Abstract
As general concepts of sup-hesitant fuzzy right (resp., left, interior, two-sided) ideals of semigroups, the concepts of sup+α-hesitant fuzzy right (resp., left, interior, two-sided) ideals and sup-β-hesitant fuzzy right (resp., left, interior, two-sided) ideals are introduced and their properties are investigated. Then, the concepts are established by fuzzy sets, Łukasiewicz fuzzy sets, Łukasiewicz anti-fuzzy sets, Pythagorean fuzzy sets, hesitant fuzzy sets, hybrid sets, interval-valued fuzzy sets and cubic sets. Finally, we characterize which is intra-regular, completely regular, simple semigroups or another type of semigroups in terms of sup+α-type and sup-β-type of hesitant fuzzy sets.
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