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.
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Kazancı, O., Yamak, S. Generalized fuzzy bi-ideals of semigroups. Soft Comput 12, 1119–1124 (2008). https://doi.org/10.1007/s00500-008-0280-5
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DOI: https://doi.org/10.1007/s00500-008-0280-5