Abstract
In this paper, we introduce the notion of $\sup$-hesitant fuzzy ideals of semigroups, which is the general notion of hesitant fuzzy ideals and interval-valued fuzzy ideals. In addition, $\sup$-hesitant fuzzy ideals are characterized in terms of sets, fuzzy sets, hesitant fuzzy sets and interval-valued fuzzy sets. Finally, $\sup$-hesitant fuzzy translations and $\sup$-hesitant fuzzy extensions of $\sup$-hesitant fuzzy ideals of semigoups are discussed, and their relations are investigated.
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