Neural fuzzy relational systems with a new learning algorithm

Fuzzy relational systems can represent symbolic knowledge in a formal numerical (subsymbolic) framework, with the aid of fuzzy relation equations. The disadvantage of this methodology is the need for a priori knowledge in order to construct the fuzzy relation equation. In this paper, a neural network model is proposed in order to represent fuzzy relational systems without the need of the construction of the fuzzy relation equation. The network ensures the ideal perfect recall of fuzzy associative memories when the a posteriori constructed fuzzy relation equation has a non-empty solution set. It is actually a single layer of generalized neurons (compositional neurons) that perform the sup-t-norm composition. An on-line learning algorithm adapting the weights of its interconnections is incorporated into the neural network. These weights are actually the elements of the fuzzy relation representing the fuzzy relational system. The algorithm is based on the knowledge about the topographic structure of the respective fuzzy relation.