Random generation of capacities and its application in comprehensive decision aiding

Abstract

The capacities and the Choquet integral are powerful tools to represent decision problems with dependencies and aggregate correlated decision criteria. Random generation of suitable capacities is a vital and challenging task in this decision model because of an exponential number of the involved parameters as well as the associated monotonicity restrictions. In this paper we present various approaches to representing decision makers’ preferences on aggregation through linear constraints, random generation of capacities from the selected polytope, testing the uniformity of the resulting distribution, and constructing the dominance relations between the alternatives, which are subsequently used to get the most credible ranking of the alternatives.