Abstract
Objectives: We study some algebraic properties of the operations disjunction (∨L ) and conjunction (∧L) from Lukasiewicz’s type over Pythagorean fuzzy matrices. Methods/Statistical Analysis: We extend these operations of intuitionistic fuzzy matrices to pythagorean fuzzy matrices and proved their algebraic properties. Findings: We discuss some algebraic properties like distributivity, associativity, commutativity, and complementary of these operations. We establish the set of all Pythagorean fuzzy matrices forms a commutative monoid under these operations. Also, we describe a monoid homomorphism over pythagorean fuzzy matrices. Application: Yager constructed the Pythagorean fuzzy decision matrix and its aggregation operators which is used to solve multicriteria decision-making problems. Keywords: Conjunction, Disjunction, Intuitionistic Fuzzy Set, Intuitionistic Fuzzy Matrix, Pythagorean Fuzzy Set, Pythagorean Fuzzy Matrix
Highlights
The idea of Intuitionistic Fuzzy Matrix (IFM) was introduced by[1]
In12, they are discussed some results for Pythagorean Fuzzy Set (PFS) and its algebraic properties
In18, they are proved the set of all IFMs is a commutative monoid under these operations
Summary
The idea of Intuitionistic Fuzzy Matrix (IFM) was introduced by[1]. In2 and[3] to generalize the concept of[4] fuzzy matrix. Pythagorean Fuzzy Set (PFS) was introduced by[11]. Matrix (PFM) and studied its algebraic operations. We discussed the De Morgan’s laws, absorption and distributive properties of PFMs. Lukasiewicz’s type over IFSs. In17 introduced two operations ∨L and ∧L from Lukasiewicz’s type over IFMs are studied. In18, they are proved the set of all IFMs is a commutative monoid under these operations. ∨L and ∧L from Lukasiewicz’s type over PFMs. Commutative Monoids and Monoid Homomorphism on Lukasiewicz Disjunction and Conjunction Operations Over Pythagorean Fuzzy Matrices using the relations between ∨L and ∧L using modal operations. PFMs and their opertions and Section 3, some properties of the operations ∨L and ∧L from Lukasiewicz’s type over. The set of all PFMs forms a commutative monoid under these operations. We describe a monoid homomorphism over Pythagorean fuzzy matrices
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