WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 23, 2024
A New Trend of Bipolar-Valued Fuzzy Cartesian Products, Relations, and Functions
Authors: Fadi M. A. Al-Zu’bi, Abdul Ghafur Ahmad, Abd Ulazeez Alkouri, Maslina Darus
Abstract: A bipolar-valued fuzzy set (BVFS) is a generalization of the fuzzy set (FS). It has been applied to a
wider range of problems that cannot be represented by FS. New forms of the bipolar-valued fuzzy Cartesian
product (BVFCP), bipolar-valued fuzzy relations (BVFRs), bipolar-valued fuzzy equivalence relations
(BVFERs), and Bipolar-valued fuzzy functions (BVFFs) are constructed to be a cornerstone of creating new
approach of BVF group theory. Unlike other approaches, the definition of BVFCP “A×B” is exceptionally
helpful at reclaiming again the subset A and B by using a fitting lattice. Also, the present approach reduced the
calculations and numerical steps in contrast to fuzzy and classical BVF cases. Results relating to those on
relations, equivalence relations, and functions in the fuzzy cases are proved for BVFRs, BVFERs, and BVFFs.
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Keywords: Bipolar Valued Fuzzy Cartesian Product, Bipolar Valued Fuzzy Relation, Bipolar Valued Fuzzy
Equivalence Relations, Bipolar valued Fuzzy Functions, Fuzzy Cartesian Product, Fuzzy
Relation, Fuzzy Equivalence Relations, Fuzzy Functions
Pages: 502-514
DOI: 10.37394/23206.2024.23.53
WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 23, 2024, Art. #53