Поведение конечно-нестационарных детерминированных автоматов в нечеткой среде

Aleksandra Yu. Ponomareva

doi:10.21638/11701/spbu01.2016.105

Authors

Aleksandra Yu. Ponomareva St. Petersburg State University, Universitetskaya nab., 7-9, St. Petersburg, 199034, Russian Federation;

DOI:

https://doi.org/10.21638/11701/spbu01.2016.105

Abstract

In this paper we propose a method of finding optimal control of generalized deterministic abstract automaton, which structure is given at an arbitrary finite graph, functioning in the fuzzy given environment. The control is found for achieving fuzzy goal, which is given as a fuzzy set in any fixed finite vertex of the structural graph of the automaton. A solution of the problem consists of two stages, the first of which gives maximally possible degree of the achieving fuzzy goal depending from the way from initial vertex of a graph to fixed, and the second stage allows to construct a set of input words, providing an achieving this goal on chosen way. In conclusion, an example of application of proposed method of construction regular expressions controlling sequences to a given abstract finite-nonstationary deterministic automaton is given. Refs 5. Figs 2.

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References

Литература

1. Мосягина Е. Н., Чирков М. К. Оптимальное управление периодически-нестационарными автоматными моделями в нечетких условиях (Теория автоматных моделей). СПб.: СПбГУ, 2014. 144 с.

2. Пономарева А. Ю., Чирков М. К. Оптимизация обобщенных конечно-нестационарных минимаксных нечетких автоматов // Вестник С-Петерб. ун-та. Сер. 1. Т. 1 (59). Вып. 4. 2014. С. 561-570.

3. Кофман А. Введение в теорию нечетких множеств. М.: Радио и связь, 1982. 432 с.

4. Zadeh L. A. Fuzzy Sets // Information and Control. Vol. 8. 1965. P. 338-353.

5. URL: http://www.unn.ru/pages/e-library/methodmaterial/ﬁles/alekseev_zakharova.pdf

References

1. Mosyagina E.N., Chirkov M.K., An optimal control of periodically-nonstationary automata models in the fuzzy conditions (Theories of automata models) (St. Petersburg, SPbU, 2014, 144 p.) [in Russian].

2. Ponomareva A.Yu., Chirkov M.K., “Optimization of generalized finite-nonstationary minimax fuzzy automata”, Vestnik of St.Petersburg University. Series 1 1(59), issue 4, 561–570 (2014) [in Russian].

3. Kaufmann A., Introduction a la th´eorie des sour-ensembles flous (Paris, Masson, 1977).

4. Zadeh L.A., “Fuzzy Sets”, Information and Control 8, 338–353 (1965).

5. http://www.unn.ru/pages/e-library/methodmaterial/files/alekseev_zakharova.pdf [in Russian].