OWA (Ordered Weighted Averaging)

OWA is a ranking method for when you hold a decision table and want the decision-maker's risk attitude (cautious, optimistic or balanced) to shape the aggregation of criteria explicitly. Its output is a suitability score between 0 and 1 for every alternative, together with the rank that score produces. Yager proposed it in 1988; it has found its widest use in geographic-information-system (GIS) land-suitability analysis, a field where the choice between "every criterion must be satisfied" and "some criteria are enough" is argued over constantly.

Most aggregation methods pick one of two extremes: either "the weakest criterion decides" (AND logic, pessimistic) or "the strongest criterion is enough" (OR logic, optimistic). OWA's idea is that these two extremes are really the two edges of a single continuum, and the decision-maker should be able to choose any point along it. To do this, OWA weights criterion values not by which criterion produced them but by the rank they hold within that alternative, from highest to lowest. The highest value always receives the same positional weight, whichever criterion happens to supply it.

This idea carries a philosophical consequence: OWA is both compensatory and tunable. If positional weights are spread evenly, OWA collapses into a plain weighted average; loading weight onto the highest value produces an optimistic attitude, close to OR; loading weight onto the lowest value produces a cautious attitude, close to AND. The method answers the question "which logic are we using" not from the data but from the positional weights the decision-maker has chosen.

The method proceeds through five steps.

First, scale equalisation. Every criterion is mapped onto the 0–1 range: "more is better" criteria are divided by their own largest value, "less is better" criteria are inverted. If your data is already a suitability score on this scale, drawn from expert assessment or a prior analysis, this step can be skipped, but only because the data was genuinely defined that way, not because raw figures happen to look as if they already sit between 0 and 1.

Second, ordering. OWA sorts each alternative's own scaled values, however many criteria there are, from largest to smallest. Criterion identity is set aside at this point; what matters now is position: highest value, second-highest and so on. Each position keeps a record of which criterion supplied it, so the criterion's own weight travels together with its position.

Third, position-weighted summation. The decision-maker has already fixed a positional weight sequence (λ): how much weight the highest value receives, how much the second receives, and so on. OWA multiplies the ordered values by both this positional weight and the criterion's own weight, sums the products, and scales the total by the sum of the same products.

Fourth, optional diagnostics. OWA can produce two further indicators: orness (where the chosen positional weights fall on the optimistic-pessimistic axis) and the preferred degree of compensation. These are computed from the chosen positional weights, not from the data, and summarise the decision-maker's attitude.

Fifth, ranking. Alternatives are ranked from the highest score to the lowest.

The formulas behind each step, the intermediate tables and the citation formats are given on the DecisionMind method page; this card carries no formulas.

The score is a suitability indicator computed with the positional weights chosen for this particular analysis; it cannot be compared against a different positional-weight choice or a different analysis. A score of 0.62 does not mean "sixty-two per cent suitable"; it only shows where this alternative stands relative to the others under the chosen risk attitude.

The orness indicator must be read alongside it. When orness is close to 0.5, the aggregation is balanced and OWA approaches a plain weighted average (WLC/SAW). As orness moves towards 1, the method turns optimistic and the strongest criterion gains weight. As orness moves towards 0, the method turns cautious and the weakest criterion becomes decisive. An OWA score reported without its orness value is a score whose governing attitude is unstated.

Thus instead of writing:

"OWA showed that this site is the most suitable"

the report should read:

"With the chosen positional weights (orness = 0.50, a balanced attitude), this site comes out ahead of the others"

OWA works with crisp data. DecisionMind holds no extension of this base method.

You need: alternatives in rows, criteria in columns, one number per cell; direction information for every criterion; criterion weights summing to 1; and a positional weight sequence (λ) also summing to 1. λ can be fixed by hand towards a preference such as "every position equally important" (OWA = WLC), "weight the best" (optimistic) or "weight the worst" (cautious); Yager's quantifier-guided approach also lets λ be derived from natural-language phrases such as "most criteria" or "at least half". Benefit criteria must hold positive values, because scaling divides by the largest value. A minimum of two alternatives and two criteria is required; three to twelve criteria work comfortably.

OWA is a sound choice if you want the decision-maker's risk attitude (cautious, balanced, optimistic) reflected explicitly when criteria are combined. Its typical territory includes land-use suitability analysis, site selection, environmental assessment and urban planning; this attitude adjustment is a frequently sought feature in GIS-based studies.

It should not be used where criterion weights are already settled and no positional risk-attitude adjustment is needed; a plain weighted sum (WLC/SAW) is then sufficient and the extra complexity OWA brings is unnecessary. When the number of criteria grows very large, tracking which criterion a positional weight corresponds to also becomes difficult.

Risk attitude (cautious/optimistic/balanced) should show explicitly in the result → OWA

Criterion weights already settled, no need for a risk-attitude adjustment → WLC/SAW

No compromise allowed on one criterion, sub-threshold alternatives must be screened out → screening first, then ranking

Criteria need weights → AHP, BWM, SWARA (subjective); Entropy, CRITIC (objective)

OWA's greatest strength is its flexibility. Changing a single positional weight sequence can turn the same data into a cautious, balanced or optimistic result, which makes sensitivity analysis a natural part of the method. Its exact equivalence to a plain weighted average (WLC/SAW) under equal positional weights means it can always be checked against a baseline. The orness indicator makes the chosen attitude numerical and traceable; the decision-maker can see, as a single figure, how optimistic the analysis has been.

Its limitations stem from its position-based structure. First, positional weights attach to rank rather than to a criterion, so which criterion receives which weight changes from alternative to alternative, and confusing positional weight with criterion weight is a common error. Second, adding a new alternative to the set can shift the positions of the ordered values and so affect other alternatives' scores; the risk of rank reversal seen in TOPSIS applies here too. Third, the choice of positional weights is left largely to the decision-maker; if this choice is not justified, OWA can turn into a subjective tool tuned to produce a desired outcome (Malczewski and Rinner, 2015).

The most common mistake is confusing positional weight with criterion weight. The positional weight given to the highest value always goes to that position, whichever criterion happens to fill it; assuming "the first positional weight always belongs to this criterion" is wrong.

A second mistake is jumping straight to an optimistic or cautious sequence without ever checking the equal-positional-weight baseline; whether OWA under equal weights matches a plain weighted average should be established first. A third is skipping the scaling step (F1) and ordering raw figures directly; a scale that does not reflect the criterion's true preference structure puts the ranking in the wrong place too. A fourth is sharing an OWA result without stating orness, which presents a result whose governing attitude is unknown.

The governing principle is this:

An OWA result is a product of the chosen positional weights (the risk attitude), not of the data alone; if this attitude is not stated explicitly in the report, the result is presented incompletely.