An application of incline matrices in dynamic analysis of generalized fuzzy bidirectional associative memories

Fuzzy Sets and Systems

Volumn 158, Issue 12, 2007, Pages 1340-1347

  Han, Song Chol ^a,b   Gu, Yun Dong ^c   Li, Hong Xing ^b  

^a KIM IL SUNG UNIVERSITY   (North Korea)

^b BEIJING NORMAL UNIVERSITY   (China)

^c NORTH CHINA ELECTRIC POWER UNIVERSITY   (China)

Author keywords

Algebra; Convergence; Equilibrium; FBAM; Fuzzy relations; Incline; Incline matrix; Stability; Stable state

Indexed keywords

FUZZY RELATIONS; INCLINE MATRIX;

CONVERGENCE OF NUMERICAL METHODS; EIGENVALUES AND EIGENFUNCTIONS; FUZZY SETS; SYSTEMS ENGINEERING;

ASSOCIATIVE STORAGE;

EID: 34247129565     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2007.02.002     Document Type: Article

References (29)

1. Ahn S.S. Permanents over inclines and other semirings. Pure Math. Appl. 8 2-4 (1997) 147-154
2. Ahn S.S., and Kim H.S. R-maps and L-maps in inclines. Far East J. Math. Sci. 1 5 (1999) 797-804
3. Cao Z.Q. Eigenvectors of fuzzy matrices under incline operations. Fuzzy Math. 6 4 (1986) 53-56
4. Cao Z.Q., Kim K.H., and Roush F.W. Incline Algebra and Applications (1984), Wiley, New York
5. Cechlarova K. Powers of matrices over distributive lattices-a review. Fuzzy Sets and Systems 138 (2003) 627-641
6. Cheng Q.S., and Fan Z.T. The stability problem for fuzzy bidirectional associative memories. Fuzzy Sets and Systems 132 1 (2002) 83-90
7. Duan J.S. The transitive closure. convergence of powers and adjoint of generalized fuzzy matrices, Fuzzy Sets and Systems 145 (2004) 301-311
8. Dudek W., Hong S.M., and Jun Y.B. Fuzzy set theory applied to incline algebras. Demonstratio Math. 37 1 (2004) 35-44
9. Z.T. Fan, Q.S. Cheng, A survey on the powers of fuzzy matrices and FBAMs, Internat. J. Comput. Cognition 〈http://www.YangSky.com/yangijcc.htm〉 2(2) (2004) 1-25.
10. Fan Z.T., and Zhong Y.X. The convergence of the fuzzy bidirectional associative memories. Acta Electron. Sinica 28 4 (2000) 1-4 (in Chinese)
11. Golan J.S. Semirings and Their Applications (1999), Kluwer Academic Publishers, Dordrecht
12. Han S.C., and Li H.X. Indices and periods of incline matrices. Linear Algebra Appl. 387 (2004) 143-165
13. Han S.C., and Li H.X. Invertible incline matrices and Cramer's rule over inclines. Linear Algebra Appl. 389 (2004) 121-138
14. Han S.C., and Li H.X. The semigroup of incline Hall matrices. Linear Algebra Appl. 390 (2004) 183-196
15. Han S.C., and Li H.X. Some conditions for matrices over an incline to be invertible and general linear group on an incline. Acta Math. Sinica 21 5 (2005) 1093-1098
16. Han S.C., and Li H.X. Power sequence of lattice matrices with ∧ - ∨ composition. Southeast Asian Bull. Math. 29 (2005) 873-886
17. Han S.C., Li H.X., and Gu Y.D. Standard eigenvectors of incline matrices. Linear Algebra Appl. 389 (2004) 235-248
18. Han S.C., Li H.X., and Wang J.Y. On nilpotent incline matrices. Linear Algebra Appl. 406 (2005) 201-217
19. Kim C.B., and Kim B.N. A note on the incline algebras. Far East J. Math. Sci. 12 1 (2004) 23-39
20. Kim K.H., and Roush F.W. Inclines of algebraic structures. Fuzzy Sets and Systems 72 (1995) 189-196
21. Kim K.H., Roush F.W., and Markowsky G. Representation of inclines. Algebra Colloq. 4 4 (1997) 461-470
22. Kim K.H., and Roush F.W. Inclines and incline matrices: a survey. Linear Algebra Appl. 379 (2004) 457-473
23. Klement E.P., Mesiar R., and Pap E. Triangular Norms (2000), Kluwer, Dordrecht
24. Kosko B. Fuzzy associated memories. In: Kandel A. (Ed). Fuzzy Expert Systems (1987), Addison-Wesley, Reading, MA
25. Kosko B. Bidirectional associative memories. IEEE Trans. Systems Man Cybernet. 18 1 (1988) 49-60
26. Lee S.C., and Lee E.T. Fuzzy sets and neural networks. J. Cybernet. 4 (1974) 83-103
27. Lee S.C., and Lee E.T. Fuzzy neural networks. Math. Biosci. 23 (1975) 151-177
28. Liu P.Y., and Li H.X. Fuzzy Neural Network Theory and Application (2004), World Scientific, Singapore
29. Tan Y.J. On the powers of matrices over a distributive lattice. Linear Algebra Appl. 336 (2001) 1-14