Journal of Soft Computing and Applications

Volume 2013 (2013), Article ID jsca-00012, 11 Pages

doi: 10.5899/2013/jsca-00012


Research Article


The pseudo inverse matrices to solve general fully fuzzy linear systems


S. Moloudzadeh1 *, P. Darabi1, H. Khandani2


1Department of Mathematics, Science and Research Branch, Islamic Azad university, Tehran, Iran.

2Department of Mathematics, Mahabad Branch, Islamic Azad University, Mahabad, Iran.


* Corresponding author. Email address: saeidmoloudzadeh@gmail.com; Tel:+989143891299


Received: 23 September 2012; Accepted: 23 October 2012


Copyright © 2013 S. Moloudzadeh, P. Darabi and H. Khandani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this paper, we present a solution of an arbitrary general fully fuzzy linear systems $(FFLS)$ in the form \widetilde{A}\otimes \widetilde{x}=\widetilde{b}. Where coefficient matrix \widetilde{A} is an {m \times n} fuzzy matrix and all of this system are elements of LR type fuzzy numbers. Our method discuss a general FFLS (square or rectangle fully fuzzy linear systems with trapezoidal or triangular LR fuzzy numbers). To do this, we transform fully fuzzy linear system in to two crisp linear systems, then obtain the solution of this two systems by using the pseudo inverse matrix method. Numerical examples are given to illustrate our method.


Keywords: Fully fuzzy linear system (FFLS); Overdetermined linear system; Pseudo inverse matrix; Underdetermined linear.

References

  1. S. Abbasbandy, M. Otadi, M. Mosleh, mnimal solution of general dual fuzzy linear systems, Chaos Solitons and Fractals, 37 (2008) 1113-1124.


  2. T. Allahviranloo, S. Salahshour, M. Khezerloo, Maximal- and minimal symmetric solutions of fully fuzzy linear systems, Journal of Computational and Applied Mathematics, 235 (2011) 4652-4662.


  3. T. Allahviranloo, S. Salahshour, Bounded and symmetric solutions of fully fuzzy linear systems in dual form, Procedia Computer Science, 3 (2011) 1494-1498.


  4. B. Asady, S. Abbasbandy, M. Alavi, Fuzzy general linear systems, Applied Mathematics and Computation, 169 (2005) 34-40.


  5. M. Dehghan, B. Hashemi, M. Ghatee, Computational methods for solving fully fuzzy linear systems, Applied Mathematics and Computation, 179 (2006) 328-343.


  6. M. Dehghan, B. Hashemi, Solution of the fully fuzzy linear systems using the decomposition procedure, Applied Mathematics and Computation, 182 (2006) 1568-1580.


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


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


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


  10. B. N. Data, Numerical linear Algebra and Applications, cole publisher company-first edition, (1995).


  11. C. D. Meyer, Matrix Analysis and Applied linear Algebra, siam, (2000).


  12. K. Wang, B. Zheng, In consistent fuzzy linear systems, Applied Mathematics and Computation, 181 (2006) 937-981.


  13. B. Zheng, K. Wang, General fuzzy linear systems, Applied Mathematics and Computation, 181 (2006) 1276-1286.