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  • P-ISSN3059-0604
  • E-ISSN3059-1309
  • KCI

ISSN : 3059-0604

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Vol.19 No.1

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BIPOLAR FUZZY SET THEORY APPLIED TO SUB-SEMIGROUPS WITH OPERATORS IN SEMIGROUPS

BIPOLAR FUZZY SET THEORY APPLIED TO SUB-SEMIGROUPS WITH OPERATORS IN SEMIGROUPS

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
2012, v.19 no.1, pp.23-35
https://doi.org/10.7468/jksmeb.2012.19.1.23
Kang, Mee-Kwang (Department of Mathematics, Dongeui University)
Kang, Jeong-Gi (Department of Mathematics Education, Gyeongsang National University)
Kang, Mee-Kwang, & Kang, Jeong-Gi. (2012). BIPOLAR FUZZY SET THEORY APPLIED TO SUB-SEMIGROUPS WITH OPERATORS IN SEMIGROUPS, 19(1), 23-35, https://doi.org/10.7468/jksmeb.2012.19.1.23

Abstract

Given a set ${\Omega}$ and the notion of bipolar valued fuzzy sets, the concept of a bipolar ${\Omega}$-fuzzy sub-semigroup in semigroups is introduced, and related properties are investigated. Using bipolar ${\Omega}$-fuzzy sub-semigroups, bipolar fuzzy sub-semigroups are constructed. Conversely, bipolar ${\Omega}$-fuzzy sub-semigroups are established by using bipolar fuzzy sub-semigroups. A characterizations of a bipolar ${\Omega}$-fuzzy sub-semigroup is provided, and normal bipolar ${\Omega}$-fuzzy sub-semigroups are discussed. How the homomorphic images and inverse images of bipolar ${\Omega}$-fuzzy sub-semigroups become bipolar ${\Omega}$-fuzzy sub-semigroups are considered.

keywords
bipolar fuzzy sub-semigroup, (normal) bipolar <tex> ${\Omega}$</tex>-fuzzy sub-semigroup, negative <tex> $s$</tex>-cut, positive <tex> $t$</tex>-cut

참고문헌

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(2011). Fuzzy sub-semigroups and fuzzy ideals with operators in semigroups. Ann. Fuzzy Math. Inform., 1, 1-12.

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(2011). Ideal theory of sub-semigroups based on the bipolar valued fuzzy set theory. Ann. Fuzzy Math. Inform., 2, 193-206.

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(2000). Bipolar-valued fuzzy sets and their operations (307-312). Proc. Int. Conf. on Intelligent Technologies.

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(2004). Comparison of interval-valued fuzzy sets, intuitionistic fuzzy sets, and bipolarvalued fuzzy sets. J. Fuzzy Logic Intelligent Systems, 14, 125-129.

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Fuzzy Set Theory and its Applications.

한국수학교육학회지시리즈B:순수및응용수학

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