STRUCTURAL OPTIMIZATION OF FUZZY REGRESSION MODELS WITH MINIMIZATION OF A FORECAST
ERROR ON A TRAINING AND TEST SAMPLE 

Popov Aleksandr Aleksandrovich, Doctor of engineering sciences, professor, sub-department of theoretical and applied informatics, Novosibirsk State Technical University (20 Karla Marksa avenue, Novosibirsk, Russia), a.popov@corp.nstu.ru
Kholdonov Abdurakhmon Abdulloevich, Postgraduate student, Novosibirsk State Technical University (20 Karla Marksa avenue, Novosibirsk, Russia), firuz_530_11_29@mail.ru

519.23

10.21685/2072-3059-2018-2-1

Background. The paper considers the problem of string optimization of regression models within the concept of fuzzy systems (Fuzzy Systems). Structural optimization of regression models implies the solution of the problem of determining the model of optimal complexity. The model of optimal complexity has good generalizing abilities and does 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.
Materials and Methods. As a method of estimating unknown parameters, the least-squares method is used in the so-called global version. In this case, a joint evaluation of the whole set of unknown parameters is carried out. 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 stability as a selection criterion for the models, which is a forecast error on the test
part of the sample.
Results. 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. For the computational experiment, the corresponding software was developed.
The computational experiment was carried out on model data. The piecewise linear dependence on the input factor was used as the model of the data generator.
Discussion. 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).
Conclusion. 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.

D-optimal plan, regularity criterion, least-squares method, centerof-mass method, Takagi-Sugeno model, fuzzy system, training sample, optimal experiment planning, parameter estimation, regression model, system of normal equations, test sample

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