Minimal solution of fuzzy neutrosophic soft matrix

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Journal of Linear and Topological Algebra Vol. 06, No. 02, 2017, 171- 189

Minimal solution of fuzzy neutrosophic soft matrix M. Kavithaa∗ , P. Murugadasb , S.Sriramc a b

epartment of Mathematics, Annamalai University, Annamalainagar-608002. India. Department of Mathematics, Government Arts college (Autonomous), Karur. India. c Mathematics Wing, Directorate of Distance Education, Annamalai University, Annamalainagar-608002. India. Received 22 May 2017; Revised 1 August 2017; Accepted 2 September 2017.

Abstract. The aim of this article is to study the concept of unique solvability of max-min fuzzy neutrosophic soft matrix equation and strong regularity of fuzzy neutrosophic soft matrices over Fuzzy Neutrosophic Soft Algebra (FNSA). A Fuzzy Neutrosophic Soft Matrix (FNSM) is said to have Strong Linear Independent (SLI) column (or, in the case of fuzzy neutrosophic soft square matrices, to be strongly regular) if for some fuzzy neutrosophic soft vector b the system A ⊗ x = b has a unique solution. A necessary and sufficient condition for a linear system of equation over a FNSA to have a unique solution is formulated and the equivalent condition for FNSM to have SLI column and Strong Regular (SR) are presented . Moreover Trapezoidal algorithm for testing these properties are reviewed. c 2017 IAUCTB. All rights reserved. ⃝ Keywords: Fuzzy neutrosophic soft set (FNSS), fuzzy neutrosophic soft matrices (FNSMs), linear system of equation, unique solvability, strong regularity algorithms. 2010 AMS Subject Classification: Primary 03E72; Secondary 15B15.

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Introduction

Neutrosophic was proposed by Prof. Florentin Smarandache [9] in 1995. Neutrosophic is a new branch of Philosophy that studies the origin, nature, and scope of neutralities, as well as its interactions with different ideational spectra. This theory considers every notion or idea < A > together with its opposite or negation < Anti − A > and the spectrum of “neutralities” < N eut − A > (i.e.notions or ideas located between the two extremes, ∗ Corresponding author. E-mail address: kavithakathir3@gmail.com (M. Kavitha).

Print ISSN: 2252-0201 Online ISSN: 2345-5934

c 2017 IAUCTB. All rights reserved. ⃝ http://jlta.iauctb.ac.ir


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