About One Mathematical Model of Reliability and Safety of Complex Systems

  • Araz R. AlievEmail author
  • Vagif M. Mamedov
  • Mammad I. Seyidov
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1095)


A generalization of existing results of application of the fuzzy set theory to problems of reliability and safety of systems is considered. On the basis of the introduced fuzzy measure the mathematical model of reliability and safety of complex systems is developed.


Reliability Probability Fuzzy measure Technical operation Fuzzy-probabilistic event Safety Fuzzy model Fuzzy-probabilistic model 


  1. 1.
    Aliev, A.R., Mamedov, V.M., Gasimov, G.G.: Analysis and processing of information in economic problems. Crisp and fuzzy technologies. In: 13th International Conference on Theory and Application of Fuzzy Systems and Soft Computing, ICAFS 2018. Advances in Intelligent Systems and Computing, vol. 896, pp. 65–72. Springer, Cham (2019)Google Scholar
  2. 2.
    Aliev, R.A., Abdikiev, N.M., Shakhnazarov, M.M.: Production systems with artificial intelligence. Radio and Communication, Moscow (1990). (in Russian)Google Scholar
  3. 3.
    Aliev, R.A., Aliev, R.R.: Soft Computing and its Application. World Scientific, London (2001)CrossRefGoogle Scholar
  4. 4.
    Bellman, R.E., Zadeh, L.A.: Decision-making in a fuzzy environment. Manag. Sci. 17, 141–164 (1970/71)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Dubois, D., Prade, A.: Theory of possibilities. In: Application to Knowledge Representation in Computer Science. Radio and Communication, Moscow (1990). (in Russian)Google Scholar
  6. 6.
    Gnedenko, B.V., Belyaev, Yu.K., Soloviev, A.D.: Mathematical Methods in the Theory of Reliability. Nauka, Moscow (1965). (in Russian)Google Scholar
  7. 7.
    Kiyasbeili, Sh.A., Mamedov, V.M.: On the evaluation of the durability of technical systems using the theory of fuzzy sets. Electronnoe Model. (1), 59–61 (1981). (in Russian)Google Scholar
  8. 8.
    Kiyasbeili, Sh.A., Mamedov, V.M.: On possible use of the theory of fuzzy sets for solving the problem of estimating and insuring the reliability of complex systems. Autom. Remote Control 43(12), 1617–1623 (1982)zbMATHGoogle Scholar
  9. 9.
    Kiyasbeili, Sh.A., Shishonok, N.A., Mamedov, V.M.: Some questions of the application of the theory of fuzzy sets to the problems of reliability. In: Reliability of Automated Process Control System, pp. 35–41. Naukova Dumka, Kiev (1981). (in Russian)Google Scholar
  10. 10.
    Mamedov, V.M.: F-reliability model. Trans. NAS Azerbaijan 22(2–3), 3–9 (2002). (in Russian)Google Scholar
  11. 11.
    Mamedov, V.M.: Fuzzy and soft measurements in reliability problems of complex systems. In: Proceedings of the International Conference an Soft Computing and Measurements, Saint Petersburg, vol. 2, pp. 16–18 (2003). (in Russian)Google Scholar
  12. 12.
    Shishonok, N.A., Kiyasbeili, Sh.A., Mamedov, V.M.: Using the theory of blurred sets to assess the complex influence of technical operation factors on the reliability of the ACS. Electronnoe Model. (1), 97–99 (1982). (in Russian)Google Scholar
  13. 13.
    Zadeh, L.A.: Probability measures of fuzzy events. J. Math. Anal. Appl. 23(2), 421–427 (1968)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Azerbaijan State Oil and Industry UniversityBakuAzerbaijan
  2. 2.Institute of Mathematics and MechanicsAzerbaijan National Academy of SciencesBakuAzerbaijan

Personalised recommendations