Knowledge Discovery about Preferences Using the Dominance-Based Rough Set Approach

Abstract

The aim of scientific decision aiding is to give the decision maker a recommendation concerning a set of objects (also called alternatives, solutions, acts, actions, ... ) evaluated from multiple points of view considered relevant for the problem at hand and called attributes (also called features, variables, criteria, ... ). On the other hand, a rational decision maker acts with respect to his/her value system so as to make the best decision. Confrontation of the value system of the decision maker with characteristics of the objects leads to expression of preferences of the decision maker on the set of objects. In order to recommend the most-preferred decisions with respect to classification, choice or ranking, one must identify decision preferences. In this presentation, we review multi-attribute preference models, and we focus on preference discovery from data describing some past decisions of the decision maker. The considered preference model has the form of a set of if..., then... decision rules induced from the data. In case of multi-attribute classification the syntax of rules is: if performance of object a is better (or worse) than given values of some attributes, then a belongs to at least (at most) given class, and in case of multi-attribute choice or ranking: if object a is preferred to object b in at least (at most) given degrees with respect to some attributes, then a is preferred to b in at least (at most) given degree. To structure the data prior to induction of such rules, we use the Dominance-based Rough Set Approach (DRSA). DRSA is a methodology for reasoning about ordinal data, which extends the classical rough set approach by handling background knowledge about ordinal evaluations of objects and about monotonic relationships between these evaluations. We present DRSA to preference discovery in case of multi-attribute classification, choice and ranking, in case of single and multiple decision makers, and in case of decision under uncertainty and time preference. The presentation is mainly based on publications [1,2,3].