BIPOLAR FUZZY SET THEORY APPLIED TO SUB-SEMIGROUPS WITH OPERATORS IN SEMIGROUPS
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Given a set and the notion of bipolar valued fuzzy sets, the con-cept of a bipolar Ω-fuzzy sub-semigroup in semigroups is introduced, and related properties are investigated. Using bipolar Ω-fuzzy sub-semigroups, bipolar fuzzy sub-semigroups are constructed. Conversely, bipolar Ω-fuzzy sub-semigroups are established by using bipolar fuzzy sub-semigroups. A characterizations of a bipo-lar -fuzzy sub-semigroup is provided, and normal bipolar Ω-fuzzy sub-semigroups are discussed. How the homomorphic images and inverse images of bipolar Ω-fuzzy sub-semigroups become bipolar Ω-fuzzy sub-semigroups are considered.
Abstract
Given a set and the notion of bipolar valued fuzzy sets, the con-cept of a bipolar Ω-fuzzy sub-semigroup in semigroups is introduced, and related properties are investigated. Using bipolar Ω-fuzzy sub-semigroups, bipolar fuzzy sub-semigroups are constructed. Conversely, bipolar Ω-fuzzy sub-semigroups are established by using bipolar fuzzy sub-semigroups. A characterizations of a bipo-lar -fuzzy sub-semigroup is provided, and normal bipolar Ω-fuzzy sub-semigroups are discussed. How the homomorphic images and inverse images of bipolar Ω-fuzzy sub-semigroups become bipolar Ω-fuzzy sub-semigroups are considered.
참고문헌 (6)
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