Generalization of bi-antiideals in semigroups

Abstract

Algebraic structure consisting of a set together with an associative internal binary operation on it, so called semigroup has applications in different fields of science. For a better understanding of these applications, semigroups are characterized through their subsets. Fuzzy sets deal with uncertainties, and because many real-life problems have an associated algebraic structure, fuzzification of these structures makes sense and is useful. This paper investigates the generalization of bi-antiideals in semigroups and their fuzzification to enhance understanding of algebraic structures with uncertainties. Building upon prior research, we define and explore (m, n)-bi-antiideals as an extension of bi-antiideals, studying their properties through theoretical analysis and illustrative examples. We introduce fuzzy (m, n)-bi-antiideals by leveraging fuzzy set theory to model uncertainties, establishing a connection with (m, n)-bi-antiideals via level sets.

Keywords Antiideal, bi-antiideal, (m, n)-bi-antiideal, Fuzzy (m, n)-bi-antiideal, Level set