Abstract
The notions of an $\inf$-hesitant fuzzy right (left, lateral) ideal, an $\inf$-hesitant fuzzy ideal, a $(\sup, \inf)$-hesitant fuzzy right (left, lateral) ideal, and a $(\sup, \inf)$-hesitant fuzzy ideal, which are generalizations of an interval-valued fuzzy ideal of a ternary semigroup, are introduced and their properties are investigated. Conditions for a hesitant fuzzy set to be an $\inf$-hesitant fuzzy right (left, lateral) ideal, an $\inf$-hesitant fuzzy ideal, a $(\sup, \inf)$-hesitant fuzzy right (left, lateral) ideal, and a $(\sup, \inf)$-hesitant fuzzy ideal of a ternary semigroup are provided in terms of sets, fuzzy sets, Pythagorean fuzzy sets, interval-valued fuzzy sets, and hesitant fuzzy sets. Furthermore, characterizations of an ideal of a ternary semigroup are studied via a generalization of the characteristic hesitant and the characteristic interval-valued fuzzy set.
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