A New Trend of Bipolar-Valued Fuzzy Cartesian Products, Relations, and Functions-Reference-Cited by-同舟云学术

A New Trend of Bipolar-Valued Fuzzy Cartesian Products, Relations, and Functions

Published:2024-07-29 Issue: Volume:23 Page:502-514
ISSN:2224-2880
Container-title:WSEAS TRANSACTIONS ON MATHEMATICS
language:en
Short-container-title:

Author:

Al-Zu’bi Fadi M. A.¹,Ahmad Abdul Ghafur¹,Alkouri Abd Ulazeez²,Darus Maslina¹

Affiliation:

1. Department of Mathematical Sciences, Faculty of Science & Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, MALAYSIA

2. Department of Mathematics Department, Faculty of Science, Ajloun National University, P.O. 43, Ajloun- 26810, JORDAN

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.

Publisher

World Scientific and Engineering Academy and Society (WSEAS)

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