期刊名称：Eastern-European Journal of Enterprise Technologies
印刷版ISSN：1729-3774
电子版ISSN：1729-4061
出版年度：2019
卷号：1
期号：4
页码：22-30
DOI：10.15587/1729-4061.2019.157085
语种：English
出版社：PC Technology Center
摘要：The modernization of the methods for identification of the state of objects under conditions of fuzzy input data, described by their membership functions, was performed. The selected direction of improvement of traditional methods is associated with the fundamental features of solving this problem under actual conditions of a small source data sample. Under these conditions, to solve the problem of state identification, it is advisable to transfer to the technology of description of source data, based on the mathematical apparatus of fuzzy mathematics and less demanding in terms of information. This transition required the development of new formal methods for solving specific tasks. In this case, the procedure for solution of the fuzzy system of linear algebraic equations was developed for multidimensional discriminant analysis. To solve the clustering problem, a special procedure of comparison of fuzzy distances between objects of clustering and centers of grouping was proposed. The selected direction of improvement of the traditional method for regression analysis was determined by impossibility of using the classical least squares method under conditions when all variables are described fuzzily. This fact led to the need to construct a special two-step procedure for solving the problem. In this case, the linear combination of the measure of distance of the sought-for solution from the modal one and the measures of compactness of membership function of the explained variable are minimized. The technology of fuzzy regressive analysis was implemented in the important practical case when the source fuzzy data are described by general membership functions of the (L-R) type. In addition, the analytic solution to the problem in the form of calculation formulas was obtained. The discussion showed that the modernization of the classical methods for solving the problem of the state identification, considering the fuzzy nature of representation of source data, made it possible to identify objects under actual conditions of a small sample of fuzzy source data.
关键词：fuzzy;multidimensional discriminate;cluster;regression analyses;technologies for reducing fuzzy problems to well-posed problems
