Bipolar Fuzzy Relations - Jeong-Gon Lee; Kul Hur (Mathematics, 2019)
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 <semantics> ( a , b ) </semantics> -level set of a bipolar fuzzy relation and investigate some relationships between bipolar fuzzy relations and their <semantics> ( a , b ) </semantics> -level sets.