A remark on hesitant fuzzy ideals in ordered semigroups

Abstract

We investigate the concept of hesitant fuzzy sets. This concept is a generalized notion of fuzzy sets. The concept of fuzzy sets can be applied to the study of ordered semigroups. It is well-known that in regular ordered semigroups, any fuzzy bi-ideal and fuzzy quasi-ideal coincide. In this paper, we illustrate that this fact does not hold for hesitant fuzzy sets. Furthermore, we provide an example illustrating that in a regular ordered semigroup, there is a hesitant fuzzy bi-ideal which is not a hesitant fuzzy quasi-ideal. Moreover, we present a class of hesitant fuzzy sets in which hesitant fuzzy bi-ideals and hesitant fuzzy quasi-ideals coincide.