V. V. Borisov, Y. G. Boyarinov, M. I. Dli, V. I. Michenko

The method of designing of fuzzy semi-Markov models is considered, in which: probabilities of conditions and times of stay of system in the corresponding conditions are replaced with fuzzy numbers (fuzzy sets); for calculation of fuzzy variables (probabilities of conditions and times of stay of system in the corresponding conditions) fuzzy mappings are used on the basis of fuzzy rules-based or relational models; operations of summation, product and division are replaced with the expanded fuzzy operations of summation, product and division of fuzzy numbers. Statement of optimization problem with use fuzzy semi-Markov models is offered. The method of the decision fuzzy optimization problem with use fuzzy semi-Markov models is developed. At the first stage of a method, the mappings of fuzzy variables (probabilities of conditions and times of stay of system in the corresponding conditions) are set on the basis of fuzzy rules-based or relational models. This stage is finished by designing of model of an estimation of fuzzy probability of a finding of system in an analyzed condition. At the second stage, the decision of fuzzy optimization problem with use of the offered hybrid fuzzy model is realized. This method allows essentially to reduce labour intensiveness of the decision of fuzzy optimization problem. The example of use of a method for definition of optimum periodicity of checks of a condition of system is shown.