On the global solution of a fuzzy linear system

Tofigh Allahviranloo,Arjan Skuka,Sahar Tahvili

doi:10.5899/2014/jfsva-00190

Tofigh Allahviranloo, Arjan Skuka + Show 1 more

Open Access

https://doi.org/10.5899/2014/jfsva-00190

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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 ×n fuzzy linear system A˜ x = ˜ 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.

Highlights

Fuzzy linear systems have many applications in science, such as control problems, information, physics, statistics, engineering, economics, finance and even social science
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
A fuzzy number xis shown as an ordered pair of functions x = x(r), x(r) where: i) x(r) is a left-continuous bounded monotonic increasing function

Summary

Introduction

Fuzzy linear systems have many applications in science, such as control problems, information, physics, statistics, engineering, economics, finance and even social science. In [3, 4], Allahviranloo has investigated the various numerical methods (Jacobi, Gauss Seidel) for solving such fuzzy linear systems for the first time. He proposed the Adomian and Homotopy methods for solving fuzzy linear systems in [7, 9]. Ghanbari and his colleague in [15] have proposed an approach for computing the general compromised solution of an L-R fuzzy linear system by use of a ranking function when the coefficient matrix is a crisp m × n matrix.

Preliminaries

Fuzzy linear system

The proposed method

Algorithm

Conclusions