Decomposition of Matrix under Neutrosophic Environment

Abstract

Matrices help for the effective representation of systems of linear equations and analyzing any sort of data. The decomposition of any matrix allows for the efficient implementation of matrix-based algorithms. Spectral decomposition is one of the approaches commonly used for square symmetric matrices in order to spell out variation for each of the involved components. The Neutrosophic environment is based on square symmetric matrices and likely to call Spectral decomposition. Neutrosophic is the branch of philosophy that deals with nature, the scope of neutralities and their associations with changed ideational spectra. It is the generalization of the classical set, classical fuzzy set, and intuitionistic fuzzy set. These set theories often limited to handle the problem of uncertainty. Neutrosophic basically based on three possibilities; like Degree of Truth (T), Degree of Falsehood (F) and Degree of Indeterminacy (I).In real-life uncertainties commonly happened and so neutrosophic plays an important role to measure those uncertainties such as inexplicit statements, specious or inadequate information. In order to measure the indeterminacy, a neutrosophic matrix approach is purposed and matrix named “Square-Symmetric Neutrosophic (SSN) matrix”. The SSN matrix is computed using the spectral decomposition of matrices; which do factorization of a matrix into canonical form. The increasing level of indeterminacy restrains from reaching to exact decision. If indeterminacy in (any two) SSN matrices increases, then this leads to reduce variation in data. The process is checked through the Eigenvectors which suggests that through spectral decomposition the variation of the indeterminacy in SSN matrices can be minimized.

Keywords

• neutrosophic set
• square neutrosophic matrices
• and spectral decomposition