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Bipolar Fuzzy Relations

Author

Listed:
  • Jeong-Gon Lee

    (Division of Applied Mathematics, Nanoscale Science and Technology Institute, Wonkwang University, Iksan 54538, Korea)

  • Kul Hur

    (Department of Applied Mathematics, Wonkwang University, 460, Iksan-daero, Iksan-Si, Jeonbuk 54538, Korea)

Abstract

We introduce the concepts of a bipolar fuzzy reflexive, symmetric, and transitive relation. We study bipolar fuzzy analogues of many results concerning relationships between ordinary reflexive, symmetric, and transitive relations. Next, we define the concepts of a bipolar fuzzy equivalence class and a bipolar fuzzy partition, and we prove that the set of all bipolar fuzzy equivalence classes is a bipolar fuzzy partition and that the bipolar fuzzy equivalence relation is induced by a bipolar fuzzy partition. Finally, we define an ( a , b ) -level set of a bipolar fuzzy relation and investigate some relationships between bipolar fuzzy relations and their ( a , b ) -level sets.

Suggested Citation

  • Jeong-Gon Lee & Kul Hur, 2019. "Bipolar Fuzzy Relations," Mathematics, MDPI, vol. 7(11), pages 1-18, November.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:11:p:1044-:d:283180
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