Finding the probability distribution of states in the fuzzy markov systems

Authors

DOI:

https://doi.org/10.15587/1729-4061.2017.97144

Keywords:

Markov and semi-Markov systems, complex criterion, deviation of solution from the modal one, compactness measure of solution

Abstract

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.

Author Biographies

Lev Raskin, National Technical University «Kharkiv Polytechnic Institute» Kyrpychova str., 2, Kharkiv, Ukraine, 61002

Doctor of Technical Sciences, Professor, Head of Department

Department of Computer Monitoring and logistics

Oksana Sira, National Technical University «Kharkiv Polytechnic Institute» Kyrpychova str., 2, Kharkiv, Ukraine, 61002

Doctor of Technical Sciences, Professor

Department of Computer Monitoring and logistics

Tetiana Katkova, Berdyansk University of Management and Business Svobody str., 117 а, Berdyansk, Ukraine, 71118

PhD, Assistant Professor

Department of information systems and technologies

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Published

2017-04-24

How to Cite

Raskin, L., Sira, O., & Katkova, T. (2017). Finding the probability distribution of states in the fuzzy markov systems. Eastern-European Journal of Enterprise Technologies, 2(4 (86), 32–38. https://doi.org/10.15587/1729-4061.2017.97144

Issue

Vol. 2 No. 4 (86) (2017): Mathematics and Cybernetics - applied aspects

Section

Mathematics and Cybernetics - applied aspects

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Copyright (c) 2017 Lev Raskin, Oksana Sira, Tetiana Katkova

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