Designing ANFIS with Self-Extraction of Rules

First order Takagi-Sugeno model is mainly used in the consequent part of ANFIS models enabling ease of implementation and fast training due to the linearity in the consequent parameters. The input space is then partitioned starting from a well known number of partitions. For complex systems, fuzzy clustering of the input feature space is often used in order to gather data which may have some "similarities" or may represent some system´s specificities, forming then the rules for an ANFIS model. We present in this work a new approach for designing ANFIS models where rules are extracted by means of a fuzzy clustering technique of the input feature space and polynomial functions with various orders are used in the consequent part. An algorithm for adapting the consequent part structure to the extracted rules is presented. Tested on a non linear dynamic system, the proposed approach yields very good results in terms of approximation accuracy, outperforming ANFIS with first order Takagi-Sugeno models.