Rough Approximation of a Preference Relation in a Pairwise Comparison Table

Abstract

A methodology for using rough sets for preference modelling in multi-criteria decision problems is presented. It operates on a pairwise comparison table (PCT), i.e. an information table whose objects are pairs of actions instead of single actions, and whose entries are binary relations (graded preference relations) instead of attribute values. PCT is a specific information table and, therefore, all the concepts of the rough set analysis can be adapted to it. However, the classical rough set approximations based on indiscernibility relation do not consider the ordinal properties of the criteria in a decision problem. To deal with these properties, a rough approximation based on graded dominance relations has been recently proposed. The decision rules obtained from these rough approximations can be used to obtain a recommendation in different multi-criteria decision problems. The methodology is illustrated by an example which compares the results obtained when using the rough approximation by indiscernibility relation and the rough approximation by graded dominance relations, respectively.KeywordsRough set theoryPairwise comparison tableMulti-criteria decision problemsPreference modelingDecision rules.