Cybernetics and Systems Analysis

, Volume 50, Issue 1, pp 124–133 | Cite as

The Software to Analyze the States of Complex Systems under Uncertainty based on Fuzzy Belief Network Models

  • I. M. Parasyuk
  • F. V. Kostukevich


We propose the fundamentals of the software for the analysis of states of complex systems by probabilistic inference methods based on fuzzy belief network models and their extensions. We introduce the concepts of fuzzy potentials and operations on them, develop mathematical tools of two-phase exact probabilistic inference and the procedure for evaluating and predicting the states of the system under study, and describe the architectural aspects of the computer implementation of the relevant information technology.


fuzzy probability fuzzy potential belief network models fuzzy Bayesian networks fuzzy influence diagram network transformation probabilistic inference nodal tree information technologies 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R. G. Cowell, A. P. Dawid, D. J. Spiegelhalter, and S. L. Lauritzen, Probabilistic Networks and Expert Systems, Springer-Verlag, New York (1999).MATHGoogle Scholar
  2. 2.
    U. B. Kjaerulff and A. L. Madsen, Bayesian Networks and Influence Diagrams: A Guide to Construction and Analysis, Springer, New York (2008).CrossRefGoogle Scholar
  3. 3.
    L. A. Zade, “Fundamentals of the new approach to the analysis of complex systems and decision-making processes,” in: Mathematics Today (A Collection of Papers) [Russian translation], Znanie, Moscow (1974), pp. 5–48.Google Scholar
  4. 4.
    O. V. Verovka and I. N. Parasyuk, “Probability propagation in fuzzy Bayesian belief networks with nondeterministic states,” Cybern. Syst. Analysis, 44, No. 6, 925–940 (2008).CrossRefMATHGoogle Scholar
  5. 5.
    I. N. Parasyuk and F.V. Kostukevich, “Methods of transformation of Bayesian networks for nodal tree construction and their modification,” Komp. Matematika, No. 1, 70–80 (2008).Google Scholar
  6. 6.
    I. N. Parasyuk and F. V. Kostukevich, “Fuzzy potentials and their application in algorithms of belief propagation on Bayesian networks,” Komp. Matematika, No. 1, 67–75 (2009).Google Scholar
  7. 7.
    I. N. Parasyuk and F. V. Kostukevich, “An efficient algorithm of the propagation of probabilities in fuzzy Bayesian belief networks,” Komp. Matematika, No. 2, 102–112 (2010).Google Scholar
  8. 8.
    J. Pearl, Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference, Morgan Kaufmann, San Mateo (1991).Google Scholar
  9. 9.
    S. L. Lauritzen and D. J. Spiegelhalter, “Local computations with probabilities on graphical structures and their application to expert systems,” J. Royal Statist. Soc., Ser.B, 50, No. 2, 157–224 (1988).Google Scholar
  10. 10.
    P. Heggernes, “Minimal triangulations of graphs: A survey,” Discrete Math., 306, Issue 3, 297–317 (2006).CrossRefMATHMathSciNetGoogle Scholar
  11. 11.
    P. P. Shenoy and G. Shafer, “Axioms for probability and belief-function propagation,” Uncertainty in Artif. Intellig., 4, 169–198 (1990).MathSciNetGoogle Scholar
  12. 12.
    F. Jensen, S. Lauritzen, and K. Olesen, “Bayesian updating in causal probabilistic networks by local computations,” SIAM J. Comp., No. 4, 269–282 (1990).Google Scholar
  13. 13.
    V. Lepar and P. Shenoy, “A comparison of Lauritzen–Spiegelhalter, Hugin and Shenoy–Shafer architectures for computing marginals of probability distributions,” in: G. Cooper and S. Moral (eds.), Proc. 14th Conf. on Uncertainty in Artificial Intelligence (UAI-98), Morgan Kaufmann (1998), pp. 328–337.Google Scholar
  14. 14.
    M. Detyniecki and R. R. Yager, “A note on ranking fuzzy numbers using α-weighted valuations,” Intern. J. Uncertainty, Fuzziness and Knowledge-Based Syst., 8, 573–591 (2000).CrossRefMATHMathSciNetGoogle Scholar
  15. 15.
    T. H. Cormen, C. E. Leiserson, and R. L. Rivest, Introduction to Algorithms, MIT Press (2001).Google Scholar
  16. 16.
    K. Asai, D. Vatada, S. Ivai, et al., Applied Fuzzy Systems [Russian translation], Mir, Moscow (1993).Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.V. M. Glushkov Institute of CyberneticsNational Academy of Sciences of UkraineKyivUkraine

Personalised recommendations