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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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 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.