An Analysis of Evolutionary Algorithms for Multiobjective Optimization of Structure and Learning of Fuzzy Cognitive Maps Based on Multidimensional Medical Data

  • Alexander Yastrebov
  • Łukasz Kubuś
  • Katarzyna PoczetaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11934)


The paper concerns the use of evolutionary algorithms to solve the problem of multiobjective optimization and learning of fuzzy cognitive maps (FCMs) on the basis of multidimensional medical data related to diabetes. The aim of this research study is an automatic construction of a collection of FCM models based on various criteria depending on the structure of the model and forecasting capabilities. The simulation analysis was performed with the use of the developed multiobjective Individually Directional Evolutionary Algorithm. Experiments show that the collection of fuzzy cognitive maps, in which each element is built on the basis of particular patient data, allows us to receive higher forecasting accuracy compared to the standard approach. Moreover, by appropriate aggregation of these collections we can also obtain satisfactory accuracy of forecasts for the new patient.


Fuzzy cognitive maps Multiobjective optimization Evolutionary algorithms Multidimensional medical data 


  1. 1.
    Chen, S.M.: Cognitive-map-based decision analysis based on NPN logics. Fuzzy Sets Syst. 71(2), 153–163 (1995)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Chernorutsky, I.G.: Methods of optimization in control theory. Peter, St. Petersburg (2010) (in Russian)Google Scholar
  3. 3.
    Chi, Y., Liu, J.: Learning of fuzzy cognitive maps with varying densities using a multiobjective evolutionary algorithm. IEEE Trans. Fuzzy Syst. 24(1), 71–81 (2016)CrossRefGoogle Scholar
  4. 4.
    Christoforou, A., Andreou, A.S.: A framework for static and dynamic analysis of multi-layer fuzzy cognitive maps. Neurocomputing 232, 133–145 (2017)CrossRefGoogle Scholar
  5. 5.
    Dickerson, J.A., Kosko, B.: Fuzzy virtual worlds as fuzzy cognitive maps. Presence 3, 173–189 (1994)CrossRefGoogle Scholar
  6. 6.
    Falcon, R., Napoles, G., Bello, R., Vanhoof, K.: Granular cognitive maps: a review. Granul. Comput. 4(3), 451–467 (2019)CrossRefGoogle Scholar
  7. 7.
    Fogel, D.B.: Evolutionary Computation: Toward a New Philosophy of Machine Inteligence, 3rd edn. Wiley, Hoboken (2006)Google Scholar
  8. 8.
    Homenda, W., Jastrzebska, A., Pedrycz, W.: Nodes selection criteria for fuzzy cognitive maps designed to model time series. In: Filev, D., et al. (eds.) Intelligent Systems 2014. AISC, vol. 323, pp. 859–870. Springer, Cham (2015). CrossRefGoogle Scholar
  9. 9.
    Kahn, M.: UCI Machine Learning Repository, Washington University, St. Louis, MO. Accessed 3 Aug 2019
  10. 10.
    Kolahdoozi, M., Amirkhani, A., Shojaeefard, M.H., Abraham, A.: A novel quantum inspired algorithm for sparse fuzzy cognitive maps learning. Appl. Intell. 49(10), 3652–3667 (2019)CrossRefGoogle Scholar
  11. 11.
    Kosko, B.: Fuzzy cognitive maps. Int. J. Man-Mach. Stud. 24(1), 65–75 (1986)CrossRefGoogle Scholar
  12. 12.
    Kreinovich, V., Stylios, C.: Why fuzzy cognitive maps are efficient. Int. J. Comput. Commun. Control 10(5), 825–833 (2015). Special issue on Fuzzy Sets and ApplicationsGoogle Scholar
  13. 13.
    Kubuś, Ł.: Individually directional evolutionary algorithm for solving global optimization problems-comparative study. Int. J. Intell. Syst. Appl. (IJISA) 7(9), 12–19 (2015)Google Scholar
  14. 14.
