Indian Journal of Science and Technology

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