Allocation Centers Problem on Fuzzy Graphs with Largest Vitality Degree

  • Alexander BozhenyukEmail author
  • Stanislav Belyakov
  • Margarita Knyazeva
  • Janusz Kacprzyk
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11288)


The problem of optimal allocation of service centers is considered in this paper. It is supposed that the information received from GIS is presented in the form of second kind fuzzy graphs. Method of optimal allocation as a way to determine fuzzy set of vitality for fuzzy graph is suggested. This method is based on the transition to the complementary fuzzy graph of first kind. The method allows solving not only problem of finding of optimal service centers location but also finding of optimal location for k-centers with the greatest degree and selecting of service center numbers. Based on this method the algorithm searching vitality fuzzy set for second kind fuzzy graphs is considered. The example of finding optimum allocation centers in fuzzy graph is considered as well.


Fuzzy graph Service centers Vitality fuzzy set 



This work has been supported by the Ministry of Education and Science of the Russian Federation under Project “Methods and means of decision making on base of dynamic geographic information models” (Project part, State task 2.918.2017)


  1. 1.
    Slocum, T., McMaster, R., Kessler, F., Howard, H.: Thematic Cartography and Geovisualization, 3rd edn. Pearson Education Limited, London (2014)Google Scholar
  2. 2.
    Fang, Y., Dhandas, V., Arriaga, E.: Spatial Thinking in Planning Practice. Portland State University, Portland (2014)CrossRefGoogle Scholar
  3. 3.
    Zhang, J., Goodchild, M.: Uncertainty in Geographical Information. Taylor & Francis Inc., New York (2002)Google Scholar
  4. 4.
    Belyakov, S., Rozenberg, I., Belyakova, M.: Approach to real-time mapping, using a fuzzy information function. In: Bian, F., Xie, Y., Cui, X., Zeng, Y. (eds.) GRMSE 2013. CCIS, vol. 398, pp. 510–521. Springer, Heidelberg (2013). Scholar
  5. 5.
    Goodchild, M.: Modelling error in objects and fields. In: Goodchild, M., Gopal, S. (eds.) Accuracy of Spatial Databases, pp. 107–113. Taylor & Francis Inc., Basingstoke (1989)Google Scholar
  6. 6.
    Belyakov, S., Bozhenyuk, A., Rozenberg, I.: Intuitive figurative representation in decision-making by map data. J. Multiple-Valued Logic Soft Comput. 30, 165–175 (2018)MathSciNetGoogle Scholar
  7. 7.
    Bozhenyuk, A., Belyakov, S., Rozenberg, I.: The intuitive cartographic representation in decision-making. In: Proceedings of the 12th International FLINS Conference (FLINS 2016), World Scientific Proceeding Series on Computer Engineering and Information Science, 10, pp. 13–18. World Scientific (2016)Google Scholar
  8. 8.
    Kaufmann, A.: Introduction a la Theorie des Sous-Ensemles Flous. Masson, Paris (1977)Google Scholar
  9. 9.
    Christofides, N.: Graph Theory: An Algorithmic Approach. Academic Press, London (1976)zbMATHGoogle Scholar
  10. 10.
    Malczewski, J.: GIS and Multicriteria Decision Analysis. Willey, New York (1999)Google Scholar
  11. 11.
    Rozenberg, I., Starostina, T.: Solving of Location Problems Under Fuzzy Data with Using GIS. Nauchniy Mir, Moscow (2006)Google Scholar
  12. 12.
    Bozhenyuk, A., Rozenberg, I.: Allocation of service centers in the GIS with the largest vitality degree. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds.) IPMU 2012. CCIS, vol. 298, pp. 98–106. Springer, Heidelberg (2012). Scholar
  13. 13.
    Bozheniuk, V., Bozhenyuk, A., Belyakov, S.: Optimum allocation of centers in fuzzy transportation networks with the largest vitality degree. In: Proceedings of the 2015 Conference of the International Fuzzy System Association and the European Society for Fuzzy Logic and Technology, pp. 1006–1011. Atlantis Press (2015)Google Scholar
  14. 14.
    Bozhenyuk, A., Belyakov, S., Gerasimenko, E., Savelyeva, M.: Fuzzy optimal allocation of service centers for sustainable transportation networks service. In: Kahraman, C., Sarı, İ.U. (eds.) Intelligence Systems in Environmental Management: Theory and Applications. ISRL, vol. 113, pp. 415–437. Springer, Cham (2017). Scholar
  15. 15.
    Monderson, J., Nair, P.: Fuzzy Graphs and Fuzzy Hypergraphs. Springer, Heidelberg (2000). Scholar
  16. 16.
    Bershtein, L., Bozhenyuk, A.: Fuzzy graphs and fuzzy hypergraphs. In: Dopico, J., de la Calle, J., Sierra, A. (eds.) Encyclopedia of Artificial Intelligence, Information SCI, pp. 704–709. Hershey, New York (2008)Google Scholar
  17. 17.
    Rosenfeld, A.: Fuzzy graph. In: Zadeh, L.A., Fu, K.S., Shimura, M. (eds.) Fuzzy Sets and Their Applications to Cognitive and Decision Process, pp. 77–95. Academic Press, New York (1975)CrossRefGoogle Scholar
  18. 18.
    Mordeson, J., Mathew, S., Malik, D.: Fuzzy Graph Theory with Applications to Human Trafficking. Springer, Cham (2018). Scholar
  19. 19.
    Bozhenyuk, A., Rozenberg, I., Yastrebinskaya, D.: Finding of service centers in GIS described by second kind fuzzy graphs. World Appl. Sci. J. 22(Special Issue on Techniques and Technologies), 82–86 (2013)Google Scholar
  20. 20.
    Bozhenyuk, A., Belyakov, S., Knyazeva, M., Rozenberg, I.: Optimal allocation centersin second kind fuzzy graphs with the greatest base degree. Adv. Intell. Syst. Comput. 679, 312–321 (2018)CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Southern Federal UniversityTaganrogRussia
  2. 2.Systems Research Institute Polish Academy of SciencesWarsawPoland

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