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Dehghan, Mehdi; Hashemi, Behnam; Ghatee, Mehdi

Solution of the fully fuzzy linear systems using iterative techniques. (English) Zbl 1144.65021

Chaos Solitons Fractals 34, No. 2, 316-336 (2007).
The authors are concerned with the iterative solution of fully fuzzy linear systems. In this sense they consider classical iterative methods, as Jacobi, Gauss-Seidel, successive overrelaxation as well as some methods from nonlinear programming. In all cases they present numerical experiments related to stability and error analysis of the corresponding algorithms.
Reviewer: Constantin Popa (Constanţa)

Cited in 39 Documents

MSC:

65F10 Iterative numerical methods for linear systems
08A72 Fuzzy algebraic structures

Keywords:

fully fuzzy linear systems; iterative solution; stability; error analysis; Jacobi method; Gauss-Seidel method; successive overrelaxation

Software:

mctoolbox
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\textit{M. Dehghan} et al., Chaos Solitons Fractals 34, No. 2, 316--336 (2007; Zbl 1144.65021)
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References:

[1] Abbod, M. F.; von Keyserlingk, D. G.; Linkens, D. A.; Mahfouf, M., Survey of utilisation of fuzzy technology in medicine and healthcare, Fuzzy Sets Syst, 120, 331-349 (2001)
[2] Avdelas, G.; Hadjidimos, A., Optimum accelerated overrelaxation method in a special case, Math Comput, 36, 183-187 (1981) · Zbl 0463.65020
[3] Bazaraa, M. S.; Sherali, H. D.; Shetty, C. M., Nonlinear programming, theory and algorithms (1993), John Wiley and Sons: John Wiley and Sons New York · Zbl 0774.90075
[4] Buckley, J. J.; Qu, Y., Solving systems of linear fuzzy equations, Fuzzy Sets Syst, 43, 33-43 (1991) · Zbl 0741.65023
[5] Caldas, M.; Jafari, S., \(h\)-Compact fuzzy topological spaces, Chaos, Solitons & Fractals, 25, 229-232 (2005) · Zbl 1070.54501
[6] Datta, B. N., Numerical linear algebra and applications (1995), Brooks/Cole Pub.: Brooks/Cole Pub. California
[8] DeMarr, R., Nonnegative matrices with nonnegative inverses, Proc Amer Math Soc, 35, 307-308 (1972) · Zbl 0257.15002
[9] Dubois, D.; Prade, H., Operations on fuzzy numbers, Int J Syst Sci, 9, 613-626 (1978) · Zbl 0383.94045
[10] Dubois, D.; Prade, H., Systems of linear fuzzy constraints, Fuzzy Sets Syst, 3, 37-48 (1980) · Zbl 0425.94029
[11] Dubois, D.; Prade, H., Fuzzy sets and systems: theory and applications (1980), Academic Press: Academic Press New York · Zbl 0444.94049
[12] El Naschie, M. S., From experimental quantum optics to quantum gravity via a fuzzy Kahler manifold, Chaos, Solitons & Fractals, 25, 969-977 (2005) · Zbl 1070.81118
[13] Evans, D. J., The extrapolated modified Aitken iteration method for solving elliptic difference equations, Comput J, 6, 193-201 (1963) · Zbl 0119.33404
[14] Friedman, M.; Ming, M.; Kandel, A., Fuzzy linear systems, Fuzzy Sets Syst, 96, 201-209 (1998) · Zbl 0929.15004
[15] Giachetti, R. E.; Young, R. E., Analysis of the error in the standard approximation used for multiplication of triangular and trapezoidal fuzzy numbers and the development of a new approximation, Fuzzy Sets Syst, 91, 1-13 (1997) · Zbl 0915.04003
[16] Gvozdik, A. A., Solution of fuzzy equations, UDC, 518.9, 60-67 (1985) · Zbl 0593.65031
[17] Hadjidimos, A., Accelerated overrelaxation method, Math Comput, 32, 149-157 (1978) · Zbl 0382.65015
[18] Hageman, L. A.; Young, D. M., Applied iterative methods (1981), Academic Press: Academic Press New York · Zbl 0459.65014
[19] Hansen, E., Interval arithmetic in matrix computations, Part I, SIAM J Numer Anal, 2, 308-320 (1965) · Zbl 0135.37303
[20] Hansen, E., Interval arithmetic in matrix computations, Part II, SIAM J Numer Anal, 4, 1-9 (1967) · Zbl 0209.46601
[21] Hansen, E. R., Interval forms of Newton’s method, Computing, 20, 153-163 (1978) · Zbl 0384.65019
[22] Hansel, E.; Walster, W. G.; Hansen, E. R.; Walster, G. W., Global optimization using interval analysis (2003), Marcel Dekker: Marcel Dekker USA
[23] Higham, N. J., Accuracy and stability of numerical algorithms (1996), SIAM: SIAM Philadelphia · Zbl 0847.65010
[25] Kreinovich, V.; Lakeyev, A. V.; Rohn, J.; Kahl, P. T., Computational complexity and feasibility of data processing and interval computations. Computational complexity and feasibility of data processing and interval computations, Series: Appl Optimiz, 10 (1998), Springer · Zbl 0945.68077
[26] Madalena Martins, M., On an accelerated overrelaxation iterative method for linear systems with strictly diagonally dominant matrix, Math Comput, 152, 1269-1273 (1980) · Zbl 0463.65021
[27] Missirils, N. M.; Evans, D. J., On the convergence of some generalized preconditioned iterative methods, SIAM J Numer Anal, 18, 591-596 (1981) · Zbl 0464.65018
[28] Rao, S. S.; Chen, L., Numerical solution of fuzzy linear equations in engineering analysis, Int J Numer Methods Eng, 42, 829-846 (1998) · Zbl 0911.73077
[29] Stefanini, L.; Sorini, L.; Letizia Guerra, M., Simulation of fuzzy dynamical systems using the LU-representation of fuzzy numbers, Chaos, Solitons & Fractals, 29, 638-652 (2006) · Zbl 1142.37372
[30] Wagenknecht, M.; Hampel, R.; Schneider, V., Computational aspects of fuzzy arithmetics based on Archimedean t-norms, Fuzzy Sets Syst, 123, 49-62 (2001) · Zbl 0997.65071
[31] Young, D. M., Iterative solution of large linear systems (1971), Academic Press: Academic Press New York · Zbl 0204.48102
[32] Zadeh, L. A., Fuzzy sets, Inform Control, 8, 338-353 (1965) · Zbl 0139.24606
[33] Zhang, H.; Liao, X.; Yu, J., Fuzzy modeling and synchronization of hyperchaotic systems, Chaos, Solitons & Fractals, 26, 835-843 (2005) · Zbl 1093.93540
[34] Zhao, R.; Govind, R., Solutions of algebraic equations involving generalized fuzzy numbers, Inform Sci, 56, 199-243 (1991) · Zbl 0726.65048
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