Rough approximation of a preference relation by a multi-attribute stochastic dominance for determinist and stochastic evaluation problems

Let A be a set of actions evaluated by a set of attributes. Two kinds of evaluations will be considered in this paper: determinist or stochastic in relation to each attribute. The multi-attribute stochastic dominance (MSDr) for a reduced number of attributes will be suggested to model the preferences in this kind of problem. The case of mixed data, where we have the attributes of different natures is not well known in the literature, although it is essential from a practical point of view. To apply the MSD, the subset R of attributes from which approximation of the global preference is valid should be known. The theory of Rough Sets gives us an answer on this issue allowing us to determine a minimal subset of attributes that enables the same classification of objects as the whole set of attributes. Tn our approach these objects are pairs of actions. In order to represent preferential information we shall use a pairwise comparison table. This table is built fur subset B subset ofA described by stochastic dominance (SD) relations for particular attributes and a total order for the decision attribute given by the decision maker (DM). Using a Rough Set approach to 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 Set approach of looking for the reduction or the set of attributes gives us the possibility of operating with MSDr. (C) 2001 Elsevier Science B.V. All rights reserved.