Solving fully fuzzy linear systems by using implicit Gauss–Cholesky algorithm

Saeid Abbasbandy1, Mir Sajjad Hashemi1
1Department of Mathematics, Imam Khomeini International University, Ghazvin, Iran

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J. Abaffy and E. Spedicato, The ABS Projection Algorithm: Mathematical Techniques for Linear and Non-Linear Systems, Ellis Horwood, Chichester, UK (1989).

J. Abaffy, M. Bertocchi, and A. Torriero, “Perturbations of M-matrices via ABS methods and its application to input–output analysis,” Appl. Math. Comput., 94, 145–170 (1998).

S. Abbasbandy, R. Ezzati, and A. Jafarian, “LU decomposition method for solving fuzzy system of linear equations,” Appl. Math. Comput., 172, 633–643 (2006).

S. Abbasbandy, M. Otadi, and M. Mosleh, “Minimal solution of general dual fuzzy linear systems,” Chaos, Solitons and Fractals, 37, 1113–1124 (2008).

T. Allahviranloo, N. A. Kiani, M. Barkhordary, and M. Mosleh, “Homomorphic solution of fully fuzzy linear systems,” Comput. Math. Model., 19, 282–291 (2008).

K. Amini, N. Mahdavi-Amiri, and M. R. Peyghami, “Extended reduced rank two Abaffian update schemes in the ABS-type methods,” Appl. Math. Comput., 185, 255–265 (2007).

M. Dehghan, B. Hashemi, and M. Ghatee, “Computational methods for solving fully fuzzy linear systems,” Appl. Math. Comput., 179, 328–343 (2006).

M. Dehghan, B. Hashemi, and M. Ghatee, “Solution of the fully fuzzy linear systems using iterative techniques,” Chaos, Solitons and Fractals, 34, 316–336 (2007).

D. Dubois and H. Prade, “Systems of linear fuzzy constraints,” Fuzzy Sets Syst., 3, 37–48 (1980).

D. Dubois and H. Prade, Fuzzy Sets and Systems: Theory and Applications, Academic Press, New York (1980).

M. Friedman, M. Ming, and A. Kandel, “Fuzzy linear systems,” Fuzzy Sets Syst., 96, 201–209 (1998).

E. E. Kerre, Fuzzy Sets and Approximate Reasoning, Xian Jiaotong University Press, Xian, People’s Republic of China (1999).

L.-P. Pang, E. Spedicato, Z.-Q. Xia, and W. Wang, “A method for solving the system of linear equations and linear inequalities,” Math. Comput. Modelling, 46, 823–836 (2007).

S. N. Sivanandam, S. Sumathi, and S. N. Deepa, Introduction to Fuzzy Logic Using MATLAB, Springer, Berlin–Heidelberg (2007).

L. Stefanini, L. Sorini, and G. M. Letizia, “Simulation of fuzzy dynamical systems using the LU-representation of fuzzy numbers,” Chaos, Solitons and Fractals, 29, 638–652 (2006).