On fuzzy associative memory with multiple-rule storage capacity

Kosko's fuzzy associative memory (FAM) is the very first neural network model for implementing fuzzy systems. Despite its success in various applications, the model suffers from very low storage capacity, i.e., one rule per FAM matrix. A lot of hardware and computations are usually required to implement the model and, hence, it is limited to applications with small fuzzy rule-base. In this paper, the inherent property for storing multiple rules in a FAM matrix is identified. A theorem for perfect recalls of all the stored rules is established and based upon which the hardware and computation requirements of the FAM model can be reduced significantly. Furthermore, we have shown that when the FAM model is generalized to the one with max-bounded-product composition, single matrix implementation is possible if the rule-base is a set of semi-overlapped fuzzy rules. Rule modification schemes are also developed and the inference performance of the established high capacity models is reported through a numerical example.