This paper advances the theoretical foundations and the methodology of spatial decision analysis in which multi-attribute consequences of decision alternatives vary over a spatial region. First, we introduce necessary and sufficient conditions for representing the decision maker's preferences among such decision alternatives with an additive spatial value function. This new axiomatization allows for the representation of preferences when the spatial region consists of an infinite number of locations, which is often the case in practical applications. Moreover, we show that spatial value functions suggested in the existing literature can be interpreted as special cases of our additive spatial value function. Second, motivated by the high effort required to elicit preferences in spatial decision problems, we develop a method for utilizing the additive spatial value function with incomplete preference information about spatial weights describing the importance of locations and attribute weights. This method provides defensible decision recommendations through the use of dominance concepts and decision rules. The applicability of the developed value function and analysis method is illustrated with a real-life application in air defense planning.
- Decision analysis
- Incomplete preference information
- Military applications
- Multi-attribute value theory
- Spatial decision analysis