Journal of Fuzzy Set Valued Analysis

Volume 2014 (2014), Article ID jfsva-00190, 8 Pages

doi: 10.5899/2014/jfsva-00190



On the global solution of a fuzzy linear system


Tofigh Allahviranloo1 *, Arjan Skuka2, Sahar Tahvili3


1Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.

2Department of Software Engineering, Faculty of Engineering, Izmir University, Izmir, Turkey.

3Division of Applied Mathematics, The School of Education, Culture and Communication, Mälardalen university, Västerås-Sweden.


* Correspondence author Email address: tofigh@allahviranloo.com Tel: +989123508816.


Received: 21 November 2013; Accepted: 28 November 2013


Copyright © 2014 Tofigh Allahviranloo, Arjan Skuka and Sahar Tahvili. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The global solution of a fuzzy linear system contains the crisp vector solution of a real linear system. So discussion about the global solution of a n\times n fuzzy linear system A\tilde{x}=\tilde{b} with a fuzzy number vector b in the right hand side and crisp a coefficient matrix A is considered. The advantage of the paper is developing a new algorithm to find the solution of such system by considering a global solution based upon the concept of a convex fuzzy numbers. At first the existence and uniqueness of the solution are introduced and then the related theorems and properties about the solution are proved in details. Finally the method is illustrated by solving some numerical examples.


Keywords: Fuzzy linear system; Algebraic solution; Fuzzy number.

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