FUZZY INTERIOR IDEALS IN HYPERSEMIGROUPS

Abstract

We introduce the concept of interior ideal and the concept of fuzzy interior ideal in hypersemigroups and we prove, among others, that in regular also in intra-regular hypersemigroups the interior ideals and the fuzzy interior ideals coincide. We also prove that an hypergroupoid H is simple if and only if every fuzzy ideal of H is a constant function; and that an hypersemigroup H is simple if and only if every fuzzy interior ideal of H is a constant function, equivalently if, for every element a of H, we have H = H * {a} * H.