Ezzati, R., Yousefzadeh, A. (2014). Positive solution of non-square fully Fuzzy linear system of equation in general form using least square method. Journal of Linear and Topological Algebra (JLTA), 03(01), 23-33.

R. Ezzati; A. Yousefzadeh. "Positive solution of non-square fully Fuzzy linear system of equation in general form using least square method". Journal of Linear and Topological Algebra (JLTA), 03, 01, 2014, 23-33.

Ezzati, R., Yousefzadeh, A. (2014). 'Positive solution of non-square fully Fuzzy linear system of equation in general form using least square method', Journal of Linear and Topological Algebra (JLTA), 03(01), pp. 23-33.

Ezzati, R., Yousefzadeh, A. Positive solution of non-square fully Fuzzy linear system of equation in general form using least square method. Journal of Linear and Topological Algebra (JLTA), 2014; 03(01): 23-33.

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

^{}Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran

Abstract

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

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