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

Authors:
Song-Chol Han;Yun-Dong Gu;Hong-Xing Li
Affiliations:
Department of Mathematics and Mechanics, Kim Il Sung University, Pyongyang, Democratic People's Republic of Korea and School of Mathematical Sciences, Beijing Normal University, Beijing 100875, PR ...;School of Mathematics and Physics, North China Electric Power University, Beijing 102206, PR China;School of Mathematical Sciences, Beijing Normal University, Beijing 100875, PR China
Venue:
Fuzzy Sets and Systems
Year:
2007

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Abstract

This paper studies an application of the incline matrix theory in the dynamic analysis of incline-valued fuzzy bidirectional associative memories (L-FBAMs, for short). It is proved that the strong convergence and the strong stability of an L-FBAM are equivalent to the existence of indices and the convergence in finite steps of the product matrices of connection incline matrices of the L-FBAM, respectively. It is shown that the convergence index, the period of limit-cycles, the stable states and equilibria of a strongly convergent L-FBAM are expressed by the indices, the periods and the standard eigenvectors of the product matrices of connection incline matrices of the L-FBAM, respectively.