Generalized orthopair fuzzy matrices

I Silambarasan

doi:10.30538/oms2021.0165

Abstract

A q-rung orthopair fuzzy matrix (q-ROFM), an extension of the Pythagorean fuzzy matrix (PFM) and intuitionistic fuzzy matrix (IFM), is very helpful in representing vague information that occurs in real-world circumstances. In this paper we define some algebraic operations, such as max-min, min-max, complement, algebraic sum, algebraic product, scalar multiplication \((nA)\), and exponentiation \((A^n)\). We also investigate the algebraic properties of these operations. Furthermore, we define two operators, namely the necessity and possibility to convert q-ROFMs into an ordinary fuzzy matrix, and discuss some of their basic algebraic properties. Finally, we define a new operation(@) on q-ROFMs and discuss distributive laws in the case where the operations of \(\oplus_{q}, \otimes_{q}, \wedge_{q}\) and \(\vee_{q}\) are combined each other.

Highlights

T he concept of an intuitionistic fuzzy matrix (IFM) was introduced by Khan et al [1] and Im et al [2] to generalize the concept of Thomason’s fuzzy matrix [3]
After the introduction of IFM theory, many researchers attempted the important role in IFM theory [5–14]
Yager [15] introduced the concept of a Pythagorean fuzzy set (PFS) and developed some aggregation operations for PFS

Summary

Introduction

T he concept of an intuitionistic fuzzy matrix (IFM) was introduced by Khan et al [1] and Im et al [2] to generalize the concept of Thomason’s fuzzy matrix [3]. Proved equality between IFMs. After the introduction of IFM theory, many researchers attempted the important role in IFM theory [5–14]. Yager [15] introduced the concept of a Pythagorean fuzzy set (PFS) and developed some aggregation operations for PFS. Using the theory of PFS ans q-ROFS, Silambarasan and Sriram [26] defined the Pythagorean fuzzy matrix (PFM) theory and its algebraic operations. They constructed nA and An of a Pythagorean fuzzy matrix A and using these operations They defined the commutative monoid on Pythagorean fuzzy matrices and proved that the set of all PFMs forms a commutative monoid [27]. In. Section 6, we define a new operation(@) on q-ROFMs and investigated their algebraic properties.

Preliminaries

PFM operations on q-ROFMs

Conclusion