Continuous Processes with Fuzzy States and Their Applications

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详细

Scalar characteristics of continuous processes with fuzzy states—mean and correlation functions—are introduced and studied. Their algebraic properties as well as some properties related to the differentiation and integration of fuzzy functions of a real argument are established. The dependence between the characteristics of a fuzzy signal at the input and output of a dynamic system described by a high-order differential equation with constant coefficients is shown.

作者简介

V. Khatskevich

Military Training and Research Center of the Air Force, Air Force Academy named after N.E. Zhukovsky and Yu.A. Gagarin

编辑信件的主要联系方式.
Email: vlkhats@mail.ru
Voronezh, Russia

参考

  1. Вентцель Е.С., Овчаров Л.А. Теория случайных процессов и их инженерные приложения. М.: Кнорус, 2016. 439 с.
  2. Аверкин А.Н. Нечеткие множества в моделях управления и искусственного интеллекта. М.: Наука, 1986.
  3. Buckley J.J., Eslami E., Feuring T. Fuzzy mathematics in economic and engineering. Heidelberg, N.Y.: Physica-Verl., 2002.
  4. Пегат А. Нечеткое моделирование и управление. М.: БИНОМ. Лаборатория знаний, 2015.
  5. Aumann R.J. Integrals of set-valued functions // J. Math. Anal. Appl. No. 12. 1965. P. 1-12.
  6. Puri M.L., Ralescu D.A. Di erential of fuzzy functions // J. Math. Anal. Appl. 91. 1983. P. 552-558.
  7. Kaleva O. Fuzzy di erential equations // Fuzzy sets and systems. V. 24. No. 3. 1987. P. 301-317.
  8. Seikkala S. On the fuzzy initial value problem // Fuzzy Sets and Systems. 24 (No. 3). 1987. P. 319-330.
  9. Hukuhara M. Integration des applications mesurables dont la valeur est un compact convexe // Func. Ekvacioj. No. 11. 1967. P. 205-223.
  10. Khatskevich V.L. Means, quasi-scalar product and covariance of fuzzy numbers. Journal of Physics: Conference Series. 2021, 1902(1), 012136.
  11. Jong Yeoul Park, Han H. Existence and uniqueness theorem for a solution of fuzzy di erential equations // International Journal of Mathematics and Mathematical Sciences, 1996. P. 271-280.
  12. Ahmad L., Farooq M., Abdullah S. Solving nth order fuzzy di erential equation by fuzzy Laplace transform // Ind. J. Pure Appl. Math. 2014.
  13. Мочалов И.А., Хрисат М.С., Шихаб Еддин М.Я. Нечеткие дифференциальные уравнения в задачах управления. Часть II. М.: Информационные технологии, т. 21, № 4. 2015.
  14. Деменков Н.П., Микрин Е.А., Мочалов И.А. Нечеткое оптимальное управление линейными системами. Часть 1. Позиционное управление. Информационные технологии. Т. 25, № 5. 2019.
  15. Esmi E., Sanchez D.E., Wasques V.F., de Barros L.C. Solutions of higher order linear fuzzy di erential equations with interactive fuzzy values // Fuzzy Sets and Systems. V. 419. 2021. P. 122-140.
  16. Далецкий Ю.Л., Крейн М.Г. Устойчивость решений дифференциальных ура нений в банаховом пространстве. М.: Наука, 1970.
  17. Красносельский М.А., Бурд В.Ш., Колесов Ю.С. Нелинейные почти периодические колебания. М.: Наука, 1970. 351 с.
  18. Dubois D., Prade H. The mean value of fuzzy number // Fuzzy sets and systems. 1987. P. 279-300.
  19. Kaleva O., Seikkala S. On fuzzy metric spaces // Fuzzy Sets and Systems. V. 12. 1984. P. 215-229.
  20. Fuller R., Majlender P. On weighted possibilistic mean value and variance of fuzzy numbers // Fuzzy sets and systems. V. 136. 2003. P. 363-374.

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