SOME ALGEBRAIC STRUCTURE OF SPHERICAL NEUTROSOPHIC MATRICES

SOME ALGEBRAIC STRUCTURE OF SPHERICAL NEUTROSOPHIC MATRICES

I. Silambarasan

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Abstract

In this paper, we introduce spherical neutrosophic matrices (SNMs) as gen- eralization of intuitionistic fuzzy matrices, Pythagorean fuzzy matrices, picture fuzzy matrices and spherical fuzzy matrices. Some algebraic operations such as max-min, min-max, complement, algebraic sum and algebraic product are defined in SNMs and investigated. Further, scalar multiplication (nA) and exponentiation (An) operations of a spherical neutrosophic matrix A using algebraic operations are constructed, and their desirable properties are proved. Finally, define a new operation(@) on spherical neutro- sophic matrices and discuss distributive law in the case where the operations of ⊕, ⊗, ∧ and ∨ are combined each other.

Keywords

Intuitionistic fuzzy matrix, Pythagorean fuzzy matrix, Picture fuzzy ma- trix. Spherical fuzzy matrix, Spherical Neutrosophic Matrix, Algebraic sum, Algebraic product, Scalar multiplication, Exponentiation operations.