    Kubuś, Ł., Poczeta, K., Yastrebov, A.: A new learning approach for fuzzy cognitive maps based on system performance indicators. In: 2016 IEEE International Conference on Fuzzy Systems, Vancouver, Canada, pp. 1398–1404 (2016)Google Scholar
  15. 15.
    Mateou, N.H., Andreou, A.S.: Tree-structured multi-layer fuzzy cognitive maps for modelling large scale, complex problems. In: 2005 Proceedings of International Conference on Computational Intelligence for Modelling, Control and Automation and International Conference on Intelligent Agents, Web Technologies and Internet Commerce, pp. 133–141 (2005)Google Scholar
  16. 16.
    Papageorgiou, E.I., Poczeta, K.: A two-stage model for time series prediction based on fuzzy cognitive maps and neural networks. Neurocomputing 232, 113–121 (2017)CrossRefGoogle Scholar
  17. 17.
    Papakostas, G.A., Koulouriotis, D.E., Polydoros, A.S., Tourassis, V.D.: Towards Hebbian learning of fuzzy cognitive maps in pattern classification problems. Expert Syst. Appl. 39, 10620–10629 (2012)CrossRefGoogle Scholar
  18. 18.
    Peng, Z., Wu, L., Chen, Z.: NHL and RCGA based multi-relational fuzzy cognitive map modeling for complex systems. Appl. Sci. 5(4), 1399–1411 (2015)CrossRefGoogle Scholar
  19. 19.
    Poczeta, K., Kubus, L., Yastrebov, A.: Analysis of an evolutionary algorithm for complex fuzzy cognitive map learning based on graph theory metrics and output concepts. BioSystems 179, 39–47 (2019)CrossRefGoogle Scholar
  20. 20.
    Poczeta, K., Kubuś, Ł., Yastrebov, A.: An evolutionary algorithm based on graph theory metrics for fuzzy cognitive maps learning. In: Martín-Vide, C., Neruda, R., Vega-Rodríguez, M.A. (eds.) TPNC 2017. LNCS, vol. 10687, pp. 137–149. Springer, Cham (2017). Scholar
  21. 21.
    Rutkowski, L.: Methods and Techniques of Artificial Intelligence (in Polish). Wydawnictwo Naukowe PWN, Warsaw (2005)Google Scholar
  22. 22.
    Salmeron, J.L., Froelich, W.: Dynamic optimization of fuzzy cognitive maps for time series forecasting. Knowl.-Based Syst. 105, 29–37 (2016)CrossRefGoogle Scholar
  23. 23.
    Salmeron, J.L., Papageorgiou, E.I.: Fuzzy grey cognitive maps and nonlinear Hebbian learning in process control. Appl. Intell. 41, 223–234 (2014)CrossRefGoogle Scholar
  24. 24.
    Schaffer, J.: Multiple objective optimization with vector evaluated genetic algorithms. In: Proceedings of the First International Conference on Genetic Algortihms, pp. 93–100 (1985)Google Scholar
  25. 25.
    Stach, W., Kurgan, L., Pedrycz, W., Reformat, M.: Genetic learning of fuzzy cognitive maps. Fuzzy Sets Syst. 153(3), 371–401 (2005)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Stach, W., Pedrycz, W., Kurgan, L.A.: Learning of fuzzy cognitive maps using density estimate. IEEE Trans. Syst. Man Cybern. Part B 42(3), 900–912 (2012)CrossRefGoogle Scholar
  27. 27.
    Słoń, G.: Application of models of relational fuzzy cognitive maps for prediction of work of complex systems. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2014. LNCS (LNAI), vol. 8467, pp. 307–318. Springer, Cham (2014). Scholar
  28. 28.
    Wu, K., Liu, J.: Learning large-scale fuzzy cognitive maps based on compressed sensing and application in reconstructing gene regulatory networks. IEEE Trans. Fuzzy Syst. 25(6), 1546–1560 (2017)CrossRefGoogle Scholar
  29. 29.
    Yastrebov, A., Gad, S., SŁoń, S.: Bank of artificial neural networks MLP type in symptom systems of technical diagnostics. Pol. J. Environ. Stud. 17(2A), 118–123 (2008)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Kielce University of TechnologyKielcePoland

Personalised recommendations