Roughness in membership continuous function

Abstract EN

In this paper, we introduce the new definition of rough membership function using con-tinuous function and we discuss several concepts and properties of rough continuous set value func-tions 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 equiv-alence class by continuous functions and prove some theorems on certain types of set value func-tions 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.