Structural Optimization of Fuzzy Regression Models with Minimizing of the Predictive Modeling Errors on the Test Sampling

摘要

The article considers the problem of structural optimization of regression models within the concept of fuzzy systems. As a result of its decisions are determined by a model of optimal complexity. They have good generalizing abilities and do not carry the effect of retraining. Various criteria for selection of models are presented, which are based on splitting the sample into the training and test parts. As rules systems, the Takagi-Sugeno model was used. When dividing the domain of input factors, trapezoidal membership functions were used. The problem of splitting a sample into a test and training part is proposed to be solved using the D-optimal experimental design method. At the same time, the main attention is paid to using the criterion of regularity as a selection criterion for the models, which is a forecast error on the test part of the sample. To evaluate the efficiency of this criterion and the procedure for splitting the sample into a training and test part, a computational experiment was performed. The computational experiment was carried out on model data. The results of the computational experiments are given in separate tables and figures. The control of the accuracy of the tested models was based on the mean square error (MSE). The computational experiment showed that the regularity criterion, based on the use of a test sample obtained by the procedure of optimal experiment planning, allows to determine the model of optimal complexity.