LOCAL-OWA - neighbourhood-adaptive Ordered Weighted Averaging

Overview

V(A^{lo}_i) reflects criterion performance, the local importance of each criterion within the alternative's neighbourhood (range-sensitivity), and the global risk attitude encoded in λ. The score amplifies LOCAL-WLC: an alternative that excels on the criterion that is most locally variable AND most favoured by the order weights (rank-1 with high λ_1) gains a disproportionate boost. Always inspect the local weight table (G.local_weights), the range-ratio table (G.range_ratios), and the ORness scalar to understand what drove the ranking.

Output

locally-adapted, risk-adjusted normalised utility, higher is better

Data

Crisp, complete numeric + neighbourhood assignments

Weights

Needs a weight source

Size

4+ alternatives, 2-8 criteria works best

Used for

Residential quality evaluation, urban vulnerability assessment, land suitability analysis, ecological zoning, GIS-based environmental planning

Fits when / Look elsewhere when

Assumptions to verify

• Neighbourhood partition is meaningful (not arbitrary zone boundaries)
• Each neighbourhood contains at least 2 alternatives
• Range-sensitivity principle holds locally: criteria with wider neighbourhood spread should receive higher local weight
• A single global risk attitude (ORness) is appropriate - if risk attitude must vary spatially, use SOWA
• Global normalisation is appropriate (all alternatives in same measurement context)

Edge cases and pitfalls

• The denominator in F5 is alternative-specific, not neighbourhood-specific. For two alternatives in the same neighbourhood, the denominator can differ if their sort permutations σ_i differ (i.e. if their best criterion differs). This is a subtle but critical implementation point.

• Cross-neighbourhood score comparisons are valid because global normalisation (F1) precedes local weight adaptation. Never apply per-neighbourhood normalisation instead of global.

• Neighbourhood boundary choice affects local weights (r^q_k) and thus amplifies or suppresses the ORness effect. A neighbourhood partition that makes all local ranges equal to global ranges collapses LOCAL-OWA to standard OWA.

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