OWA - Ordered Weighted Averaging

Overview

V(A^o_i) ∈ [0,1] after linear-max value scaling. Higher score = more preferred alternative. The score interpretation depends on order weights: with optimistic λ (high ORness), the score rewards alternatives strong on at least one criterion; with pessimistic λ (low ORness), it rewards alternatives performing well across all criteria. The ORness and trade-off statistics printed alongside the ranking reveal which decision strategy was applied.

Output

utility, higher is better

Data

Crisp, complete numeric matrix

Weights

Needs a weight source

Size

2+ alternatives, 3-12 criteria works best

Used for

Land suitability analysis, site selection, Environmental assessment, urban planning, vulnerability analysis

Fits when / Look elsewhere when

Assumptions to verify

• Criteria preferences are independent (additivity/linearity assumption holds)
• Decision maker can articulate risk attitude via order weights (or accept uniform λ = WLC)
• Criterion values are positive and non-zero for all benefit criteria (required by linear-max value function)
• Value function correctly represents criterion preference structure before OWA aggregation

Edge cases and pitfalls

• Order weights are position-based, not criterion-specific: λ_1 always goes to the highest value for each alternative, regardless of which criterion produced it. Confusing order weights with criterion weights is a frequent error.

• Rank reversal risk: adding or removing an alternative changes the sorted value positions and hence the reordered criterion weights u_k, potentially altering scores of other alternatives.

• Equal order weights (λ_k = 1/n) make OWA identical to WLC/SAW - use this as a baseline sanity check before tuning order weights.

• The value function in F1 must reflect the decision maker's true preference structure. Using raw values without scaling can distort the ordering step.

Works with

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