A method for solving fully fuzzy linear system
الموضوعات :M. Mosleh 1 , S. Abbasbandy 2 , M. Otadi 3
1 - Department of Mathematics, Islamic Azad University, Firuozkooh Branch,
Firuozkooh, Iran.
2 - Department of Mathematics, Science and Research Branch, Islamic Azad
University, Tehran 14515/775, Iran.
3 - Department of Mathematics, Islamic Azad University, Firuozkooh Branch,
Firuozkooh, Iran.
الکلمات المفتاحية: Fuzzy linear system, fuzzy number, Minimal solution,
ملخص المقالة :
In this paper, a numerical method for nding minimal solution of a mn fullyfuzzy linear system of the form Ax = b based on pseudo inverse calculation,is given when the central matrix of coecients is row full rank or column fullrank, and where A~ is a non-negative fuzzy mn matrix, the unknown vectorx is a vector consisting of n non-negative fuzzy numbers and the constant b isa vector consisting of m non-negative fuzzy numbers.
[1] S. Abbasbandy, A. Jafarian and R. Ezzati, Conjugate gradient method for
fuzzy symmetric positive de nite system of linear equations, Appl. Math.
Comput. 171 (2005) 1184-1191.
[2] S. Abbasbandy, R. Ezzati and A. Jafarian, LU decomposition method for
solving fuzzy system of linear equations, Appl. Math. Comput. 172 (2006)
633-643.
[3] S. Abbasbandy, J.J. Nieto and M. Alavi, Tuning of reachable set in one
dimensional fuzzy di erential inclusions, Chaos, Solitons & Fractals 26
(2005) 1337-1341.
[4] S. Abbasbandy, M. Otadi and M. Mosleh, Minimal solution of general dual
fuzzy linear systems, Chaos Solitons & Fractals 37 (2008) 1113-1124.
[5] S. Abbasbandy, M. Otadi and M. Mosleh, Numerical solution of a system
of fuzzy polynomials by fuzzy neural network, Inform. Sci. 178 (2008)
1948-1960.
[6] T. Allahviranloo, Succesive over relaxation iterative method for fuzzy
system of linear equations, Appl. Math. Comput. 162 (2005) 189-196.
[7] T. Allahviranloo, Numerical methods for fuzzy system of linear equations,
Appl. Math. Comput. 155 (2004) 493-502.
[8] T. Allahviranloo, M. Afshar Kermani, Solution of a fuzzy system of linear
equation,Appl. Math. Comput.175 (2006) 519-531.
[9] B. Asady, S. Abbasbandy and M. Alavi, Fuzzy general linear systems,
Appl. Math. Comput. 169 (2005) 34-40.
[10] S. Barnet, Matrix Methods and Applications, Clarendon Press, Oxford,
1990.
[11] M. Caldas and S. Jafari, -Compact fuzzy topological spaces, Chaos
Solitons & Fractals 25 (2005) 229-232.
[12] M. Dehghan, B. Hashemi, M. Ghatee, Solution of the fully fuzzy linear
systems using iterative techniques, Chaos Solitons & Fractals 34 (2007)
316-336.
[13] M. Dehghan, B. Hashemi, M. Ghatee, Computational mathods for solving
fully fuzzy linear systems, Appl. Math. Comput. 179 (2006) 328-343.
[14] D. Dubois and H. Prade, Operations on fuzzy numbers, J. Systems Sci. 9
(1978) 613-626.
[15] D. Dubois and H. Prade, Systems of linear fuzzy constraints. Fuzzy Sets
Sys. 3 (1980) 37-48.
[16] G. Feng and G. Chen, Adaptive control of discrete-time chaotic systems:
a fuzzy control approach, Chaos Solitons & Fractals 23 (2005) 459-467.
[17] M. Friedman, Ma Ming and A. Kandel, Fuzzy linear systems, Fuzzy Sets
Sys. 96 (1998) 201-209.
[18] M. Friedman, Ma Ming and A. Kandel, Duality in fuzzy linear systems,
Fuzzy Sets and Sys. 109 (2000) 55-58.
[19] R. Goetschel, W. Voxman, Elementary calculus, Fuzzy Sets and Systems
18 (1986) 31-43.
[20] W. Jiang and Q. Guo-Dong and D. Bin, H1 Variable universe adaptive
fuzzy control for chaotic system, Chaos Solitons & Fractals 24 (2005)
1075-1086.
[21] A. Kaufmann and M. M. Gupta, Introduction Fuzzy Arithmetic, Van
Nostrand Reinhold, New York, 1985.
[22] S . Muzzioli and H. Reynaerts, Fuzzy linear systems of the form A1x+b1 =
A2x + b2, Fuzzy Sets and Sys. 157 (2006) 939-951.
[23] J. H. Park, Intuitionistic fuzzy metric spaces, Chaos Solitons & Fractals
22 (2004) 1039-1046.
[24] X. Wang, Z. Zhong and M. Ha, Iteration algorithms for solving a system
of fuzzy linear equations, Fuzzy Sets and Sys. 119 (2001) 121-128.
[25] L. A. Zadeh, The concept of a linguistic variable and its application to
approximate reasoning, Inform. Sci. 8 (1975) 199-249.
