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.

I. Introduction

Based on the available knowledge about system models, there are two basic types of systems: model-known systems and model-unknown systems. The model-known systems are those whose models can be obtained from some scientific laws (e.g., physical laws) whereas, the model-unknown systems are those whose real models are impossible or difficult to obtain. A lot of real life systems are model-unknown, especially for social, economic, and marketing fields as the mechanism of these systems are too complicated to be known. In these situations, we face the model-unknown systems. In recent years, fuzzy systems have been proved one of the most powerful methodologies to model the model-unknown systems. The fundamental reason that fuzzy systems can be used as models of model-unknown systems is that fuzzy systems are universal approximators [1], [2], [12], [27], [34]–[37]. That is, for any given system whose mathematical model is unknown but continuous, a fuzzy system that can approximate the given system to the required accuracy can be obtained by choosing the parameters of the fuzzy system properly. For modeling a given model-unknown system by a fuzzy system model, the main task is to find or identify the parameters of the fuzzy model based on the available information such that the resulting fuzzy estimator can represent the given system as good as possible.