The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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BIPOLAR FUZZY SET THEORY APPLIED TO SUB-SEMIGROUPS WITH OPERATORS IN SEMIGROUPS

  • Kang, Mee-Kwang (Department of Mathematics, Dongeui University) ;
  • Kang, Jeong-Gi (Department of Mathematics Education, Gyeongsang National University)
  • Received : 2011.11.06
  • Accepted : 2012.02.02
  • Published : 2012.02.28
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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.

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References

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