Proximity-Adjusted WLC - spatially explicit weighted linear combination

Overview

V(A^p_i) reflects both criterion performance and spatial proximity to the reference location. An alternative far from the reference will have low proximity-adjusted weights - its criterion values count for very little in the aggregation even if they are high. This is by design: the method explicitly encodes a spatial preference bias toward the reference location. Always inspect the proximity-adjusted weight matrix (output G.proximity_adjusted_weights) to understand how spatial position is affecting the result.

Output

spatially-adjusted utility, higher is better

Data

Crisp, complete numeric + spatial coordinates

Weights

Needs a weight source

Size

2+ alternatives, 2-8 criteria works best

Used for

Residential quality evaluation, site selection, urban planning, GIS-based suitability analysis

Fits when / Look elsewhere when

Assumptions to verify

• A meaningful reference location can be justified (e.g. city centre, service hub, decision maker's location)
• Euclidean distance is an appropriate proximity measure (flat terrain, no barriers)
• Criterion values are positive (linear-max normalisation requirement)
• Decision maker accepts that spatial proximity modifies effective criterion importance

Edge cases and pitfalls

• Rank reversal by design: adding a new alternative changes Σ d^s_{ij}, redistributing all proximity-adjusted weights. Scores of existing alternatives shift. This is not a bug - it reflects the spatial redistribution principle.

• Reference location choice is critical. Moving the reference even slightly changes all d^s_{ij} values and can invert rankings. Perform sensitivity analysis over reference location if uncertain.

• The standardised distance d^s = 1 goes to the nearest alternative(s), not to an alternative at a fixed location. If the nearest alternative changes, all d^s values rescale.

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