Intuitionistic Fuzzy Rough Approximation Operators Based on Intuitionistic Fuzzy Triangle Norm

In rough set theory, the lower and upper approximation operators defined by binary relations satisfy many interesting properties. Various generalizations of Pawlak´s rough approximations have been made in the literature over these years. This paper proposes a general framework for the study of intuitionistic fuzzy rough approximation operators based on intuitionistic fuzzy triangle norm. In the constructive approach, a pair of lower and upper induced from intuitionistic fuzzy relation are defined. Basic properties of intuitionsitic fuzzy rough approximation operators are then examined. By introducing intuitionistic fuzzy residual implication, Further properties of intuitionistic fuzzy rough approximation operators are then investigated. we propose that classical rough set and fuzzy rough are special types of intuitionistic fuzzy rough set based on intuitionistic fuzzy triangle norm.