Abstract
As a generalization of the concepts of interval-valued fuzzy ideals and hesitant fuzzy ideals of \(\Gamma\)-semigroups, the concept of \(\mathcal{SUP}\)-hesitant fuzzy ideals is introduced. Characterizations of \(\mathcal{SUP}\)-hesitant fuzzy ideals are discussed in terms of sets, fuzzy sets, intuitionistic fuzzy sets, interval-valued fuzzy sets, and hesitant fuzzy sets. Further, \(\mathcal{SUP}\)-hesitant fuzzy translations of \(\mathcal{SUP}\)-hesitant fuzzy ideals of \(\Gamma\)-semigroups are introduced and their related properties are investigated.
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