Positive solution of non-square fully Fuzzy linear system of equation in general form using least square method

Subject Areas : History and biography

R. Ezzati ¹ , A. Yousefzadeh ²

1 - Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
2 - Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran

Received: 2014-05-30 Accepted : 2014-08-25 Published : 2014-03-01

Keywords: Fuzzy linear system, fuzzy number, Ranking Function, Fuzzy number vector solution,

Abstract :

In this paper, we propose the least-squares method for computing the positivesolution of a $m\times n$ fully fuzzy linear system (FFLS) of equations, where $m > n$, based onKaffman's arithmetic operations on fuzzy numbers that introduced in [18]. First, we considerall elements of coefficient matrix are non-negative or non-positive. Also, we obtain 1-cut of thefuzzy number vector solution of the non-square FFLS of equations by using pseudoinverse.If 1-cuts vector is non-negative, we solve constrained least squares problem for computingleft and right spreads. Then, in the special case, we consider 0 is belong to the support ofsome elements of coefficient matrix and solve three overdetermined linear systems and if thesolutions of these systems held in non-negative fuzzy solutions then we compute the solutionof the non-square FFLS of equations. Else, we solve constrained least squares problem forobtaining an approximated non-negative fuzzy solution. Finally, we illustrate the efficiencyof the proposed method by solving some numerical examples.

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