An input-output clustering approach to the synthesis of ANFIS networks

A useful neural network paradigm for the solution of function approximation problems is represented by adaptive neuro-fuzzy inference systems (ANFIS). Data driven procedures for the synthesis of ANFIS networks are typically based on clustering a training set of numerical samples of the unknown function to be approximated. Some serious drawbacks often affect the clustering algorithms adopted in this context, according to the particular data space where they are applied. To overcome such problems, we propose a new ANFIS synthesis procedure where clustering is applied in the joint input-output data space. Using this approach, it is possible to determine the consequent part of Sugeno first-order rules and therefore the hyperplanes characterizing the local structure of the function to be approximated. Successively, the fuzzy antecedent part of each rule is determined using a particular fuzzy min-max classifier, which is based on the adaptive resolution mechanism. The generalization capability of the resulting ANFIS architecture is optimized using a constructive procedure for the automatic determination of the optimal number of rules. Simulation tests and comparisons with respect to other neuro-fuzzy techniques are discussed in the paper, in order to assess the efficiency of the proposed approach.