LOCAL-OWA (neighbourhood-sensitive Ordered Weighted Average)

LOCAL-OWA is a ranking method for situations where alternatives sit on a map or within a regional structure, and the same criterion is not equally important everywhere. Its output is a score between 0 and 1 for every alternative and a rank built on that score. Malczewski and Liu proposed it in 2014 for GIS-based multi-criteria analysis; it is a neighbourhood-sensitive extension of the standard Ordered Weighted Average (OWA) method.

Classical weighted-sum methods, such as WLC, give each criterion a single fixed weight across the whole region. LOCAL-OWA questions this assumption: a criterion's importance actually depends on how much DIFFERENCE it makes in that particular region. In a neighbourhood where every alternative takes almost the same value on a criterion, that criterion fails to distinguish the alternatives; but if the same criterion varies widely in another neighbourhood, it becomes decisive there. This idea is known as the range-sensitivity principle (Keeney, 1992): the wider a criterion's local range of variation, the greater the weight that criterion should carry in that neighbourhood.

LOCAL-OWA combines these local weights with the Ordered Weighted Average idea proposed by Yager (1988). In OWA, weight is not attached to a criterion but to the RANK of an alternative's value on that criterion (best, second-best, third-best); this lets the decision-maker express whether they are "optimistic or pessimistic", that is, whether they weight the best criteria most heavily or prefer a balanced profile instead. LOCAL-OWA combines these two ideas by holding the order weights fixed while letting the underlying criterion weights vary by neighbourhood: the decision-maker's overall risk attitude stays the same everywhere, but which criterion feeds that attitude changes with local context.

The philosophical consequence is that LOCAL-OWA is both compensatory and context-sensitive. A weakness on one criterion can be offset by another criterion (compensation), but the weights governing this offsetting change according to the neighbourhood an alternative sits in (context-sensitivity). The decision-maker does not build a single global preference but a locally adapted, yet still consistent, preference structure.

The method proceeds through seven steps.

First, general scale equalisation. Every criterion is scaled to between 0 and 1 across ALL alternatives, without any distinction by neighbourhood. It is essential that this step is always done globally rather than by neighbourhood, or else scores from different neighbourhoods become incomparable.

Second, computing the global and local ranges. For every criterion, the global range across all alternatives (the largest value minus the smallest) and the local range within each neighbourhood are calculated separately. The ratio of the local range to the global range shows how discriminating that criterion is within that neighbourhood.

Third, building the local criterion weights. For each neighbourhood, the criterion's global weight is multiplied by this ratio and rescaled. A criterion that barely varies locally receives a low local weight; a criterion that varies widely within a neighbourhood receives a high local weight.

Fourth, ordering and matching. Each alternative's scaled criterion values are sorted from largest to smallest within that alternative. Which criterion corresponds to each position in this order (first, second) is recorded; this matching can differ from alternative to alternative, because each alternative may be strongest on a different criterion.

Fifth, ordered weighted aggregation. The decision-maker's position-dependent order weights (more to the first position, less to the last, for instance) are combined with the local criterion weights found in the third step. The result is a score between 0 and 1.

Sixth, summarising the overall risk attitude. Two figures are calculated from the order weights, summarising how optimistic (weighting the best criterion) or how balancing the decision-maker is across criteria. These are single, fixed figures for the whole analysis.

Seventh, ranking. All alternatives, even if they come from different neighbourhoods, are ranked from the highest to the lowest by the same score. This comparison is valid because the scale equalisation in the first step was always done globally.

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

The score shows how strong an alternative is on the criteria that discriminate within its own neighbourhood, weighted by the decision-maker's overall risk attitude. A score close to 1 means the alternative is strong on the criteria that matter in its own neighbourhood; it does not mean the alternative would be equally good in a different neighbourhood, because which criterion counts as important changes from neighbourhood to neighbourhood.

Two alternatives' scores are comparable even if they come from different neighbourhoods, because the scale equalisation is always done across the whole data set. But the same score gap can arise from two different causes: either the alternative's raw values are genuinely better, or the criteria in that alternative's neighbourhood are more strongly discriminating. The report must not conflate the two. Also, whether the order weights were chosen optimistically or pessimistically can strongly change the result depending on which criterion an alternative is strong on; the ranking can change if a different risk attitude is chosen with the same neighbourhood structure.

