Rough Sets on Fuzzy Approximation Spaces and Intuitionistic Fuzzy Approximation Spaces

Abstract

In the past few years the original concept of rough sets, as introduced by Pawlak [26] has been extended in many different directions. Some of these extensions are obtained by relaxing the requirement of the basic relations to be equivalence relations [14,15,31,32,34,35,37,38].That is by dropping the requirement of transitivity or symmetry. One such approach is to replace the equivalence relations by fuzzy proximity relations. The notions of rough sets thus generated are called rough sets defined upon fuzzy approximation spaces [14,15]. A generalization of this is obtained by taking intuitionistic fuzzy proximity relations instead of equivalence relations, called rough sets on intuitionistic fuzzy approximation spaces [37,38]. In this chapter we shall be concentrating on the study of these two notions of rough sets. It is our objective to define these types of rough sets along with related concepts and establish their properties which are parallel to those of basic rough sets. Several real life applications shall be considered in the sequel to illustrate the power and necessity of these generalized models of rough sets in the representation and study of imperfect knowledge.