

MACBETH never asks an expert for a number; it only asks which of the categories "no difference, very weak, weak, moderate, strong, very strong, extreme" the attractiveness gap between two alternatives falls into, and turns these verbal judgements into a consistent numerical scale.

PIPRECIA takes criteria in any order and asks, for each one, a single question: is it more important than the previous criterion, equally important, or less important; unlike SWARA, it does not require the criteria to be pre-ranked by importance.

A subjective weighting method that has an expert arrange cards representing criteria from least to most important, measures the size of an importance gap through blank cards placed between them, and fixes the scale with a single extreme ratio.

A subjective weighting method that assigns weights to criteria from ranking information alone, asking for no numerical comparison at all, and computes them with a closed formula.

A subjective weighting method that takes direct scores from several experts and derives criterion weights from how consistently discriminating each expert's own scoring is.

A subjective weighting method that asks the expert to score, directly out of 100, the benefit of "swinging" each criterion from its worst to its best value, then normalises those scores to produce weights.

A method that derives criterion weights not from expert opinion but from the data itself: the more a criterion separates alternatives from one another, the more weight it receives.

A method that derives criterion weights from the data itself: a criterion earns more weight the more it separates the alternatives and the less it repeats what other criteria already say.

MEREC derives criterion weights by looking at how much the alternatives' overall performance assessment would change if that criterion were removed from the table. The criterion that changes things most when removed receives the most weight.

An objective weighting method that derives criterion weights from both each criterion's own spread and that criterion's relationship with the overall evaluation, by solving a system of non-linear equations.

CILOS derives criterion weights from the data itself by measuring how much choosing the best alternative on one criterion costs you on every other criterion.

FARE starts from a relationship table showing how strongly and in which direction each criterion affects the others, and gives the highest weight to the criterion that influences the rest the most.

FCILOS 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.

Fuzzy 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.

Fuzzy 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.

When 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.

When 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.

When 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.

An objective weighting method that derives a criterion's weight from how unequally the alternatives' shares are distributed on that criterion: where the share is concentrated in a few alternatives the criterion receives a high weight, where the share is spread equally across everyone it receives a low weight.

An objective weighting method that derives criterion weights by using two different objective measures together: how well the data discriminates between alternatives, and the loss that would follow from disregarding a criterion.

Rather than asking an expert for criterion weights, LODECI derives them from the sharpest difference found between alternatives: however far apart at least one pair of alternatives sits on a criterion, that criterion gains a correspondingly greater say in the decision.

LOPCOW derives criterion weight from the spread within the data itself: the more a criterion makes alternatives "lose out" relative to the best, the more weight that criterion gains.

MPSI takes an intermediate value that the Preference Selection Index method uses silently, inside itself, to rank alternatives, and presents it directly as a visible criterion weight.

NMD derives criterion weight from the data's own mean: the further, on average, the alternatives sit from the best value on a criterion, the more weight that criterion gains.

PCA Weighting derives criterion weight from the shared movement between criteria: the more a criterion draws on the few "principal axes" that actually separate the alternatives, the more weight it earns.

Scenario-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.

The plainest objective weighting method there is: it derives a criterion's weight not by asking an expert but from how much the alternatives differ from one another on that criterion.

An objective method that treats the exact midpoint between a criterion's smallest and largest value as its "symmetry point" and derives criterion weights from how far the alternatives spread away from that point.

An objective method that treats each criterion's cumulative values as a zigzag line and derives criterion weight from the ratio of that line's length to its average slope.

DEA is a benchmarking method that compares multiple units of the same kind by how well they convert inputs into outputs. It gives every unit an efficiency score between 0 and 1; it is not a preference-ranking method.

HFEA is a method that, when expert opinions are given as more than one possible score (hesitant), evaluates every option under the weighting most favourable to itself and produces an efficiency score showing whether it is efficient.

HFPE takes the several options HFEA leaves on the efficient frontier and distinguishes them into a single ranking by evaluating each one not only through its own eyes but through the eyes of every other option as well.

