Inverse of a fuzzy matrix of fuzzy numbers

International Journal of Computer Mathematics

Volumn 86, Issue 8, 2009, Pages 1433-1452

  Dehghan, Mehdi ^a   Ghatee, Mehdi ^a   Hashemi, Behnam ^a,b  

^a AMIRKABIR UNIVERSITY OF TECHNOLOGY   (Iran)

^b SHIRAZ UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

inverse; Degree of regularity; Extension principle; Fuzzy arithmetic operators; Fuzzy inverse; Fuzzy matrix; Interval matrix; Natural cubic splines

Indexed keywords

-INVERSE; DEGREE OF REGULARITY; EXTENSION PRINCIPLES; FUZZY ARITHMETICS; FUZZY INVERSE; FUZZY MATRIX; INTERVAL MATRIX; NATURAL CUBIC SPLINES;

FUZZY RULES; INTERPOLATION; INVERSE PROBLEMS;

MATRIX ALGEBRA;

EID: 70449563198     PISSN: 00207160     EISSN: 10290265     Source Type: Journal    
DOI: 10.1080/00207160701874789     Document Type: Article

References (50)

1. M.B. Allen and E.L. Isaacson, Numerical Analysis for Applied Sciences, JohnWiley and Sons, Inc., NewYork, 1997.
2. J.J. Buckley andY. Qu, Solving systems of linear fuzzy equations, Fuzzy Sets Syst. 43 (1991), pp. 33-43.
3. J.J. Buckley, T. Feuring, and Y. Hayashi, Solving fuzzy equations using evaluationary algorithms and neural nets, Soft Comput. 6 (2002), pp. 116-123.
4. H.H. Cho, Regular fuzzy matrices and fuzzy equations, Fuzzy Sets Syst. 105 (1999), pp. 445-451.
5. M.Dehghan and B. Hashemi, Iterative solution of fuzzy linear systems,Appl. Math. Comput. 175 (2006), pp. 645-674.
6. ---, Solution of the fully fuzzy linear systems using the decomposition procedure, Appl. Math. Comput. 182 (2006), pp. 1568-1580.
7. ---, Determination of the degrees of P-property and nonneg-ative invertibility for a fuzzy matrix, Int. J. Approx. Reason. 46 (2007), pp. 98-108.
8. M. Dehghan, M. Ghatee, and B. Hashemi, Some computations on fuzzy matrices, Submitted for publication.
9. M. Dehghan, B. Hashemi, and M. Ghatee, Solution of the fully fuzzy linear systems using iterative techniques, Chaos, Solitons Fractals 37 (2007), pp. 316-336.
10. R. DeMarr, Nonnegative matrices with nonnegative inverses, Proc. Am. Math. Soc. 35 (1972), pp. 307-308.
11. D. Dubois and H. Prade, Operations on fuzzy numbers, Int. J. Syst. Sci. 9 (1978), pp. 613-626.
12. ---, Systems of linear fuzzy constraints, Fuzzy Sets Syst. 3 (1980), pp. 37-48.
13. ---, Fuzzy Sets and Systems: Theory and Applications, Academic Press, NewYork, 1980.
14. L. El Ghaoui, Inversion error, condition number, and approximate inverses of uncertain matrices, Linear Algebra Appl. 343-344 (2002), pp. 171-193.
15. R.E. Giachetti and R.E. Young, Analysis of the error in the standard approximation used for multiplication of triangular and trapezoidal fuzzy numbers and the development of a new approximation, Fuzzy Sets Syst. 91 (1997), pp. 1-13.
16. ---, A parametric representation of fuzzy numbers and their arithmetic operators, Fuzzy Sets Syst. 91 (1997), pp. 185-202.
17. G.H. Golub and C.F. Van Loan, Matrix Computations, Johns Hopkins University Press, Baltimore, 1989.
18. E. Hansen, Interval arithmetic in matrix computations, Part I, SIAM J. Numer. Anal. 2 (1965), pp. 308-320.
19. ---, Interval arithmetic in matrix computations, Part II, SIAM J. Numer. Anal. 4 (1967), pp. 1-9.
20. B. Hashemi, Topics in fuzzy numerical linear algebra, M.Sc. Thesis, Amirkabir University of Technology (Tehran Polytechnic), Tehran, April 2006.
21. H. Hashimoto, Subinverses of fuzzy matrices, Fuzzy Sets Syst. 12 (1984), pp. 155-168.
22. J. Herzberger and D. Bethke, On two algorithms for bounding the inverse of and interval matrix, Interval Comput. 1 (1991), pp. 44-53.
