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Solution of a fuzzy system of linear equation. (English) Zbl 1095.65036
The n×n fuzzy system of linear equations (FSLE) has been first studied by M. Friedman, M. Ma and 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×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:
65F20Overdetermined systems, pseudoinverses (numerical linear algebra)