• 대한수학회논문집
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• 제31권1호
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• pp.17-25
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• 2016

The notion of hesitant fuzzy semigroups with two frontiers is introduced, and related properties are investigated. Relations between a hesitant fuzzy semigroups with a frontier and a hesitant fuzzy semigroups with two frontiers are discussed. It is shown that the hesitant intersection of two hesitant fuzzy semigroups with two frontiers is a hesitant fuzzy semigroup with two frontiers. We provide an example to show that the hesitant union of two hesitant fuzzy semigroups with two frontiers may not be a hesitant fuzzy semigroup with two frontiers.

• 대한수학회논문집
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• 제30권3호
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• pp.143-154
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• 2015

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.

• Journal of applied mathematics & informatics
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• 제41권2호
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• pp.413-437
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• 2023

In this paper, we introduce the concepts of (inf, sup)-hesitant fuzzy subsemigroups and (inf, sup)-hesitant fuzzy (generalized) bi-ideals of semigroups, and investigate their properties. The concepts are established in terms of sets, fuzzy sets, negative fuzzy sets, interval-valued fuzzy sets, Pythagorean fuzzy sets, hesitant fuzzy sets, and bipolar fuzzy sets. Moreover, some characterizations of bi-ideals, fuzzy bi-ideals, anti-fuzzy bi-ideals, negative fuzzy bi-ideals, Pythagorean fuzzy bi-ideals, and bipolar fuzzy bi-ideals of semigroups are given in terms of the (inf, sup)-type of hesitant fuzzy sets. Also, we characterize a semigroup which is completely regular, a group and a semilattice of groups by (inf, sup)-hesitant fuzzy bi-ideals.