A Study on Multi-Intuitionistic Fuzzy Sets and Their Application in Ordered Semigroups

In this paper, we introduce the notion of multi-intuitionistic fuzzy sets in ordered semigroups. The concepts of multi-intuitionistic fuzzy subsemigroups, multi-intuitionistic fuzzy left (right, two-sided, interior) ideals of an ordered semigroup are introduced and some algebraic properties of multi-intuitionistic fuzzy subsemigroups and such their multi-intuitionistic fuzzy ideals are studied. Moreover, the relationships among their multi-intuitionistic fuzzy ideals are investigated. We prove that in regular, intra-regular, and semisimple ordered semigroups, the concepts of multi-intuitionistic fuzzy interior ideals and multi-intuitionistic fuzzy ideals coincide. Finally, the new multi-intuitionistic fuzzy sets are considered.