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Article:

# Fuzzy modeling and genetic optimization of the time series in the intellectual technical diagnostics system

Keywords:

E.N. Egov – Assistant, Department «Information Systems», Ulyanovsk State Technical University E-mail: e.egov@ulstu.ru N.G. Yarushkina – Dr. Sc. (Eng.), Professor, Department «Information Systems», Ulyanovsk State Technical University E-mail: jng@ulstu.ru D.V. Yashin – Post-graduate Student, Department «Information Systems», Ulyanovsk State Technical University E-mail: taurusrulez@yandex.ru

Time series analysis plays an important role in solving many problems of the modern world. At the moment, there is a need to develop methods of forecasting, which would ensure obtaining an adequate assessment of changes and make timely decisions based on the received parameters. Since most real events are characterized by some uncertainty, then each observation time series can be associated with a fuzzy variable with a membership function, thereby obtaining a fuzzy time series. This paper presents two solutions to the problem of data mining by algorithmization prediction by using fuzzy entropy measures of time series (BP), and genetic optimization transform F-. The first method is based on statistical analysis of BP changes when moving from one point to another. The change is fixed by a pair of parameters. At each point defined by the values of these parameters is determined by the situation, the values of the parameters of a pair of one point change in the transition to the next point. On the basis of statistical information about the frequency of occurrence of each situation is determined by the probability of occurrence of a situation. When forecasting the determined values of the parameters shown in the last point, and a situation in which these parameters are the same starting point of the situation and the likelihood of this situation, the greatest of them all, whose initial value corresponds to the last point. As a pair of parameters are the values of the fuzzy labels and basic tendencies of each point of the series. To improve the accuracy of forecasting another pair of parameters has been added - value of the measure of entropy for the membership function and the value of the entropy measure for the deviation from the forecast of trends. Since the resulting entropy values are numeric measures, it may be the complexity associated with a large number of situations in the unlikely occurrence of value again. To solve this problem, each measure of entropy is defined linguistic scale, on which are recorded the values of parameters. When calculating the value of a target point used by all the four parameters that complement each other, thereby improving the accuracy of prediction. The second method modifies the F transformation method by optimizing the partition of the original time series basis functions using a specially designed genetic algorithm. F transformation method was developed by I. Perfilyeva. It can be attributed to the methods of fuzzy approximation based on fuzzy transformation. This article presents a modified method of F transformation  the method of asymmetric F conversion. When using the original F transform vertices of the original time series basic functions are covered, and most often in the optimization of the partition used only parameters such as the number of features and the number of vertices covered by basic functions. Our method asymmetric F conversion so named due to the fact that it was decided to adjust the number of vertices covered each basis function separately and form the basis functions to the number of vertices covered function of the left and right of the top, selected as a center function, It might be different. genetic algorithm has been developed to optimize the partition of the original time series basis functions. The chromosome of this algorithm is coded information about what is covered by the basic function of each vertex of the time series. special operators crossover and mutation have been developed. After splitting time series basis functions are calculated approximated equidistant values of the time series by the inverse F conversion, which will later be used in the prediction of time series based on autoregression model.
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