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Ranking
SOWA - Spatial Ordered Weighted Averaging
Zone-stratified OWA - order weights λ_k vary per spatial zone, encoding spatially heterogeneous risk attitudes (ORness) while criterion weights w_k remain global
Makropoulos, C. K., Butler, D.2006doi:10.1016/j.envsoft.2004.10.010 ↗
Overview
V(A^s_i) reflects both criterion performance and the spatial risk attitude of the zone the alternative belongs to. An alternative with extreme values (very high on its best criterion, very low on its worst) will be strongly penalised if it lies in a pessimistic zone (low ORness) and strongly rewarded if it lies in an optimistic zone (high ORness). Always inspect the ORness map (output G.orness_per_zone) and the rank-shift chart (H3) to understand how zone assignments are driving the result. The zone_order_weights assignment is the key modelling decision - it embeds a spatial theory of risk.
- Output
- zone-adjusted normalised utility, higher is better
- Data
- Crisp, complete numeric (value-scaled) + zone assignments + zone order weights
- Weights
- Needs a weight source
- Size
- 2+ alternatives, 2-8 criteria works best
- Used for
- Urban water management, flood risk assessment, environmental zoning, land use suitability, GIS-based infrastructure planning
Fits when / Look elsewhere when
Fits when
- •Explicitly models spatially heterogeneous risk attitudes through zone-specific ORness
- •Inherits OWA's full ORness-trade-off flexibility within each zone
- •Reduces to standard OWA (one zone) or WLC (uniform λ=1/n) - no discontinuity
- •Counterfactual scores (what-if zone reassignment) are computationally trivial and illustrative
Assumptions to verify
- Zone boundaries are meaningful and justified (e.g. hazard zones, administrative districts)
- Each zone's λ vector correctly encodes the spatial risk attitude of that region
- Criterion weights w_k are globally applicable (same importance across all zones)
- Value-scaling to [0,1] is appropriate before aggregation
Limitations
- •Zone_order_weights are difficult to elicit - requires domain expert knowledge of spatial risk attitudes
- •Results are sensitive to zone boundary definition
- •Alternatives with extreme criterion profiles (high best, low worst) are most affected by zone ORness - this can appear counter-intuitive
- •Spatial heterogeneity of risk attitudes may be better modelled continuously (e.g. distance-decay ORness) rather than discretely
Edge cases and pitfalls
Zone boundary design is a modelling choice with large consequences. Moving one alternative from a pessimistic to an optimistic zone can flip its ranking substantially. Perform sensitivity analysis over zone assignments.
The zone order-weight vector (λ^z) must be elicited from domain knowledge, not set arbitrarily. A common misuse is assigning the same λ to all zones - this collapses SOWA to standard OWA and defeats the spatial extension.
The denominator in F4 is alternative-specific (depends on the sort permutation σ_i). Do not use a fixed denominator per zone - it changes with each alternative's criterion ordering.
How to cite
Makropoulos, C. K.; Butler, D. (2006). Spatial ordered weighted averaging: incorporating spatially variable attitude towards risk in spatial multi-criteria decision-making. Environmental Modelling & Software. https://doi.org/10.1016/j.envsoft.2004.10.010
System ID, as it appears in reports and the API
SOWA