Determination of the degrees of P-property and nonnegative invertibility for a fuzzy matrix

International Journal of Approximate Reasoning

Volumn 46, Issue 1, 2007, Pages 98-108

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

^a AMIRKABIR UNIVERSITY OF TECHNOLOGY   (Iran)

^b SHIRAZ UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Fuzzy matrix; Interval matrix; Lyapunov diagonal stability; Nonnegative invertibility; P property

Indexed keywords

ALGORITHMS; LYAPUNOV FUNCTIONS; NUMBER THEORY;

INTERVAL MATRIX; LYAPUNOV DIAGONAL STABILITY; NONNEGATIVE INVERTIBILITY; P-PROPERTY;

FUZZY LOGIC;

EID: 34548132066     PISSN: 0888613X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijar.2006.09.002     Document Type: Article

References (30)

1. Berman A., and Hershkowitz D. Graph theoretical methods in studying stability. AMS Summer Research Conference on Linear Algebra and its Role in System Theory (1984), Bowdoin College, Maine
2. Buckley J.J., and Qu Y. Solving systems of linear fuzzy equations. Fuzzy Set. Syst. 43 (1991) 33-43
3. Cottle R.W., Pang J.S., and Stone R.E. The Linear Complementarity Problem (1992), Academic Press, New York
4. M. Dehghan, B. Hashemi, M. Ghatee, Solution of the fully fuzzy linear systems using the decomposition procedure, Appl. Math. Comput., in press.
5. M. Dehghan, B. Hashemi, M. Ghatee, Solution of the fully fuzzy linear systems using iterative techniques, Chaos, Solitons & Fractals, in press.
6. M. Dehghan, M. Ghatee, B. Hashemi, Inverse of a fuzzy matrix of fuzzy numbers, submitted for publication.
7. Dubois D., and Prade H. Systems of linear fuzzy constraints. Fuzzy Set. Syst. 3 (1980) 37-48
8. Dubois D., and Prade H. Fuzzy Sets and Systems: Theory and Applications (1980), Academic Press, New York
9. Fiedler M., and Ptak V. Some generalizations of positive definiteness and monotonicity. Numer. Math. 9 (1966) 163172
10. Gale D., and Nikaido H. The Jacobian matrix and global univalence of mappings. Math. Ann 19 (1965) 81-93
11. Griffin K., and Tsatsomeros M. Principal Minors, Part I: a method for computing all the principal minors of a matrix. Lin. Alg. Appl. 419 (2006) 107-124
12. B. Hashemi, Topics in fuzzy numerical linear algebra. M.Sc. Thesis, Amirkabir University of Technology (Tehran Polytechnic), Tehran, April 2006.
13. Hershkowitz D. Recent directions in matrix stability. Lin. Alg. Appl. 171 (1992) 161-186
14. Jaulin L., Kieffer M., Didrit O., and Walter E. Applied interval analysis, with examples in parameter and state estimation. Robust Control and Robotics (2001), Springer-Verlag, London
15. Kearfott R.B., and Kreinovich V. Applications of Interval Computations (1996), Kluwer Academic Publishers, Dordrecht
16. Kreinovich V., Lakeyev A., Rohn J., and Kahl P. Computational Complexity and Feasibility of Data Processing and Interval Computations (1997), Kluwer, Dordrecht
17. Kreinovich V. Optimal finite characterization of linear problems with inexact data. Reliable Comput. 11 (2005) 479-489
18. M. Mansour, Robust stability of interval matrices, in: Proc. 28th Conf. on Decision and Control, Tampa, FL, 1989, pp. 46-51.
19. Miller R.K., and Michel A.N. Ordinary Differential Equations (1982), Academic Press, New York
20. Neumaier A. Interval Methods for System of Equations (1990), Cambridge University Press, Cambridge
21. Nguyen H.T., and Kreinovich V. How stable is a fuzzy matrix?. Proc. 3rd IEEE Conf. Fuzzy Systems 2 (1994) 1023-1027
22. Nguyen H.T., and Kreinovich V. Nested intervals and sets: concepts, relations to fuzzy sets, and applications. In: Kearfott R.B., et al. (Ed). Applications of Interval Computations (1996), Kluwer Academic Publishers, Netherlands 254-290
23. Pena J.M. A class of P-matrices with applications to the localization of the eigenvalues of a real matrix. SIAM J. Matrix Anal. Appl. 22 (2001) 1027-1037
24. Rohn J. Inverse-positive interval matrices. Zeitschr. Angewandte Math. Mech. 67 (1987) 492-493
25. Rohn J. Systems of linear interval equations. Lin. Alg. Appl. 126 (1989) 39-78
26. J. Rohn, G. Rex, Interval P-matrices, Technical report No. 618, Academy of Science of the Czech Republic, December 1994.
27. J. Rohn, G. Rex, Checking properties of interval matrices, Technical report No. 686, Academy of Science of the Czech Republic, September 1996.
28. Schafer U. A linear complementarity problem with a P-matrix. SIAM Rev. 46 (2004) 189-201
29. Wang W.J., and Yan S.F. Stability confidence for fuzzy matrices. Fuzzy Set. Syst. 103 (1999) 507-511
30. Watkins D.S. Fundamentals of Matrix Computations (2002), Wiley-Interscience, New York