On infinite products of fuzzy matrices

SIAM Journal on Matrix Analysis and Applications

Volumn 22, Issue 4, 2001, Pages 1190-1203

  Guu, Sy Ming ^a   Lur, Yung Yih ^b   Pang, Chin Tzong ^a  

^a YUAN ZE UNIVERSITY   (Taiwan)

^b FORTUNE INSTITUTE OF TECHNOLOGY   (Taiwan)

Author keywords

Boolean matrices; Convergence of infinite products of fuzzy matrices; Fuzzy matrices

Indexed keywords

EID: 0035597887     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479800366021     Document Type: Article

References (20)

1. I. DAUBECHIES AND J. C. LAGARIAS, Sets of matrices all infinite products of which converge, Linear Algebra Appl, 161 (1992), pp. 227-263.
2. D. DUBOIS AND H. PRADE, Fuzzy Sets and Systems: Theory and Applications, Academic Press, San Diego, 1980.
3. Z.-T. FAN AND D.-F. LIU, Convergence of the power sequence of a nearly monotone increasing fuzzy matrix, Fuzzy Sets and Systems, 88 (1997), pp. 363-372.
4. Z.-T. FAN AND D.-F. LIU, On the oscillating power sequence of a fuzzy matrix, Fuzzy Sets and Systems, 93 (1998), pp. 75-85.
5. S.-M. GUU, H.-H. CHEN, AND C.-T. PANG, Convergence of products of fuzzy matrices, Fuzzy Sets and Systems, to appear.
6. D. J. HARTFIEL, On infinite products of nonnegative matrices, SIAM J. Appl. Math, 26 (1974), pp. 297-301.
7. H. HASHIMOTO, Convergence of powers of a fuzzy transitive matrix, Fuzzy Sets and Systems, 9 (1983), pp. 153-160.
8. K. H. KIM, Boolean Matrix Theory and Applications, Marcel Dekker, New York, 1982.
9. K. H. KIM AND F. W. ROUSH, Fuzzy matrix theory, in Analysis of Fuzzy Information, Vol. 1, J. C. Bezdek, ed., CRC Press, Boca Raton, FL, 1987, pp. 107-129.
10. G. J. KLIR AND T. A. FOLGER, Fuzzy Sets, Uncertainty, and Information, Prentice-Hall, Englewood Cliffs, NJ, 1988.
11. W. KOLODZIEJCZYK, Convergence of powers of s-transitive fuzzy matrices, Fuzzy Sets and Systems, 26 (1988), pp. 127-130.
12. J.-X. LI, Periodicity of powers of fuzzy matrices, Fuzzy Sets and Systems, 48 (1992), pp. 365-369.
13. J.-X. LI, Convergence of powers of controllable fuzzy matrices, Fuzzy Sets and Systems, 62 (1994), pp. 83-88.
14. M. MIZUMOTO, Fuzzy Theory and Its Applications, Science Publications, 1988 (in Japanese).
15. S. V. OVCHINNIKOV, Structure of fuzzy relations, Fuzzy Sets and Systems, 6 (1981), pp. 169-195.
16. F. ROBERT, Discrete Iterations: A Metric Study, Springer-Verlag, Berlin, 1986.
17. D. ROSENBLATT, On the graphs of finite idempotent Boolean relation matrices, J. Res. Nat. Bur. Standards B, 67B (1963), pp. 249-259.
18. B. DE SCHUTTER AND B. DE MOOR, On the sequence of consecutive powers of a matrix in a Boolean algebra, SIAM J. Matrix Anal. Appl., 21 (1999), pp. 328-354.
19. M. G. THOMASON, Convergence of powers of a fuzzy matrix, J. Math. Anal. Appl., 57 (1977), pp. 476-480.
20. L. A. ZADEH, Similarity relations and fuzzy orderings, Inform. Sci., 3 (1971), pp. 177-200.