Fuzzy logical bidirectional associative memory

Abstract

We introduce a bidirectional associative memory (BAM). The stable points of the memory are naturally interpreted as (non-sharp) concepts - the memory performs association of extents and intents of concepts. We show that this memory is stable and that the set of all stable points forms a complete lattice. We propose a learning algorithm and prove that it enables perfect learning provided the training set forms a consistent conceptual structure. Examples demonstrating the results are presented. Unlike in the case of other associative memories (M. Arbib (Ed.), The Handbook of Brain Theory and Neural Networks, MIT Press, London, 1995) the formal apparatus, architecture, dynamics and convergence proof etc. are based on algebraic structures of fuzzy logic in narrow sense.