Generalization of Bi-antiideals in Semigroups (European Journal of Pure and Applied Mathematics, 2025)
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. In this paper, our aim is to characterize a semigroup through a generalized concept of its bi-antiideals and to fuzzify this concept. In particular, by using fuzzy sets, we studied fuzzy $(m,n)$-bi-antiideals of a semigroup and linked it to $(m,n)$-bi-antiideals by mean of level sets.
Keywords: antiideal; bi-antiideal; $(m,n)$-bi-antiideal; Fuzzy $(m,n)$-bi-antiideal; Level set