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Solution of a fuzzy system of linear equation. (English) Zbl 1095.65036
The $n\times n$ fuzzy system of linear equations (FSLE) has been first studied by {\it M. Friedman}, {\it M. Ma} and {\it A. Kandel} [Fuzzy Sets Syst. 96, No. 1, 201--209 (1998); comment and reply ibid. 140, 559--561 (2003; Zbl 0929.15004)]. In the paper under review, the general $m\times n$ FSLE is considered, and its weak solution is expressed by the generalized inverse of the coefficient matrix. Conditions for the existence of a fuzzy solution are derived and a numerical procedure for calculating the solution is designed. In case $m> n$ the least-squares solution is found by applying an orthogonal matrix to the coefficient matrix.

##### MSC:
 65F20 Overdetermined systems, pseudoinverses (numerical linear algebra)
Full Text:
##### References:
 [1] Friedman, M.; Ming, M.; Kandel, A.: Fuzzy linear systems. Fuzzy sets syst. 96, 201-209 (1998) · Zbl 0929.15004 [2] Allahviranloo, T.: Numerical methods for fuzzy system of linear equations. Appl. math. Comput. 155, 493-502 (2004) · Zbl 1067.65040 [3] Allahviranloo, T.: Successive over relaxation iterative method for fuzzy system of linear equation. Appl. math. Comput. 162, 189-196 (2005) · Zbl 1062.65037 [4] Allahviranloo, T.: The Adomian decomposition method for fuzzy system of linear equations. Appl. math. Comput. 163, 553-563 (2005) · Zbl 1069.65025 [5] Allahviranloo, T.: A comment on fuzzy linear systems. Fuzzy sets syst. 140, 554 (2003) · Zbl 1050.15003 [6] D.R. Kincaid, E.W., Cheney, Numerical analysis mathematics of scientific computing, 1991. · Zbl 0745.65001