MORPHISM PROPERTIES ON ROUGH FUZZY IDEALS IN Γ- RINGS

Abstract

The term “Rough Set”(RS) in mathematics describes a distinct method of handling ambiguity and uncertainty. It is significant in both pure and applied mathematics. RS allows us to eliminate redundant or irrelevant attributes and it remains effective in the fields of knowledge acquisition, industrial control, medical diagnosis, expert systems, and data mining. Algebraic structure is a key component of RS theory. Combining the RS with abstract algebra is one method for generalizing it. Several studies proposed and examined the concepts of RS with groups and rings in approximation spaces. In general, a homomorphism is a structure preserving map between two algebraic structures of the same type. This study establishes some theorems, discusses $\mathrm{\Gamma }$ homomorphism and epimorphism in the $\mathrm{\Gamma }$- ring structure, and also demonstrates some of its characteristics.