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Zbl 1137.65336
Dehghan, Mehdi; Hashemi, Behnam
Iterative solution of fuzzy linear systems. (English)
[J] Appl. Math. Comput. 175, No. 1, 645-674 (2006). ISSN 0096-3003

One of the major applications using fuzzy number arithmetic is treating linear systems whose parameters are all or partially represented by fuzzy numbers. For solving a general fuzzy linear system, an useful idea proposed by Friedman et al. is the embedding method in which the original fuzzy system is transformed to a doubly-dimensional ordinary system and then a classical iteration such as Jacobi iteration is applied. Using this idea, in this paper, several well-known iterative methods (SOR, AOR, and so on) and their extrapolated form are extended for solving fuzzy linear systems. Convergence theorems are proved. Some numerical examples are presented to illustrate these algorithms.
[Liu Xinguo (Qingdao)]

MSC 2000:: *65F10 Iterative methods for linear systems
15A06 Linear equations (linear algebra)

Keywords: fuzzy linear system; iterative method; extrapolated form; convergence

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