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 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 \(m\times n\) 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.
Reviewer: Oleksandr Kukush (Kyïv)
MSC:
| 65F20 | Numerical solutions to overdetermined systems, pseudoinverses |
Keywords:
Fuzzy system of linear equation; Overdetermined; Normal equation; Pseudo inverse; Generalized inverse; least-squares solutionCitations:
Zbl 0929.15004References:
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