ANFIS synthesis by hyperplane clustering

Adaptive Neuro-Fuzzy Inference Systems (ANFIS) are one of the most popular type of fuzzy neural networks. An usual approach to the synthesis of ANFIS networks is based on clustering a training set of numerical examples of the unknown mapping to be approximated, Several different clustering procedures can be adopted for this purpose, but most of them are affected by serious drawbacks. In the present paper, we propose a novel clustering approach in order to overcome these problems. It determines directly the consequent part of ANFIS rules; successively, the fuzzy antecedent part of each rule is determined by using a Min-Max classifier. The resulting ANFIS architecture is optimized by means of a constructive procedure, which we further propose in this paper. It allows to determine automatically the optimal number of rules by applying well-known results of learning theory. Simulation tests and comparison with other techniques are discussed in order to prove the validity of the proposed approach.