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Abbasbandy, S.; Otadi, M.; Mosleh, M.

Minimal solution of general dual fuzzy linear systems. (English) Zbl 1146.15002

Chaos Solitons Fractals 37, No. 4, 1113-1124 (2008).
Summary: Systems of fuzzy linear equations play a major role in several applications in various areas such as engineering, physics and economics. In this paper, we investigate the existence of a minimal solution of general dual systems of fuzzy linear equations. Two necessary and sufficient conditions for the existence of a minimal solution are given. Also, some examples in engineering and economy are considered.

Cited in 25 Documents

MSC:

15A06 Linear equations (linear algebraic aspects)
08A72 Fuzzy algebraic structures

Keywords:

dual systems of fuzzy linear equations
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\textit{S. Abbasbandy} et al., Chaos Solitons Fractals 37, No. 4, 1113--1124 (2008; Zbl 1146.15002)
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References:

[1] Abbasbandy, S.; Alavi, M., A method for solving fuzzy linear systems, Iranian J Fuzzy Syst, 2, 37-43 (2005) · Zbl 1104.15004
[2] Abbasbandy, S.; Alavi, M., A new method for solving symmetric fuzzy linear systems, Math Sci J Islamic Azad Univ Arak, 1, 55-62 (2005) · Zbl 1104.15004
[3] Abbasbandy, S.; Jafarian, A.; Ezzati, R., Conjugate gradient method for fuzzy symmetric positive definite system of linear equations, Appl Math Comput, 171, 1184-1191 (2005) · Zbl 1121.65311
[4] Abbasbandy, S.; Ezzati, R.; Jafarian, A., LU decomposition method for solving fuzzy system of linear equations, Appl Math Comput, 172, 633-643 (2006) · Zbl 1088.65023
[5] Abbasbandy, S.; Nieto, J. J.; Alavi, M., Tuning of reachable set in one dimensional fuzzy differential inclusions, Chaos, Solitons & Fractals, 26, 1337-1341 (2005) · Zbl 1073.65054
[6] Asady, B.; Abbasbandy, S.; Alavi, M., Fuzzy general linear systems, Appl Math Comput, 169, 34-40 (2005) · Zbl 1119.65325
[7] Barnet, S., Matrix methods and applications (1990), Clarendon Press: Clarendon Press Oxford
[8] Caldas, M.; Jafari, S., \(θ\)-Compact fuzzy topological spaces, Chaos, Solitons & Fractals, 25, 229-232 (2005) · Zbl 1070.54501
[9] Delves, L. M.; Mohamed, J. L., Computational methods for integral equations (1989), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0592.65093
[10] Dubois, D.; Prade, H., Operations on fuzzy numbers, J Syst Sci, 9, 613-626 (1978) · Zbl 0383.94045
[11] Elnaschie, M. S., A review of \(E\)-infinity theory and the mass spectrum of high energy particle physics, Chaos, Solitons & Fractals, 19, 209-236 (2004) · Zbl 1071.81501
[12] Elnaschie, M. S., The concepts of \(E\) infinity: an elementary introduction to the Cantorian-fractal theory of quantum physics, Chaos, Solitons & Fractals, 22, 495-511 (2004) · Zbl 1063.81582
[13] Elnaschie, M. S., On a fuzzy Kahler manifold which is consistent with the two slit experiment, Int J Nonlinear Sci Numer Simul, 6, 95-98 (2005)
[14] Elnaschie, M. S., Elementary number theory in superstrings, loop quantum mechanics, twisters and \(E\)-infinity high energy physics, Chaos, Solitons & Fractals, 27, 297-330 (2006) · Zbl 1148.11321
[15] Elnaschie, M. S., Superstrings, entropy and the elementary particles content of the standard model, Chaos, Solitons & Fractals, 29, 48-54 (2006) · Zbl 1098.81816
[16] Feng, G.; Chen, G., Adaptive control of discrete-time chaotic systems: a fuzzy control approach, Chaos, Solitons & fractals, 23, 459-467 (2005) · Zbl 1061.93501
[17] Friedman, M.; Ming, Ma; Kandel, A., Fuzzy linear systems, Fuzzy Sets Syst, 96, 201-209 (1998) · Zbl 0929.15004
[18] Freidman, M.; Ming, Ma; Kandel, A., Numerical solutions of fuzzy differential and integral equations, Fuzzy Sets Syst, 106, 35-48 (1999) · Zbl 0931.65076
[19] Friedman, M.; Ming, Ma; Kandel, A., Duality in fuzzy linear systems, Fuzzy Sets Syst, 109, 55-58 (2000) · Zbl 0945.15002
[20] Jiang, W.; Guo-Dong, Q.; Bin, D., \(H_∞\) variable universe adaptive fuzzy control for chaotic system, Chaos, Solitons & Fractals, 24, 1075-1086 (2005) · Zbl 1083.93013
[21] Kanfmann, A.; Gupta, M. M., Introduction fuzzy arithmetic (1985), Van Nostrand Reinhold: Van Nostrand Reinhold New York
[22] Kincaid, D.; Cheney, W., Numerical analysis, mathematics of scientific computing (1996), Brooks/Cole Publishing Co: Brooks/Cole Publishing Co Pacific Grove, CA · Zbl 0877.65002
[23] Ming, Ma; Friedman, M.; Kandel, A., A new fuzzy arithmetic, Fuzzy Sets Syst, 108, 83-90 (1999) · Zbl 0937.03059
[24] Muzzioli, S.; Reynaerts, H., Fuzzy linear systems of the form \(A_1x+b_1=A_2x+b_2\), Fuzzy Sets Syst, 157, 939-951 (2006) · Zbl 1095.15004
[25] Nozari, K.; Fazlpour, B., Some consequences of spacetime fuzziness, Chaos, Solitons & Fractals, 34, 224-234 (2007) · Zbl 1132.83306
[26] Park, J. H., Intuitionistic fuzzy metric spaces, Chaos, Solitons & Fractals, 22, 1039-1046 (2004) · Zbl 1060.54010
[27] Tanaka, Y.; Mizuno, Y.; Kado, T., Chaotic dynamics in the Friedman equation, Chaos, Solitons & Fractals, 24, 407-422 (2005) · Zbl 1070.83535
[28] Wang, X.; Zhong, Z.; Ha, M., Iteration algorithms for solving a system of fuzzy linear equations, Fuzzy Sets Syst, 119, 121-128 (2001) · Zbl 0974.65035
[29] Congxin, Wu.; Ming, Ma., On the integrals, series and integral equations of fuzzy set-valued functions, J Harbin Inst Technol, 21, 11-19 (1990) · Zbl 0970.26519
[30] Zadeh, L. A., The concept of a linguistic variable and its application to approximate reasoning, Inform Sci, 8, 199-249 (1975) · Zbl 0397.68071
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