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Solution of fuzzy linear systems by using fuzzy centre. (English) Zbl 1194.15005
Linear systems with crisp \(n\times n\) matrix and fuzzy right-hand sides were introduced by M. Friedman, M. Ma and A. Kandel [Fuzzy Sets Syst. 96, No. 2, 201–209 (1998); comment and reply ibid. 140, 559–561 (2003; Zbl 0929.15004)], and discussed by many other authors [T. Allahviranloo and M. Afshar Kermani, Appl. Math. Comput. 175, No. 1, 519–531 (2006; Zbl 1095.65036); S. Abbasbandy and M. Alavi, Iran. J. Fuzzy Syst. 2, No. 2, 37–43 (2005; Zbl 1104.15004); B. Zheng and K. Wang, Appl. Math. Comput. 181, No. 2, 1276–1286 (2006; Zbl 1122.15005)] under the name of fuzzy linear systems [cf. however R. Fullér, Fuzzy Sets Syst. 34, No. 3, 347–353 (1990; Zbl 0696.15003) or J. J. Buckley and Y. Qu, Fuzzy Sets Syst. 43, No. 1, 33–43 (1991; Zbl 0741.65023)].
This paper restricts problem to the case of trapezoidal fuzzy numbers, which has linear parametric form. Then solution vector is also represented by trapezoidal fuzzy numbers and can be determined by classical methods of linear algebra. The method is illustrated by a \(2\times 2\) system with vector of triangular fuzzy numbers.

MSC:
15A06 Linear equations (linear algebraic aspects)
03E72 Theory of fuzzy sets, etc.
26E50 Fuzzy real analysis
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