Abstract
Objectives: This article is to extend and present an idea related to intuitionistic fuzzy matrix to Pythagorean fuzzy matrix. Methods/Statistical Analysis: The main feature of the Pythagorean fuzzy matrix is to relax the condition that the sum of the membership degree and the non-membership degree to which an alternative satisfying a criterion provided by an expert may be bigger than one, but they square off is equal to or less than one. Particularly those involving the operation A → B define a standard the Pythagorean fuzzy implication with other operations. Findings: We define some new operations for Pythagorean fuzzy matrices (→, $, # ) and discuss their algebraic properties with some existing operations (∨, ∧, ⊕, @ ) in detail. Also, we prove some new results associated with the standard Pythagorean fuzzy implication (→). Finally, implication operation A → B has been extended for Pythagorean fuzzy matrices. Application: An application of Pythagorean fuzzy decision matrix and its aggregation operators constructed by Yager and which are used to solve multicriteria decision-making problems. Recently, a new model based on Pythagorean fuzzy matrix has been presented to manage the uncertainty in real-world decision-making problems. Keywords: Algebraic Sum And Algebraic Product, Implication Operation, Intuitionistic Fuzzy Matrix, Pythagorean Fuzzy Matrix
Highlights
In1 introduced the Intuitionistic Fuzzy Matrices (IFMs) and at the same time by[2], to generalize Thomason’s3 fuzzy matrix
Each element in an IFM is expressed by an ordered pair aij, ai′j with aij, ai′j ∈[0,1] and 0 ≤ aij + ai′j ≤ 1
We prove set of all Pythagorean fuzzy matrices from a commutative monoid[8]
Summary
In1 introduced the Intuitionistic Fuzzy Matrices (IFMs) and at the same time by[2], to generalize Thomason’s3 fuzzy matrix. Each element in an IFM is expressed by an ordered pair aij , ai′j with aij , ai′j ∈[0,1] and 0 ≤ aij + ai′j ≤ 1. Recently[4] get a decomposition of an intuitionistic fuzzy matrix by mistreatment the new composition operator and modal operators. The idea of the Pythagorean Fuzzy Set (PFS) initial time was introduced by[5] and developed some aggregation operations for PFS. In6 outlined some novel operational laws of PFS and discuss its fascinating properties. Using the theory of PFS, In7, we defined the Pythagorean
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