Knowledge bounded least squares method for the identification of fuzzy systems

This paper presents the knowledge bounded least squares method that uses both linguistic information (i.e., human knowledge and experience) and numerical data to identify fuzzy models. Based on the concept of fuzzy interval systems, the basic idea of this method is: first, to utilize all the available linguistic information to obtain a fuzzy interval system and then use the obtained fuzzy interval system to give the admissible model set (i.e., the set of all fuzzy models which are acceptable and reasonable from the point of view of linguistic information); second, to find a fuzzy model in the admissible fuzzy model set which best fits the available numerical data. It is shown that such a fuzzy model can be obtained by a quadratic programming approach. By comparing this method with the least squares method, it is proved that the fuzzy model obtained by the proposed method fits the real model better than the fuzzy model obtained by the least squares method.