On (m, n)-Fuzzy Sets and Their Application in Ordered Semigroups

In this paper, we introduce the concepts of (m, n)-fuzzy subsemigroups, (m, n)-fuzzy left (right, two-sided, bi-, (1, 2)-) ideals of an ordered semigroup and some their algebraic properties are studied, thereafter the relationship among their (m, n)-fuzzy ideals was investigated. Moreover, we characterize left (resp., right, two-sided, bi-) ideals by using (m, n)-fuzzy left (resp., right, two-sided, bi-) ideals. Finally, we characterize regular ordered semigroups and intra-regular ordered semigroups in terms of (m, n)-fuzzy left ideals, (m, n)-fuzzy right ideals, and (m, n)-fuzzy bi-ideals.