Rough approximation of pairwise comparisons described by multi‐attribute stochastic dominance

Given a finite set A of actions evaluated by a set of attributes, preferential information is considered in the form of a pairwise comparison table including pairs of actions from subset B⊂A described by stochastic dominance relations on particular attributes and a total order on the decision attribute. Using a rough sets approach for the analysis of the subset of preference relations, a set of decision rules is obtained, and these are applied to a set A\B of potential actions. The rough sets approach of looking for the reduction of the set of attributes gives us the possibility of operating on a multi‐attribute stochastic dominance for a reduced number of attributes. Copyright © 1999 John Wiley & Sons, Ltd.     

A characterization of ‘min’ as a procedure for exploiting valued preference relations and related results

This paper is concerned with procedures which transform valued preference relations on a set of alternatives into crisp relations. We present a simple characterization of a procedure that ranks alternatives in decreasing order of their minimal performance. This is done by means of three axioms that are shown to be independent. Among other results, we characterize in a very similar manner a procedure called ‘leximin’ and investigate two families of procedures whose intersection is the ‘min’ procedure.