Fuzzy Modeling with Local and Global Objectives

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 single rule, local fitness, while the entire model approximates the whole training set, global fitness. We propose an approach that is a modification of a current method for estimating the consequence portion of a TSK model with predefined membership functions. Then we propose a method for developing membership functions which partition the input space into regions that are more easily modeled in the TSK framework to provide consistent local behavior for all the rules of the model. This approach ensures that a TSK model constructed not only approximates the input-output mapping relationship in the data, but also captures insights about the local behavior of the model.