Abstract
In this paper, as a generalization of the concepts of hesitant fuzzy bi-ideals and hesitant fuzzy right (resp. left) ideals of semigroups, the concepts of hesitant fuzzy (m, n)-ideals and hesitant fuzzy (m, 0)-ideals (resp. (0, n)-ideals) are introduced. Furthermore, conditions for a hesitant fuzzy (m, n)-ideal ((m, 0)-ideal, (0, n)-ideal) to be a hesitant fuzzy bi-ideal (right ideal, left ideal) are provided. Moreover, several correspondences between bi-ideals (right ideals, left ideals) and hesitant fuzzy (m, n)-ideals ((m, 0)-ideals, (0, n)-ideals) are obtained. Also, the characterizations of different classes of semigroups in terms of their hesitant fuzzy (m, n)-ideals and hesitant fuzzy (m, 0)-ideals ((0, n)-ideals) are investigated.