Rough sets methodology for sorting problems in presence of multiple attributes and criteria

We consider a sorting (classification) problem in the presence of multiple attributes and criteria, called the MA&C sorting problem. It consists in 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 their domains; however, the domains of attributes are not preference-ordered, while the domains of criteria (scales) are totally ordered by preference relations. Among the attributes we distinguish between qualitative attributes and quantitative attributes. In order to construct a comprehensive preference model that could be used to support the sorting task, we consider preferential information of the decision maker in the form of assignment examples, i.e. exemplary assignments of some reference actions to the decision classes. The preference model 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 three relations together: indiscernibility, similarity and dominance defined on qualitative and quantitative attributes, and on criteria, respectively. The usefulness of this approach is illustrated by an example.