On Tripolar Complex Fuzzy Sets and Their Application in Ordered Semigroups

The tripolar complex fuzzy set is a generalization of the tripolar fuzzy sets. In this paper, we introduce the notion of tripolar complex fuzzy sets in ordered semigroups. The concepts of tripolar complex fuzzy subsemigroups and tripolar complex fuzzy left (right, two-sided) ideals are introduced. Some algebraic properties of such tripolar complex fuzzy subsemigroups and their tripolar complex fuzzy ideals are studied. We characterize subsemigroup and left (resp., right, two-sided) ideals by using tripolar complex fuzzy subsemigroups and tripolar complex fuzzy left (resp., right, two-sided) ideals. Finally, we characterized intra-regular ordered semigroups in terms of tripolar complex fuzzy left ideals and tripolar complex fuzzy right ideals.