Applications of Bipolar Fuzzy Almost Ideals in Semigroups

Abstract

In this paper, we give the concept of bipolar fuzzy almost ideal, minimal almost bipolar fuzzy ideals, and prime (semiprime, strongly prime) bipolar fuzzy almost ideals in semigroups. We investigate the basic properties of bipolar fuzzy almost ideals in semigroups. Finally, we study the relationship between almost ideals and bipolar fuzzy almost ideals in semigroups.

Characterization of almost filters and their fuzzifications of semigroups

“…an almost ideal (AI) F of a semigroup S mean that F is both an LAI and an RAI of S; (9) an almost bi-ideal (ABI) of S if FrF ∩ F = ∅ for all r ∈ S.…”

“…Research on various types of almost ideals and fuzzy almost ideals has also been conducted in specialized areas such as Γ -semigroups [7,18,19], ordered semigroups [20,23], ternary semigroups [22], semihypergroups [6,13,15,21,24], and LA-semihypergroups [14], including studies on bipolar fuzzy sets [9,10].…”