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A hesitant fuzzy set approach to ideal theory in \(\Gamma\)-semigroups. (English) Zbl 1406.20070

Summary: We apply the hesitant fuzzy sets theory to \(\Gamma\)-semigroups and provide some characterizations of hesitant fuzzy left (right and bi-) ideals. We introduce the hesitant fuzzy left (resp., right and two-sided) ideal, hesitant fuzzy bi-ideal, and hesitant fuzzy interior ideal in \(\Gamma\)-semigroup and study some properties of them. Finally, a characterization of a simple \(\Gamma\)-semigroup by means of a hesitant fuzzy simple \(\Gamma\)-semigroup is obtained.

MSC:

20N25 Fuzzy groups
20M99 Semigroups
20M12 Ideal theory for semigroups
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