Bipolar Fuzzy Relations

Jeong-Gon Lee and Kul Hur
Additional contact information
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

Mathematics, 2019, vol. 7, issue 11, 1-18

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.

Keywords: bipolar fuzzy relation; bipolar fuzzy reflexive (resp., symmetric and transitive) relation; bipolar fuzzy equivalence relation; bipolar fuzzy partition; ( a , b )-level set (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/7/11/1044/pdf (application/pdf)
https://www.mdpi.com/2227-7390/7/11/1044/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:7:y:2019:i:11:p:1044-:d:283180

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().