DOI
10.34229/KCA2522-9664.25.6.4
UDC 51.681.3
O.I. Provotar
Taras Shevchenko National University of Kyiv, Kyiv, Ukraine,
a.i.provotar@knu.ua
O.O. Suprun
Taras Shevchenko National University of Kyiv, Kyiv, Ukraine,
oleh.suprun@knu.ua
ELEMENTS OF THE PROBABILITY THEORY OF FUZZY EVENTS
WITH ENGINEERING APPLICATIONS
Abstract. The use of approaches of probability theory and probabilistic processes when considering fuzzy sets, which are widely used in expert diagnostic systems, as well as when designing controllers, is proposed. A formula for calculating the probability of a fuzzy event is presented, which is based on the idea of identifying fuzzy events as fuzzy sets. A number of applications of this formula are considered by analogy with the classical theory of probability, namely, conditional, complete, geometric probability, etc., as well as the use of Bayes and Bernoulli formulas. The obtained approaches are relevant for constructing engineering systems and models in both scientific and industrial spheres.
Keywords: рrobability theory, fuzzy sets, fuzzy events, total probability.
full text
REFERENCES
- 1. Rutkowski L. Metody i techniki sztucznej inteligencji. Warszava: Wydawnictwo Naukove PWN, 2009. 452 s. (in Polish).
- 2. Ross T.J. Fuzzy logic with engineering application. University of New Mexico, USA: John Wilej & Sons, LTD, 2004. 628 p.
- 3. Zadeh L.A. Fuzzy sets. Information and Control. 1965. Vol. 8. Р. 338–353.
- 4. Buckley J.J., Siler W.. Fuzzy expert systems and fuzzy reasoning. Hoboken, New Jersey: John Wiley & Sons, Inc., 2005. 402 p.
- 5. Gnedenko B. Course in Probability Theory [in Ukrainian]. Kyiv: URSS, 2005. 448 p.
- 6. Provotar O.I., Provotar O.O. Fuzzy probabilities of fuzzy events. Kibernetika i sistemnyj analiz. 2020. Vol. 56, No. 2. P. 3–13.
- 7. Provotar O.I., Provotar O.O. On the approximate calculation of the probability measure of a fuzzy event. Kibernetyka ta systemnyi analiz. 2021. Vol. 57, No. 1. P. 3–11.
- 8. Buckley J.J. Fuzzy probabilities. Heidelberg: Physica-Verlag, 2003. 162 p.
- 9. Provotar O.I. About the calculation of fuzzy events probabilities by means of Interval arithmetics. IEEE International Conference on Advanced Trends in Information Theory (ATIT). (18–20 December, 2019, Kyiv, Ukraine). 2019. P. 360–364. https://doi.org/10.1109/ATIT49449.2019.9030438.
