Iterative solution of fuzzy linear systems. (English) Zbl 1137.65336

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.


65F10 Iterative numerical methods for linear systems
15A06 Linear equations (linear algebraic aspects)
Full Text: DOI


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