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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.
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참고문헌 (6)
참고문헌 신청
C. S. Kim / 2011 / Ideal theory of sub-semigroups based on the bipolar valued fuzzy set theory / Ann. Fuzzy Math. Inform 2 : 193 ~ 206
D. Dubois / 1980 / Fuzzy sets and systems: Theory and Applications / Academic Press
H.-J. Zimmermann / 1985 / Fuzzy Set Theory and its Applications / Kluwer-Nijho® Publishing
K. Hur / 2011 / Fuzzy sub-semigroups and fuzzy ideals with operators in semigroups / Ann. Fuzzy Math. Inform 1 : 1 ~ 12
K. M. Lee / 2000 / Bipolar-valued fuzzy sets and their operations. Proc. Int. Conf. on Intelligent Technologies : 307 ~ 312
D. Dubois / 1980 / Fuzzy sets and systems: Theory and Applications / Academic Press
H.-J. Zimmermann / 1985 / Fuzzy Set Theory and its Applications / Kluwer-Nijho® Publishing
K. Hur / 2011 / Fuzzy sub-semigroups and fuzzy ideals with operators in semigroups / Ann. Fuzzy Math. Inform 1 : 1 ~ 12
K. M. Lee / 2000 / Bipolar-valued fuzzy sets and their operations. Proc. Int. Conf. on Intelligent Technologies : 307 ~ 312
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