Communications of the
Korean Mathematical Society CKMS

Characterizations of hesitant fuzzy left (right) ideals are considered. The notion of hesitant fuzzy (generalized) bi-ideals is introduced, and related properties are investigated. Relations between hesitant fuzzy generalized bi-ideals and hesitant fuzzy semigroups are discussed, and characterizations of (hesitant fuzzy) generalized bi-ideals and hesitant fuzzy bi-ideals are considered. Given a hesitant fuzzy set ${\mathcal H}$ on a semigroup $S$, hesitant fuzzy (generalized) bi-ideals generated by ${\mathcal H}$ are established.

Keywords: hesitant fuzzy semigroup, hesitant fuzzy left (right) ideal, hesitant fuzzy product, $(\varepsilon, \delta)$-characteristic hesitant fuzzy set, $(\varepsilon, \delta)$-identity hesitant fuzzy set, hesitant fuzzy (generalized) bi-ideal

MSC numbers: 20M12, 20M99, 08A72