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

Document Type

Article

Source of Publication

WSEAS Transactions on Mathematics

Publication Date

1-1-2024

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.

ISSN

1109-2769

Publisher

World Scientific and Engineering Academy and Society (WSEAS)

Volume

23

First Page

502

Last Page

514

Disciplines

Mathematics

Keywords

Bipolar Valued Fuzzy Cartesian Product, Bipolar Valued Fuzzy Equivalence Relations, Bipolar valued Fuzzy Functions, Bipolar Valued Fuzzy Relation, Fuzzy Cartesian Product, Fuzzy Equivalence Relations, Fuzzy Functions, Fuzzy Relation

Scopus ID

85200588885

Indexed in Scopus

yes

Open Access

yes

Open Access Type

Gold: This publication is openly available in an open access journal/series

Link to Full Text

Share

COinS