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

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.