Convergence of generalized fuzzy bidirectional associative memory neural networks with thresholds

Based on the fuzzy operator “ν” and a t-norm T, a generalized dynamical model named the fuzzy bidirectional associative memory neural networks (ν -T FBAMs) with thresholds is set up. It shows that every equilibrium of the system is Lyapunov stable if T satisfies Lipschitz condition. It is proved that the existence of the indices of the matrix U, which is the product of the system connection fuzzy matrices, is sufficient condition for the system to be strongly convergent, and the convergence in finite steps of U is sufficient condition for the system to be strongly stable in finite steps. Also we give some stable states and equilibriums of the system by the standard eigenvectors of U.

I. Introduction

Since bidirectional associative memory neural networks (BAMs) were first introduced by Kosko in [1], they have been successfully applied to various fields such as pattern recognition, image process and automatic control [2]–[5]. These applications depend heavily on the dynamical behaviors of the networks, such as stability, convergence, etc. Therefore various interesting results on the stability and other behaviors of fuzzy bidirectional associative memory neural networks (FBAMs) have been derived. Fan and Zhong [6] studied fuzzy bidirectional associative memory neural networks based on the max-min composition , and established some necessary and sufficient conditions for the convergence of the FBAMs. Cheng and Fan [7] considered the stability of the FBAMs based on the composition ( FBAMs). Han [9] studied the incline-valued FBAMs (L-FBAMs), and proved that the strong convergence and strong stability of the L-FBAMs are equivalent to the existence of indices and the convergence in finite steps of the product matrices of connection matrices of the L-FBAMs. The stable states and equilibriums of the L-FBAMs were also given in [9].