23. H.N. Ismail and N.N. Morsi, Fuzzy rank of a fuzzy matrix, Fuzzy Sets Syst. 41 (1991), pp. 243-249.
24. C. Jansson, Calculation of exact bounds for the solution set of linear interval systems, Linear Algebra Appl. 251 (1997), pp. 321-340.
25. C. Jansson and J. Rohn, An algorithm for checking regularity of interval matrices, SIAM J. Matrix Anal. Appl. 20 (1999), pp. 756-776.
26. L. Jaulin, et al., Applied Interval Analysis, With Examples in Parameter and State Estimation, Robust Control and Robotics, Springer-Verlag, London, U.K., 2001.
27. R.B. Kearfott and V. Kreinovich, Applications of Interval Computations, Kluwer Academic Publishers, Dordrecht/Boston/London, 1996.
28. K.H. Kim and F.W. Roush, Generalized fuzzy matrices, Fuzzy Sets Syst. 4 (1980), pp. 293-315.
29. D. Kincaid andW. Cheney, Numerical Analysis Mathematics of Scientific Computing, Brooks/Cole, California, 1991.
30. V. Kreinovich, Optimal finite characterization of linear problems with inexact data, Reliab. Comput. 11 (2005), pp. 479-489.
31. V. Kreinovich, et al., Computational Complexity and Feasibility of Data Processing and Interval Computations, Kluwer Academic Publishers, Netherlands, 1998.
32. J. Kuttler, A fourth-order finite-difference approximation for the fixed membrance eigenproblem, Math. Comput. 25 (1971), pp. 237-256.
33. R.E. Moore, Method and Application of Interval Analysis, SIAM, Philadelphia, 1979.
34. A. Neumaier, Interval Methods for Systems of Equations, Cambridge University Press, Cambridge, 1990.
35. H.T. Nguyen and V. Kreinovich, Nested intervals and sets: concepts, relations to fuzzy sets, and applications, in Applications of Interval Computations, R.B. Kearfott et al., eds., Kluwer Academic Publishers, Netherlands, 1996, pp. 254-290.
36. M. Oussalah and J. De Schutter, Approximated fuzzy LR computations, Inform. Sci. 153 (2003), pp. 155-175.
37. C.T. Pang, Simultaneously controllable fuzzy matrices, Comput. Math. Appl. 50 (2005), pp. 1647-1658.
38. S. Poljak and J. Rohn, Radius of nonsingularity, Res. Rep. KAM Series, Charles University, 1988, pp. 88-117.
39. G. Rex and J. Rohn, Sufficient conditions for regularity and singularity of interval matrices, SIAM J. Matrix Anal. Appl. 20 (1998), pp. 437-445.
40. J. Rohn, Inverse-positive interval matrices, Z. Angew. Math. Mech. 67 (1987), pp. 492-493.
41. ---, Systems of linear interval equations, Linear Algebra Appl. 126 (1989), pp. 39-78.
42. ---, Interval matrices: Singularity and real eigenvalues, SIAM J. Matrix Anal. Appl. 14 (1993), pp. 82-91.
43. ---, Inverse interval matrix, SIAM J. Numer. Anal. 30 (1993), pp. 864-870.
44. ---, Checking properties of interval matrices, Tech. Rep. 686 of Charles University, 1996.
45. ---, Regularity of interval matrices and theorems of the alternatives, Reliab. Comput. 12 (2006), pp. 99-105.
46. S.M. Rump, Almost sharp bounds for the componentwise distance to the nearest singular matrix, Linear Multilinear Algebra 42 (1998), pp. 93-108.
47. M. Sakawa, Fuzzy Sets and Interactive Multiobjective Optimization, Plenum Press, NewYork and London, 1973.
48. M.Wagenknecht, R. Hampel, and V. Schneider, Computational aspects of fuzzy arithmetics based on Archimedean t-norms, Fuzzy Sets Syst. 123 (2001), pp. 49-62.
49. X.Wang and E. Kerre, Reasonalble properties for the ordering of fuzzy quantities(I), Fuzzy Sets Syst. 118 (2001), pp. 375-385. (Pubitemid 33592816)
50. L.A. Zadeh, Fuzzy sets, Inform. Control 8 (1965), pp. 338-353.