Fuzzy Extension of the Rough Set Approach to Multicriteria and Multiattribute Sorting

We consider a sorting (classification) problem in the presence of multiple attributes and criteria, called MA&C sorting problem. It concerns an assignment of some actions to some pre-defined and preference-ordered decision classes. The actions are described by a finite set of attributes and criteria. Both, attributes and criteria take values from corresponding domains, however, the domains of attributes are not preference-ordered, while the domains of criteria (scales) are totally ordered by preference relations. In order to construct a comprehensive preference model that could be used to support the sorting task, we are considering a preferential information of the decision maker (DM) in the form of assignment examples, i.e. exemplary assignments of some reference actions to the decision classes. The preference model being inferred from these examples is a set of “if..., then...” decision rules. The rules are derived from rough approximations of decision classes made up of reference actions. They satisfy conditions of completeness and dominance, and manage with possible ambiguity (inconsistencies) in the set of examples. Our idea of rough approximations involves two relations together: similarity, being a generalization of classic indiscernibility relation defined on attributes, and dominance relation defined on criteria. In this paper, we propose a fuzzy extension of the rough set approach to MA&C sorting problem.