Positive solution of non-square fully Fuzzy linear system of equation in general form using least square method
Authors
Abstract:
In this paper, we propose the least-squares method for computing the positive solution of a $mtimes n$ 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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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 ka man's arithmetic operations on fuzzy numbers that introduced in [18]. first, we consider all elements of coecient matrix are non-negative or non-positive. also, we obtain 1-cut of the fuzzy number vector solution of the n...
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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...
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1 Baskent University, Ankara, 06810 Turkey; phone: (+90)3122341010/1220; fax: (+90)3122341051 E-mail: [email protected] (corresponding author) 2 Baskent University, Ankara, 06810 Turkey; phone: (+90)3122341010/1790; fax: (+90)3122341179 E-mail: [email protected] 3 Ankara University, Computer Engineering Department, Ankara, 06500 Turkey; phone: (+90)3123800026/162 E-mail: [email protected]...
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Journal title
volume 03 issue 01
pages 23- 33
publication date 2014-03-01
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