Roughness in Membership Continuous Function

Abstract

In this paper, we introduce the new definition of rough membership function using continuous function and we discuss several concepts and properties of rough continuous set value functions as new results on rough continuous function and membership continuous function. Moreover, we extend the definition of rough membership function to topology spaces by substituting an equivalence class by continuous functions and prove some theorems on certain types of set value functions and some more general and fundamental properties of the generalized rough sets. Our result generalized the concept of the set valued function by using rough set theory.

Keywords

• Rough set
• Lower approximation
• Upper approximation
• Set valued mapping