Properties of rough fuzzy prime ideals in Γ rings

Abstract

Rough Set (RS) theory is a useful mathematical strategy to handle uncertainty. In 1982, Pawlak presented the idea, and numerous authors have undertaken in-depth studies on RS in both ordinary cases and fuzzy situations. In terms of both the theoretical investigations and the practical applications, progress in this field of RS theory has yielded favorable outcomes over the last three decades and it is typically considered to be an extension of classical sets. A universe in RS is separated by two subsets known as lower and upper approximations. Upper approximations are nonempty intersections of equivalence classes, whereas lower approximations are subsets of the set. In this study, rough sets are examined when the universe set has a ring structure. The main contribution of this study is to focus on rough fuzzy prime and semi-prime ideals of the gamma ring structure and explain certain respects of its upper and lower approximations. The goal of this research is to investigate some of the characterizations of prime and semi-prime ideals and prove some related results. Moreover, the study discusses rough fuzzy ideals (RFI) in Γ Residue class and gives some findings.

Keywords

• γ rings
• fuzzy set
• rough set
• rough fuzzy prime ideal
• rough fuzzy semi prime ideal