HFPEA bounds the free-weighting latitude that HFEA gives each option in its own favour, computing efficiency under weights that also honour a priority order the decision-maker has stated among the criteria.

HF-MaxScore-Portfolio does not pick a single winner; it splits a limited budget across several alternatives in whatever way maximises the total evaluation score.

HF-TRADEOFF-PORT finds a resource allocation across investment options whose returns are expressed as several possible values rather than one (hesitant), balancing return against risk according to the investor's risk type.

Average ranking takes several existing rank lists for the same alternatives and produces a single combined ranking by averaging each alternative's rank numbers.

The Borda count awards every alternative a score based on its position in a set of rank lists, then ranks the alternatives by the sum of these scores.

Dominance theory counts the cases where an alternative is never strictly behind another across all rank lists and is ahead in at least one; where no strict superiority exists, it draws no distinction between alternatives.

The Choquet integral combines criteria not with fixed weights but with an "importance measure" assigned to groups of criteria, so that synergy and redundancy relationships between criteria are taken into account.

Condorcet compares alternatives two at a time and declares the winner to be whichever alternative beats every other alternative in a pairwise comparison; if no such alternative exists, the method says so plainly.

COOK-SEIFORD finds the single assignment that minimises the total gap between each alternative's positions across different ranking sources and a possible target rank.

COPELAND compares every alternative against all its rivals in pairs and builds a complete rank from the net score obtained by subtracting the number of losses from the number of wins.

DODGSON calculates how many adjacent swaps each alternative needs in the rankings to become the majority winner, and declares the alternative requiring the fewest changes the winner.

KEMENY-YOUNG selects, from among all possible complete rankings, the single ranking that falls into the least total disagreement with every ranking source combined.

Median ranking collapses several separate rankings produced for the same alternative set into a single order, by looking at each alternative's median position across those rankings.

MPF-DOMBI-WA combines an alternative's m-polar fuzzy assessments across several criteria into a single summary assessment using the Dombi operator, and ranks alternatives by this value.

Nanson's method eliminates, in every round, whichever alternatives fall below the mean score and rescores those that remain; it repeats these elimination rounds until a single alternative is left.

PIF-DOMBI combines an alternative's positive, neutral and negative three-way assessments across several criteria into a single summary assessment using the Dombi operator, and ranks alternatives by this value.

RAT selects one of the alternatives as a reference and combines, into a single number, how far every other alternative sits ahead of or behind that reference across the rankings produced by different methods.

The Schulze method compares alternatives pairwise and finds the strongest indirect path of superiority between every pair, producing a single order that is consistent with those pairwise comparisons.

WAM multiplies each criterion's score by its own weight and sums the products, reducing the alternatives to a single figure; it strikes a perfectly linear balance among criteria, favouring none over another.

The Bonferroni mean pairs up criteria two at a time and averages the product of each pair, so that a weakness on one criterion overlapping with a weakness on another is penalised more heavily than a weakness standing alone.

The Heronian mean pairs criteria off two by two, including a criterion with itself, and averages the product of each pair; it follows a logic close to the Bonferroni mean, but also brings each criterion's own square into the calculation, which makes it slightly more tolerant of extremes than the Bonferroni mean.

The power mean generates an entire family of averages, from the harmonic mean through the geometric and arithmetic means and beyond, from a single formula by varying one power parameter; the result grows as the parameter grows.

WGM raises each criterion score to the power of its own weight and multiplies the results; an alternative that scores very low on a single criterion is punished severely, whatever its performance elsewhere.

WHM takes the reciprocal of each criterion score, averages those reciprocals with weights, then takes the reciprocal of that average; it is the most punishing aggregation form in the family, weighing a low score far more heavily than the others.

The Einstein t-norm is a parameter-free combination operation that reduces two fuzzy assessments to a single degree using a rule slightly more cautious than the algebraic product.

The Frank t-norm is an exponential family of combination rules that reduces two fuzzy assessments to a single degree with a tightness set by a parameter s.

The Hamacher t-norm is a product-based family of combination rules that reduces two fuzzy assessments to a single degree with a tightness set by a parameter γ.

