The stability problem for fuzzy bidirectional associative memories
The fuzzy bidirectional associative memories (FBAMs) are studied in this paper. It is shown that any FBAM based on the S-T composition is globally stable if both S and T are triangular norms or triangular conorms. When T is an upper semicontinuous triangular norm, some necessary and sufficient conditions are established in such a way that the FBAMs based on the max-T composition are globally stable, and the stable states and the equilibria of the FBAMs were studied. When T is a continuous triangular norm, it is proved that the sequence of reverberation states of the learning FBAM is nonincreasing. (C) 2002 Elsevier Science B.V. All rights reserved.
triangular norm fuzzy relation fuzzy equation global stability eigenfuzzy set