文章基本信息

标题：Finding the probability distribution of states in the fuzzy markov systems
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作者：Lev Raskin ; Oksana Sira ; Tetiana Katkova 等
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：2017
卷号：2
期号：4
页码：32-38
DOI：10.15587/1729-4061.2017.97144
语种：English
出版社：PC Technology Center
摘要：A problem on finding the stationary distributions of probabilities of states for the Markov systems under conditions of uncertainty is solved. It is assumed that parameters of the analyzed Markov and semi-Markov systems (matrix of transition intensities, analytical description of distribution functions of the durations of being in states of the system before exiting, as well as a matrix of transition probabilities) are not clearly assigned. In order to describe the fuzziness, we employ the Gaussian membership functions, as well as functions of the type. The appropriate procedure of systems analysis is based on the developed technology for solving the systems of linear algebraic equations with fuzzy coefficients. In the problem on analysis of a semi-Markov system, the estimation of components of the stationary distribution of probabilities of states of the system is obtained by the minimization of a complex criterion. The criterion considers the measure of deviation of the desired distribution from the modal one, as well as the level of compactness of membership functions of the fuzzy result of solution. In this case, we apply the rule introduced for the calculation of expected value of fuzzy numbers. The criterion proposed is modified through the introduction of weight coefficients, which consider possible differences in the levels of requirements to different components of the criterion.
关键词：Markov and semi-Markov systems;complex criterion;deviation of solution from the modal one;compactness measure of solution