Generalized fuzzy bi-ideals of semigroups

Authors:
Osman Kazancı;Sultan Yamak
Affiliations:
Karadeniz Technical University, Department of Mathematics, 61080, Trabzon, Turkey;Karadeniz Technical University, Department of Mathematics, 61080, Trabzon, Turkey
Venue:
Soft Computing - A Fusion of Foundations, Methodologies and Applications
Year:
2008

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Abstract

After the introduction of fuzzy sets by Zadeh, there have been a number of generalizations of this fundamental concept. The notion of (∈, ∈ ∨q)-fuzzy subgroups introduced by Bhakat is one among them. In this paper, using the relations between fuzzy points and fuzzy sets, the concept of a fuzzy bi-ideal with thresholds is introduced and some interesting properties are investigated. The acceptable nontrivial concepts obtained in this manner are the (∈, ∈ ∨q)-fuzzy bi-ideals and $$(\overline{\in}, \overline{\in} \vee\overline{q})$$-fuzzy bi-ideals, which are extension of the concept of a fuzzy bi-ideal in semigroup.