Positive Solution of Non-square Fully Fuzzy Linear System of Equation in General Form using Least Square Method

In this paper, we propose the least-squares method for computing the positive solution of a m × 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. c ⃝ 2014 IAUCTB. All rights reserved.