Fuzzy Associative Memories from the Perspective of Mathematical Morphology

Mathematical morphology (MM) is a theory concerned with the processing and analysis of objects using operators based on topological and geometrical concepts. We speak of a fuzzy morphological associative memory (FMAM) when a fuzzy associative memory (FAM) model is equipped with neurons that correspond to an operator of mathematical morphology. This paper shows that several FAM models, including the FAMs of Kosko, most generalized FAMs of Chung and Lee, the FAM of Junbo et al., the max-min FAM with threshold, the fuzzy logic bidirectional associative memories, and the implicative fuzzy associative memories, belong to the FMAM class. Moreover, we present two strategies for deriving a new FMAM model from a given FMAM. These strategies are based on two duality relationship of mathematical morphology: duality with respect to negation and duality with respect to adjunction.