SOWA (Spatial Ordered Weighted Averaging)

SOWA seeks an answer to the question "should alternatives in the same criterion table be assessed with a single risk attitude, or with a different attitude depending on the zone they sit in?" Its output is a score between 0 and 1 for every alternative and a ranking based on it. The method is used in geographic-information-system (GIS) based multi-criteria decisions: in work such as flood-risk mapping, land-use suitability, and urban water-infrastructure planning, risk perception can differ between zones. Makropoulos and Butler proposed it in 2006; it is a spatial extension of the standard OWA (Ordered Weighted Averaging) family.

Standard OWA sorts criterion values from highest to lowest and weights them by rank. How these weights are distributed is itself a choice of attitude: if weight piles onto the highest value, the method is optimistic and looks at the alternative's strongest side; if it piles onto the lowest value, it is pessimistic and looks at its weakest side. Standard OWA holds this attitude fixed across the whole table. SOWA's difference begins here: it defines its own attitude for every zone.

An analogy makes this clear. Consider two separate assessors; one assesses buildings in a city centre by their best performance, because their infrastructure is strong, while the other assesses a rural area by its worst performance, because its infrastructure is weak. Both assessors can be right, because the zone's own conditions determine the risk attitude. SOWA's philosophical consequence is this: the method is partly compensatory, but the degree of compensation varies from zone to zone. One zone may allow wide compensation between criteria while another allows almost none.

The method proceeds through six steps.

First, scaling the criteria onto the 0-1 range. For a benefit criterion, every value is divided by the column's largest value; for a cost criterion, the column's smallest value is divided by every value. If the data already sits within this range, this step is skipped.

Second, determining the zone attitude. Which zone each alternative belongs to is known in advance. A separate rank-weight list (λ) is defined for every zone, and this list is used to calculate the zone's degree of optimism (ORness). If ORness is close to 1, the zone is optimistic and rewards the best criterion; if close to 0, it is pessimistic and penalises the worst criterion.

Third, ranking the alternative's own criteria. Each alternative's criterion values are sorted from highest to lowest within themselves. Which criterion is best and which is worst for that alternative follows from this; this ordering can differ from alternative to alternative.

Fourth, calculating the regional score. The zone's λ list, the criterion weights, and the alternative's own ranking are combined to produce a normalised score between 0 and 1. This step blends the zone's risk attitude with the alternative's actual performance.

Fifth, regional diagnostics. ORness and the degree of trade-off are calculated for every zone; if the trade-off degree is close to 1, a wide balance is struck between criteria, and if close to 0, almost no balance is struck.

Sixth, 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 SOWA score shows how good an alternative is judged to be under the risk attitude of the zone it sits in. Two alternatives with identical criterion values can receive different scores if they sit in different zones; this is not a calculation error, it follows from the method's definition. A low score does not mean "the alternative is bad," it means "weak when assessed under this zone's risk attitude." Had the same alternative sat in a different zone, its score could have been different.

Thus instead of writing:

"SOWA found A3 to be the worst alternative"

the report should read:

"A3 is the weakest alternative when assessed under the pessimistic risk attitude of the zone it sits in; had the same alternative sat in an optimistic zone, it would have come out best"

SOWA works with crisp data: one number per cell. DecisionMind offers SOWA only in this base form; there is no separate data-type extension (fuzzy, grey, intuitionistic and so on). You need alternatives in rows, criteria in columns, one number per cell; direction information for every criterion; criterion weights summing to 1; a mapping showing which zone each alternative belongs to; and a separate rank-weight list (λ) for every zone. SOWA produces no weights of its own; it takes them from outside. A minimum of two alternatives and two criteria is required; the comfortable range for the number of criteria is two to eight.

SOWA is a suitable choice if your decision problem divides into geographic or administrative zones and there is a justified reason for the risk attitude to differ between them. If the zone boundaries themselves are contested, or if the whole decision is to be assessed with a single risk attitude anyway, SOWA is not needed; a single-attitude method such as standard OWA or TOPSIS is enough. If the same λ list is given to every zone, SOWA already reduces to standard OWA; in that case, using the spatial extension serves no purpose.

Risk attitude varying by zone, a geographic/administrative division exists → SOWA

A single risk attitude applies across the whole table → standard OWA or TOPSIS

Zone boundaries are arbitrary or unjustified → clarify the zone definition first, then consider SOWA

Weights rather than a ranking are needed → AHP, BWM, SWARA (subjective) or Entropy, CRITIC (objective)

SOWA's core strength is its ability to model geographic heterogeneity explicitly. Rather than assessing the same criterion table with a single attitude, it takes each zone's own understanding of risk into account. It brings the extremes of the OWA family (MAX, which looks at the best, MIN, which looks at the worst, and the simple average) together within a single framework, and thanks to the ORness and trade-off-degree diagnostics, every zone's attitude can be shown and justified with a number.

Its limitations stem largely from the zone definition. Zone boundaries are a modelling decision, and this decision itself can be contested; moving an alternative from one zone to another can change the result substantially (Malczewski and Rinner, 2015). Second, if the same λ list is given to every zone, the method reduces to standard OWA and the point of the spatial extension is lost. Third, the method has, since 2006, been applied mainly in GIS-based environmental planning; its track record in other fields is limited.

The most common mistake is giving the same rank-weight list to every zone. This reduces SOWA to standard OWA and loses the spatial risk difference entirely. A second mistake is drawing zone boundaries arbitrarily rather than from data; zone boundaries should rest on a flood map, an administrative boundary, or a similar justification. A third is assuming the score's denominator is a fixed number for the zone. The denominator is recalculated according to each alternative's own criterion ranking; using a fixed number gives a wrong result.

The governing principle is this:

A SOWA result is a product of both the alternative's performance and the risk attitude assigned to the zone it sits in; if the zone assignment changes, so does the result, and the report must show this plainly.