Decomposition Method for Solving Fully Fuzzy Linear Systems

Subject Areas : Operation Research

M. Mosleh ¹ , M. Otadi ² , A. Khanmirzaei ³

1 - Department of mathematics, Islamic Azad University,Firuozkooh Branch,Firuozkooh,Iran
2 - Department of mathematics, Islamic Azad University,Kermanshah Branch,kermanshah,Iran
3 - Department of mathematics, Islamic Azad University,Firuozkooh Branch,Firuozkooh,Iran

Received: 2009-04-07 Accepted : 2009-06-07 Published : 2010-07-01

Keywords: Fuzzy system, Symmetric and triangular decomposition, Symmetric positive definite and triangular decomposition,

Abstract :

In this paper, we investigate the existence of a positive solution of fully fuzzy linear equation systems. This paper mainly to discuss a new decomposition of a nonsingular fuzzy matrix, the symmetric times triangular (ST) decomposition. By this decomposition, every nonsingular fuzzy matrix can be represented as a product of a fuzzy symmetric matrix S and a fuzzy triangular matrix T.

References:

[1] Abbasbandy S., Jafarian A., and Ezzati R., Conjugate gradient method for fuzzy symmetric positive definite system of linear equations, Appl. Math. Comput. 171, 1184-1191, 2005.

[2] Abbasbandy S., Ezzati R., and Jafarian A., LU decomposition method for solving fuzzy system of linear equations, Appl. Math. Comput. 172, 633-643, 2006.

[3] Abbasbandy S., Nieto J. J., and Alavi M., Tuning of reachable set in one dimensional fuzzy differential inclusions, Chaos, Solitons &Fractals 26, 1337-1341, 2005.

[4] Abbasbandy S., Otadi M., and Mosleh M., Minimal solution of general dual fuzzy linear systems, Chaos Solutions &Fractals, in press.

[5] Abbasbandy S., Otadi M., and Mosleh M., Numerical solution of a system of fuzzy polynomials by fuzzy neural network, Inform. Sci., In press.

[6] Asady B., Abbasbandy S., and Alavi M., Fuzzy general linear systems,Appl.Math.Comput.169, 34-40, 2005.

[7] Caldas M., and Jafari S., -Compact fuzzy topological spaces, Chaos Solutions &Fractals 25, 229-232, 2005.

[8] Dehghan M., Hashemi B., and Ghatee M., Solution of the fully fuzzy linear systems using iterative techniques, Chaos Solution & Fractals, in press.

[9] Demarr R., Nonnegative matrices with nonnegative inverses. Proc Amer Math Soc, 35, 307-308, 1972.

[10] Dubois D., and Prade H., Operations on fuzzy numbers, J. Systems Sci., 9, 613-626, 1978.

[11] Dbois D., and Prade H., Systems of linear fuzzy constraints. Fuzzy Sets and Systems, 3, 37-48, 1980.

[12] Elnaschie M. S., A review of E-infinity theiry and mass spectrum of high energy particle physics, Chaos, Solutions &Fractals 19, 209-236, 2004.

[13] Elnaschie M. S., The concepts of E infinity: An elementary introduction to the Cantorian-fractal theory of quantum physics, Chaos, Solution & Fractals 22, 495-511, 2004.

[14] Elnaschie M. S., On a fuzzy Kahler manifold which is consistent with the two slit experiment, Int. J. Nonlinear Science and Numerical Simulation, 6, 95-98, 2005.

[15] Elnaschie M. S., Elementary number theory in superstrings, loop quantum mechanics, twisters and E-infinity high energy physics, Chaos, Solutions & Fractals 27, 297-330, 2006.

[16] Elnaschie M. S., Superstrings, entropy and the elementary particles content of the standard model, Chaos, Solutions &Fractals 29, 48-54, 2006.

[17]   Feng G. and Chen G., Adaptive control of discrete – time chaotic systems: a fuzzy control approach, Chaos Solutions & Fractals 23, 459-467, 2005.

[18] Friedman M., Ming M., and Kandel A., Fuzzy linear systems, Fuzzy Sets and Systems 96(1998)201-209.

[19] Friedman, M. Ming M., and Kandel A., Duality in fuzzy linear systems, Fuzzy Sets and Systems 109(2000) 55-58.

[20] Golub G. H., and Yun J., Symmetric-triangular decomposition and its applications, Swets & Zeilinger, 42, 814-822, 2002.

[21] Jiang W., and Guo-Dong Q., and Bin D., Variable universe adaptive fuzzy control for chaotic system, Chaos Solutions & Fractals 24, 1075-1086, 2004.

[22] Kaufmann A., and Gupta M. M., Introduction Fuzzy Arithmetic, Van Nostrand Reinhold, New York, 1985.

[23] Muzzioli S., and Reynaerts H., Fuzzy linear systems of the form Fuzzy Sets and Systems, In press.

[24] Nozavi K., and Fazlpour B., Some consequences of space time fuzziness, Caos, Solutions & Fractals, in press.

[25] J.H.Park,Intuitionistic fuzzy metric spaces,Chaos Solutions & Fractals 22, 1039-1046, 2004.

[26] Tanaka Y., Mizuno Y., and T.Kado,Chaotic dynamics in the Fridman equation, Chaos Solutions & Fractals 24, 407-422, 2005.

[27]   Wang X., Zhong Z., and Ha M., Iteration algorithms for solving a system of fuzzy linear equations, Fuzzy Sets and Systems 119, 121-128, 2001.

[28]   Zadeh L. A., The concept of a linguistic variable and its application to approximate reasoning, Inform. Sci. 8, 199-249, 1975.