Neural fuzzy relational systems with a new learning algorithm

Fuzzy relational systems can represent symbolic knowledge in a formal numer ical (subsymbolic) framework, with the aid of fuzzy relation equations. The disadvantage of this methodology is the need for a priori knowledge in ord er to construct the fuzzy relation equation. In this paper, a neural networ k model is proposed in order to represent fuzzy relational systems without the need of the construction of the fuzzy relation equation. The network en sures the ideal perfect recall of fuzzy associative memories when the a pos teriori constructed fuzzy relation equation has a non-empty solution set. I t is actually a single layer of generalized neurons (compositional neurons) that perform the sup-t-norm composition, An on-line learning algorithm ada pting the weights of its interconnections is incorporated into the neural n etwork. These weights are actually the elements of the fuzzy relation repre senting the fuzzy relational system. The algorithm is based on the knowledg e about the topographic structure of the respective fuzzy relation. (C) 200 0 IMACS/Elsevier Science B.V. All rights reserved.