Modeling a kind of fuzzy systems using fuzzy entropy

For dynamic systems with complex, ill-conditioned or strongly nonlinear characteristics, fuzzy modeling is a very useful technique. However, it is hard to determine the fuzzy rules and fuzzy space structure. For good identification accuracy, more fuzzy input regions need to be partitioned. As a result, the number of fuzzy rules and identified parameters are exponentially increased and the generalization performance of learning algorithms is bad. In the paper, to solve these problems, we represent the system's model with Yager's (1996) relational partitioning of fuzzy rules, then propose a new self-tuning method of fuzzy modeling by means of fuzzy clustering and fuzzy entropy. Based on fuzzy clustering, the fuzzy systems' basic structure and parameters can be constructed. Using fuzzy entropy of fuzzy partitions of fuzzy systems as a constraint, we design an original learning algorithm to optimize the performance of fuzzy systems. To demonstrate the effectiveness and high efficiency of the proposed method, we give an example, which shows that this method is very satisfactory and robust with the initial knowledge of the system.