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Fuzzy linear systems. (English) Zbl 0929.15004
Fuzzy linear systems were considered by many authors [cf. e.g. R. FullĂ©r, Fuzzy Sets Syst. 34, No. 3, 347-353 (1990; Zbl 0696.15003); R. Zhao and R. Govind, Inf. Sci. 56, No. 1-3, 199-243 (1991; Zbl 0726.65048); J. J. Buckley, T. Feuring and Y. Hayashi, Int. Ser. Intell. Technol. 11, 213-232 (1997; Zbl 0893.65016)]. Here we have a linear system with fuzzy right-hand sides, where fuzzy numbers are based on definition by R. Goetschel and W. Voxman [Fuzzy Sets Syst. 10, 87-99 (1983; Zbl 0521.54001)]. The method of solution depends on a construction of 2n×2n crisp linear system with a nonnegative matrix. The paper contains many examples of practical computations.

MSC:
15A06Linear equations (linear algebra)
15A48Positive matrices and their generalizations (MSC2000)
15A33Matrices over special rings
03E72Fuzzy set theory