Abstract
The aim of this paper is to apply hesitant fuzzy sets theory in ordered Gamma- semigroups. The hesitant fuzzy ideals in ordered Gamma-semigroups are introduced and some related properties are explored. Using this concept, some characterizations on hesitant fuzzy left (right and bi-) ideals are given. The hesitant fuzzy interior ideal in oredered Gamma-semigroup are defined and their related properties are studied. Finally, the characterization of a simple ordered Gamma-semigroup in terms of a hesitant fuzzy simple ordered Gamma-semigroup is presented.