Fuzzy modeling with local and global objectives

Most of the techniques for constructing fuzzy TSK models from data focus only on minimizing the error between the model's output and the training data; however, these approaches may result in a fuzzy TSK model where the interpretation of individual rules are misleading. The goal of our research is to develop a scheme for identifying TSK models whose individual rules approximate the training data covered by a rule (i.e., local fitness), while the entire model approximates the whole training set (i.e., global fitness). The proposed approach is evaluated empirically using two function approximation problems and two datasets. The results of these experiments suggest that the proposed approach can produce fuzzy TSK models with high interpretability without sacrificing accuracy. We first propose an approach that focuses on consequence estimation of the fuzzy rules. A Kalman Filter is initialized based on local fitness. The Kalman Filter then is used to identify the consequent parameters of TSK models by minimizing global fitness. We then refine the approach by focusing on the premise structure identification to increase local fitness of the fuzzy models.