Construction of a Bi-capacity and Its Utility Functions without any Commensurability Assumption in Multi-criteria Decision Making

Abstract

We consider a multi-criteria evaluation function U defined over a Cartesian product of attributes. We assume that U is written as the combination of an aggregation function and one value function over each attribute. The aggregation function is assumed to be a Choquet integral w.r.t. an unknown bi-capacity. The problem we wish to address in this paper is the following one: if U is known, can we construct both the value functions and the bi-capacity? The approaches that have been developed so far in the literature to answer this question in an analytical way assume some commensurability hypothesis. We propose in this paper a method to construct the value functions and the capacity without any commensurability assumption. Moreover, we show that the construction of the value functions is unique up to an affine transformation. © Springer International Publishing Switzerland 2014.