OPTIMAL DESING OF THE EXPERIMENT WITH THE ACTIVE IDENTIFICATION OF FUZZY LINEAR REGRESSION MODELS

The problem of constructing linear regression models with respect to parameters and factors for the case of sufficiently wide ranges of variable variation is considered. It is proposed to use fuzzy linear regression models to restore the dependencies. The problem of a priori optimal experiment planning for fuzzy linear regression model’s identification is considered. At the same time, the area of determining the acting factors is divided into 2-3 fuzzy partitions. This model representation provides the restoration of dependencies which differ in different parts of the region determination of the input variables. The problem of construction and optimal planning of the experiment is formulated. A numerical algorithm in the form of gradient descent is used to construct optimal plans. The effectiveness of the obtained solutions is controlled by the implementation of the necessary and sufficient conditions of optimality. The problem of constructing an optimal plan is considered for the case of one and two factors with the number of fuzzy partitions 2 and 3. The analysis of the characteristics of optimal plans depending on the width of the intersection zone of fuzzy partitions is carried out. It is noted that with a decrease in the zone of intersection of fuzzy partitions, the efficiency of optimal plans increases, which affects the reduction of the determinants of dispersion matrices and their trace. Other characteristic features of the synthesized-optimal plans are noted. The conclusion is made about the efficiency of active identification of fuzzy linear regression models

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