The Schweizer-Sklar t-norm is a family of combination rules built on power functions that reduces two fuzzy assessments to a single degree with a tightness set by a parameter p.

It redraws your set of alternatives, with replacement, many times over, rebuilds the ranking from scratch on every draw, and shows how much an alternative's rank depends on that randomness.

A coefficient that compares two rankings pair by pair, reduces the difference between concordant and discordant pairs to a single figure, and measures how closely two rankings coincide.

A method that reduces how closely the rankings given by three or more rankers (experts, methods, criteria) resemble one another to a single concordance coefficient between zero and one.

A method that measures whether small changes in criterion weights overturn a ranking's winner; it does not produce a ranking itself, it says how robust an already-produced ranking is.

A screening method that sifts through a large number of factors influencing a decision result to sort out which ones genuinely matter and whether each affects the result in a plain or a tangled way, using only a small number of trials.

A sensitivity method that divides how much of the variability in a decision result comes from which factor into shares that add up to a hundred per cent, separating out whether the factors act alone or together.

A method that measures how alike two separate rankings are with a single number: plus one means perfect agreement, minus one means perfect disagreement, and zero means no relationship at all.

A consistency indicator that measures, through the geometric mean, how consistent a pairwise comparison matrix is (for instance, the importance judgements between criteria in AHP) in a single number.

A consistency indicator that calculates a pairwise comparison matrix's consistency along lines similar to Saaty's classical eigenvalue method, but through the harmonic mean, giving a more cautious result.

The Koczkodaj inconsistency index finds the most contradictory triad in a pairwise comparison table and reports the size of that contradiction as a single number.

ISM is a structural analysis method that collects the "which factor affects which" relationship among a group of factors from a panel of experts and separates them into levels, drawing a hierarchy from root cause to outcome.

This method scales every criterion column by dividing it by its own best value; for a benefit criterion the column's reference point is its largest value, and for a cost criterion its smallest value, so that the best alternative on that criterion always receives exactly 1 point.

This method rescales every criterion column by dividing it by its own total: each alternative receives a share showing how much of that column's combined performance falls to it, and every column sums to exactly 1.

This method rescales every column by dividing each cell's natural logarithm by the sum of the logarithms in that column; this preserves the proportional difference between large values while reducing the dominance of the absolute magnitude gap.

This method places every criterion column between 0 and 1 according to the range between the worst and best value in that column; the column's best value always scores 1, its worst always scores 0.

Vector normalisation is a preparatory step that divides every column of a decision table by its own Euclidean length, making all criteria unit-free and comparable.

Vector (L2) normalisation is DecisionMind's second record of the same classical preparation step that divides every column of a decision table by its own Euclidean length, making criteria unit-free and comparable.

Z-score normalisation is a preparatory step that scales every column of a decision table against its own mean and standard deviation, converting each measure into a unit-free number expressing "how many standard deviations from the mean."

Chebyshev distance is a distance measure that gauges the distance between two alternatives not by the sum of all criteria but solely by the single largest criterion difference.

Euclidean distance reduces the overall difference between two alternatives to a single straight-line length, by squaring the difference on each criterion, summing the squares and taking the square root.

Hamming distance compares two equal-length sequences and counts only how many positions differ outright; it takes no interest in the size of the difference.

Manhattan distance measures the difference between two alternatives by summing the absolute deviation on each criterion one by one; a large deviation on one criterion does not overshadow the others.

Minkowski distance is a general distance family tuned by a single number p; as p grows, the weight of the single worst criterion increases, and as it shrinks, the deviation is shared equally across criteria.

Mahalanobis distance measures how far apart two points are while taking the relationship (correlation) between criteria into account; the same raw gap can come out small or large depending on whether it fits the criteria's usual pattern of moving together.

Alpha-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.

The 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.

Centroid 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.

This 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.

MOM 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.

The score function produces a single crisp figure by subtracting an intuitionistic fuzzy number's degree of non-membership from its degree of membership; where two evaluations come out equal, a degree of accuracy steps in to resolve the difference.

Type 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.