Thus instead of writing:

"This alternative is the best alternative"

the report should read:

"This alternative has achieved the highest score on the criteria that discriminate within its own neighbourhood, under this risk attitude; the ranking may change if the neighbourhood boundaries or the risk attitude change"

LOCAL-OWA works with crisp numerical data. DecisionMind holds no extension of this method; it is offered only in its base form, working solely with crisp numbers.

You need a decision table; a grouping showing which neighbourhood each alternative belongs to; direction information for every criterion; global weights for the criteria; and order weights reflecting the decision-maker's risk attitude. The neighbourhood grouping is a decision made from outside, by the analyst or by a geographic or administrative structure; the method does not produce this grouping, it only uses it. Every neighbourhood must contain at least two alternatives, or the local range cannot be calculated. A recommended size is at least four alternatives and between two and eight criteria; typical fields of application are housing-quality assessment, urban vulnerability analysis and land-suitability studies.

LOCAL-OWA is a suitable choice if your alternatives can be grouped into a geographic or structural neighbourhood, you believe the same criterion discriminates to different degrees across different regions, and you hold a single global risk attitude (equally optimistic or balancing across the whole region). It is used in GIS-based studies such as urban planning, ecological zoning and environmental monitoring.

LOCAL-OWA is unsuitable if your neighbourhood boundaries are arbitrary or unjustified, if any neighbourhood has fewer than two alternatives, or if you believe the risk attitude itself ought to vary from region to region; in that case, methods that also localise the risk attitude, such as SOWA, should be considered. If a single fixed set of weights suffices across the whole region (criterion importance does not shift by location), standard OWA is enough and local adaptation is unnecessary.

Criterion importance varies by region, risk attitude fixed → LOCAL-OWA

Both criterion importance and risk attitude vary by region → SOWA

Criterion importance is the same everywhere → standard OWA

Direct criterion weighting is sufficient, no order weights, no neighbourhoods → WLC

LOCAL-OWA's most important strength is that it abandons the assumption that "every criterion is equally important everywhere", an assumption that rarely holds in real geographic and institutional data. It computes, transparently and traceably, which criterion is discriminating where, through the range-sensitivity principle (Keeney, 1992). Because it combines global scale equalisation with standard OWA's order weights, it lets the decision-maker express their risk attitude (optimistic, pessimistic, balancing) in one consistent place across the whole analysis; this keeps the model interpretable even as the number of neighbourhoods grows and the model becomes more complex.

Its limitations largely concern the choice of neighbourhood. How the neighbourhood boundaries are drawn directly determines the local weights; when boundaries change, the strength of the ORness effect can rise or fall (Malczewski and Liu, 2014). If all local ranges equal the global range (neighbourhood distinction makes no difference at all), the method reduces automatically to standard OWA; in this case the neighbourhood distinction has contributed nothing, and this needs to be noticed. Another limitation is that each alternative is matched to a different local weight set according to its own criterion ordering; this means even two alternatives in the same neighbourhood can have a different internal structure to their aggregation, a subtle but important point in practice. Finally, the assumption of a single global risk attitude falls short where the risk attitude itself needs to vary regionally; SOWA was developed for this case.

The most common mistake is performing scale equalisation by neighbourhood rather than globally; this makes scores from different neighbourhoods incomparable and breaks the method's core assumption. A second mistake is drawing neighbourhood boundaries according to administrative or arbitrary divisions without looking at the data, and not reporting this choice. A third is leaving only one alternative in a neighbourhood; the local range comes out at zero and every criterion in that neighbourhood appears non-discriminating. A fourth is presenting a single result as definitive without showing how strongly the order weights (the risk attitude) affect it. A fifth is giving only the final ranking without explaining, in the report, why the local weights differ from neighbourhood to neighbourhood, that is, which criterion varies more in which region.

The governing principle is this:

A LOCAL-OWA result is a score computed on a global scale but weighted according to local ranges; the neighbourhood boundaries and the risk-attitude choices must be stated clearly in the report, or the reason for the ranking cannot be understood.