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Similarity relations, eigenvalues and eigenvectors of bipolar fuzzy matrix

Article type: Research Article

Authors: Mondal, Sanjib* | Pal, Madhumangal

Affiliations: Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, India

Correspondence: [*] Corresponding author. Sanjib Mondal, Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore-721102, India. Tel.: +919609268225; E-mail: [email protected].

Abstract: Eigenvalues and eigenvectors are one of the important topics over bipolar fuzzy linear algebra. In order to develop the bipolar fuzzy linear space we introduce in this article, the similarity relations, eigenvalues and eigenvectors of bipolar fuzzy matrices (BFMs). Idempotent, diagonally dominant and spectral radius of BFMs are considered here. Also, some properties and results of eigenvalues and eigenvectors for BFMs are investigated.

Keywords: Relation, bipolar fuzzy matrix, vector, eigenvalue, eigenvector, spectral radius

DOI: 10.3233/IFS-152000

Journal: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 4, pp. 2297-2307, 2016

Published: 10 March 2016
Price: EUR 27.50

EIGENVALUES OF BFM

What is it about?

Eigenvalues and eigenvectors are one of the important topics over bipolar fuzzy linear algebra. In order to develop the bipolar fuzzy linear space we introduce in this article, the similarity relations, eigenvalues and eigenvectors of bipolar fuzzy matrices (BFMs). Idempotent, diagonally dominant and spectral radius of BFMs are considered here.

Why is it important?

In this article, first time we introduce the bipolar fuzzy similarity relations over BFMs. Over some special type of BFMs (e.g. diagonally dominant matrix etc.) we investigate some properties to find the eigenvalues and eigenvectors of the matrices and illustrated some suitable examples. Also some result about spectral radius are investigated here.

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