Textural approach to generalized rough sets based on relations

Abstract

This paper presents a discussion on rough set theory from the textural point of view. A texturing is a family of subsets of a given universal set U satisfying certain conditions which are generally basic properties of the power set. The suitable morphisms between texture spaces are given by direlations defined as pairs ( r , R ) where r is a relation and R is a corelation. It is observed that the presections are natural generalizations for rough sets; more precisely, if ( r , R ) is a complemented direlation, then the inverse of the relation r (the corelation R) is actually a lower approximation operator (an upper approximation operator).