Characterizing a semigroup by its fuzzy interior antiideals and fuzzy m-interior antiideals

Abstract

Fuzzy sets serve as an extension of traditional sets, capable of handling imprecise information. On the other hand, semigroups represent a broader category than groups, finding utility across various interdisciplinary domains. Diverse subsets of semigroups have been investigated to enhance comprehension of their practical applications. Given the significance of both these ideas, exploring fuzzy subsets within semigroups carries substantial importance. In this paper, we characterize a semigroup through one of its (fuzzy) subsets; (fuzzy) interior antiideals. More precisely, we define interior antiideals and m-interior antiideals of a semigroup, illustrate them by examples, and study their properties. Furthermore, we extend this notion into a fuzzy context, examining the characteristics of fuzzy interior antiideals and fuzzy m-interior antiideals of a semigroup.