Global and local performance in fuzzy modeling

Most of the techniques for constructing fuzzy 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 model where individual rules are misleading. The goal of our research is to develop a scheme for identifying Takagi-Sugeno-Kang (TSK) models whose individual rules approximate the training data covered by a rule (local fitness), while the entire model approximates the whole training set (global fitness). We propose an approach that first initializes a Kalman filter based on local fitness. The Kalman filter then is used to identify the consequent parameters of TSK models by minimizing global fitness. We are motivated to use fuzzy models over other modeling paradigms to obtain insights about the local behavior of the model using IF-THEN rules which decompose a complex problem into readily understandable portions. If the local behavior of the model is not consistent with the system or underlying data, then the justification for modeling in a fuzzy logic framework is diminished to a degree if not entirely. We illustrate our approach using two model identification problems