Solution of the fully fuzzy linear systems using the decomposition procedure

Applied Mathematics and Computation

Volumn 182, Issue 2, 2006, Pages 1568-1580

  Dehghan, Mehdi ^a   Hashemi, Behnam ^a  

^a AMIRKABIR UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Fully fuzzy linear system (FFLS); Jacobi method; The Adomian decomposition method

Indexed keywords

APPROXIMATION THEORY; FUZZY SETS; ITERATIVE METHODS; MATHEMATICAL OPERATORS; MATRIX ALGEBRA; PROBLEM SOLVING;

ADOMIAN DECOMPOSITION METHOD; FULLY FUZZY LINEAR SYSTEM (FFLS); FUZZY NUMBERS; JACOBI METHOD;

LINEAR SYSTEMS;

EID: 33845225451     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2006.05.043     Document Type: Article

References (44)

1. Abbaoui K., and Cherruault Y. Convergence of Adomian's method applied to differential equations. Math. Comput. Model. 28 (1994) 103-110
2. Abdou M.A. Adomian decomposition method for solving the telegraph equation in charged particle transport. J. Quant. Spectrosc. Radiat. Transfer 95 (2005) 407-414
3. Alefeld G., and Schafer U. Iterative methods for linear complementarity problems with interval data. Computing 70 (2003) 235-259
4. Allahviranloo T. The Adomian decomposition method for fuzzy system of linear equations. Appl. Math. Comput. 163 (2005) 553-563
5. b4m. Available online: .
6. Babolian E., Biazar J., and Vahidi A.R. The decomposition method for system of linear equations and system of linear Volterra integral equations. Appl. Math. Comput. 147 (2004) 19-27
7. Babolian E., and Biazar J. On the order of convergence of Adomian method. Appl. Math. Comput. 130 (2002) 383-387
8. Bidik N., Konuralp A., Oraki Bek F., and Kucukarslan S. Solution of different type of the partial differential equation by differential transform method and Adomian's decomposition method. Appl. Math. Comput. 172 (2006) 551-567
9. Buckley J.J., and Qu Y. Solving systems of linear fuzzy equations. Fuzzy Sets Syst. 43 (1991) 33-43
10. Dehghan M. The use of Adomian decomposition method for solving the one-dimensional parabolic equation with non-local boundary specifications. Int. J. Comput. Math. 81 (2004) 25-34
11. Dehghan M., and Hashemi B. Iterative solution of fuzzy linear systems. Appl. Math. Comput. 175 (2006) 645-674
12. M. Dehghan, B. Hashemi, M. Ghatee, Computational methods for solving fully fuzzy linear systems, Appl. Math. Copmput., in press, doi:10.1016/j.amc.2005.11.124.
13. M. Dehghan, B. Hashemi, M. Ghatee, Solution of the fully fuzzy linear systems using iterative techniques, Chaos Solitons Fractals, in press.
14. Deif A. Sensitivity Analysis in Linear Systems (1986), Springer, Berlin, Heidelberg, New York, Tokyo
15. DeMarr R. Nonnegative matrices with nonnegative inverses. Proc. Am. Math. Soc. (1972) 307-308
16. Dubois D., and Prade H. Systems of linear fuzzy constraints. Fuzzy Sets Syst. 3 (1980) 37-48
17. Dubois D., and Prade H. Fuzzy Sets and Systems: Theory and Applications (1980), Academic Press, New York
18. Friedman M., Ming M., and Kandel A. Fuzzy linear systems. Fuzzy Sets Syst. 96 (1998) 201-209
19. Hansen E.R. Bounding the solution of interval linear equation. SIAM J. Numer. Anal. 29 (1992) 1493-1503
20. INTLAB. Available online: .
21. Jansson C., and Rohn J. An algorithm for checking regularity of interval matrices. SIAM J. Matrix Anal. Appl. 20 (1999) 756-776
22. Kuang J.-H., and Chen C.-J. Adomian decomposition method used for solving nonlinear pull-in behavior in electrostatic micro-actuators. Math. Comput. Model. 41 (2005) 1479-1491
23. Ma M., Friedman M., and Kandel A. Duality in fuzzy linear systems. Fuzzy Sets Syst. 109 (2000) 55-58
24. Mayer G. Comparison theorems for iterative methods based on strong splittings. SIAM J. Numer. Anal. 24 (1987) 215-227
25. 2. Fuzzy Sets Syst. 157 (2006) 939-951
26. S. Muzzioli, H. Reynaerts, Solving fuzzy systems of linear equations by a nonlinear programming method: a financial application, Eur. J. Oper. Res., in press.
27. Neumaier A. Interval Methods for System of Equations (1990), Cambridge University Press, Cambridge
28. Oettli W., and Prager W. Compatibility of approximate solution of linear equations with given error bounds for coefficients and right hand sides. Numer. Math. 6 (1964) 405-409
29. Oettli W. On the solution set of a linear system with inaccurate coefficients. SIAM J. Numer. Anal. 2 (1969) 115-118
30. Polyak B.T., and Nazin S.A. Interval solutions for interval algebraic equations. Math. Comput. Simulat. 66 (2004) 207-217
31. Rao S.S., and Chen L. Numerical solution of fuzzy linear equations in engineering analysis. Int. J. Numer. Meth. Eng. 42 (1998) 829-846
32. Rohn J. Systems of linear interval equations. Linear Algebra Appl. 126 (1989) 39-78
33. Rohn J. Solvability of systems of linear interval equations. SIAM J. Matrix Anal. Appl. 25 (2003) 237-245
34. Wagenknecht M., Hampel R., and Schneider V. Computational aspects of fuzzy arithmetics based on Archimedian t-norms. Fuzzy Sets Syst. 123 (2001) 49-62
35. Wang X., Zhong Z., and Ha M. Iteration algorithms for solving a system of fuzzy linear equations. Fuzzy Sets Syst. 119 (2001) 121-128
36. Young D.M. Iterative Solution of Large Linear Systems (1971), Academic Press, New York
37. Zadeh L.A. Fuzzy sets. Inform. Control 8 (1965) 338-353
38. Oussalah M., and De Schutter J. Approximated fuzzy LR computations. Inform. Sciences 153 (2003) 155-175
39. Wazwaz A.M. Construction of solitary wave solutions and rational solutions for the Kdv equation by Adomian decomposition method. Chaos, Solitons & Fractals 12 (2001) 2283-2293
40. M. Dehghan, M. Tatari, The use of Adomian decomposition method for solving problems in calculus of variations, Math. Probl. Eng. (2006), Article ID 65379, 1-12.
41. Dehghan M. The solution of a nonclassic problem for one-dimensional hyperbolic equation using the decomposition procedure. Int. J. Comput. Math. 81 (2004) 979-989
42. M. Dehghan, M. Ghatee, B. Hashemi, Some computations on fuzzy matrices, submitted for publication.
43. M. Dehghan, B. Hashemi, Determination of the odegrees of P-property and nonnegative invertibility for a fuzzy matrix, Submitted for publication.
44. B. Hashemi, Topics in Fuzzy Numerical Linear Algebra, M.Sc. Thesis, Amirkabir University of Technology (Tehran Polytechnic), Tehran, April 2006.