Roughness of Type-2 Fuzzy Set Based on Similarity Relation

Theory of fuzzy set and theory of rough set are two useful means of describing and modeling of uncertainty in ill defined environment where precise mathematical analysis are not suitable. Classical rough set theory is based on equivalent relation. It has been indicated that it could be generated to case with a similarity relation. So far, there has been theoretical investigations on roughness measure of fuzzy set based on equivalent relation. The intention of this paper is to go further and propose a measure of roughness of a type-2 fuzzy set based on similarity relation and prove some properties of this novel measure.