Exact and approximate solutions of fuzzy LR linear systems: New algorithms using a least squares model and the abs approach

Iranian Journal of Fuzzy Systems

Volumn 7, Issue 2, 2010, Pages 1-18

  Ghanbari, R ^a   Mahdavi Amiri, N ^b   Yousefpour, R ^c  

^a FERDOWSI UNIVERSITY OF MASHHAD   (Iran)

^b SHARIF UNIVERSITY OF TECHNOLOGY   (Iran)

^c UNIVERSITY OF MAZANDARAN   (Iran)

Author keywords

ABS algorithm; Fuzzy linear system; Fuzzy LR solution; Least squares approximation

Indexed keywords

EID: 77958493481     PISSN: 17350654     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (25)

1. J. Abaffy, C. Broyden and E. Spedicato, A class of direct methods for linear systems, Nu- merische Mathematik, 45 (1984), 361-376.
2. J. Abaffy and E. Spedicato, ABS projection algorithms: mathematical techniques for linear and nonlinear equations, Ellis Horwood, Chichester, 1989.
3. S. Abbasbandy and M. Alavi, A method for solving fuzzy linear system, Iranian Journal of Fuzzy Systems, 2 (2005), 37-43.
4. F. Abramovich, M. Wagenknecht and Y. I. Khurgin, Solution of LR-type fuzzy systems of linear algebraic equations, Busefal, 35 (1988), 86-99.
5. R. Bulrisch and J. Stoer, Introduction to numerical analysis (texts in applied mathematics), 2nd edition, Springer, 1992.
6. J. J. Buckley and Y. Qu, Solving systems of linear fuzzy equations, Fuzzy Sets and Systems, 43 (1991), 33-43.
7. D. Dubois and H. Prade, Fuzzy sets and systems theory and applications, Academic Press, New York, 1980.
8. E. Egervary, On rank-diminishing operations and their applications to the solution of linear equations, ZAMP, 9 (1960), 376-386.
9. H. Esmaeili, N. Mahdavi-Amiri and E. Spedicato, A class of ABS algorithms for Diophantine linear systems, Numerische Mathematik, 91 (2001), 101-115.
10. M. Friedman, M. Ma and A. Kandel, Fuzzy linear systems, Fuzzy Sets and Systems, 96 (1998), 201-209.
11. R. Fuller, On stability in possibilistic linear equality systems with Lipschitzian fuzzy numbers, Fuzzy Sets and Systems, 34 (1990), 347-353.
12. M. Khorramizadeh and N. Mahdavi-Amiri, Integer extended ABS algorithms and possible control of intermediate results for linear Diophantine systems, 4OR, 7(2) (2009), 145-167.
13. M. Ma, M. Friedman and A. Kandel, Duality in fuzzy linear systems, Fuzzy Sets and Systems, 109 (2000), 55-58.
14. G. H. Golub and C. F. Van Loan, Matrix computations, Baltimore, MD, 3rd edition, Johns Hopkins University Press, 1996.
15. N. Mahdavi-Amiri and S. H. Nasseri, Duality results and a dual simplex method for linear programming problems with trapezoidal fuzzy variables, Fuzzy Sets and System, 158 (2007), 1961-1978.
16. H. R. Maleki, M. Tata and M. Mashinchi, Linear programming with fuzzy variables, Fuzzy Sets and Systems, 109 (2000), 21-33.
17. H. Mine, Nonnegative matrices, Wiley, New York, 1988.
18. 1, Fuzzy Sets and Systems, 157 ( 2006), 939-951.
19. H. T. Nguyen and E. A. Walker, A first course in fuzzy logic, Chapman & Hall, 2000.
20. S. Nicolai and E. Spedicato, A bibliography of the ABS methods, Optimization Methods and Software, 8 (1997), 171-183.
21. E. Spedicato, E. Bodon, A. D. Popolo and N. Mahdavi-Amiri, ABS methods and ABSPACK for linear systems and optimization: A review, 4OR, 1 (2003), 51-66.
22. E. Spedicato, Z. Xia and L. Zhang, ABS algorithms for linear equations and optimization, Journal of Computational and Applied Mathematics, 124 (2000), 155-170.
23. A. Vroman, G. Deschrijver and E. Kerre, Solving systems of linear fuzzy equations by parametric functions-an improved algorithm, Fuzzy Sets and Systems, 158 (2007), 1515-1534. (Pubitemid 46764390)
24. X. Wang, Z. Zhong and M. Ha, Iteration algorithms for solving a system of fuzzy linear equations, Fuzzy Sets and Systems, 119 (2001), 121-128.
25. H. J. Zimmermann, Fuzzy set theory and its applications, Third ed., Kluwer Academic, Norwell, 1996.