The Method of Allocation Centers in Second Kind Fuzzy Graphs With the Largest Vitality Degree

Alexander Bozhenyuk, Stanislav Belyakov and Margarita Knyazeva


The problem of optimal allocation of service centers is considered in this paper. It is supposed that the information received from GIS is presented like second kind fuzzy graphs. Method of optimal location as method of finding vitality fuzzy set of second kind fuzzy graph is suggested. Basis of this method is building procedure of reachability matrix of second kind fuzzy graph in terms of reachability matrix of first kind fuzzy graph. This method allows solving not only problem of finding of optimal service centers location but also finding of optimal location k-centers with the greatest degree and selecting of service center numbers. The algorithm of the definition of vitality fuzzy set for second kind fuzzy graphs is considered. The example of finding optimum allocation centers in second kind fuzzy graph is considered too.


second kind fuzzy graph, service centers, vitality fuzzy set


T. Slocum, R. McMaster, F. Kessler, and H. Howard, Thematic Cartography and Geovisualization. 3nd edn. Pearson Education Limited, 2014.

Y. Fang, V. Dhandas, and E. Arriaga, Spatial Thinking in Planning Practice. Portland State University, Portland, 2014.

J. Zhang, and M. Goodchild, Uncertainty in Geographical Information. New York: Taylor & Francis, Inc., 2002.

M. Goodchild. “Modelling Error in Objects and Fields”. In.: Accuracy of Spatial Databases, M. Goodchild and S. Gopal (eds.) Basingstoke: Taylor & Francis, Inc., 1989, pp. 107-113.

A. Kaufmann, Introduction a la theorie des sous-ensemles flous. Paris: Masson, 1977.

N. Christofides, Graph theory. An algorithmic approach. London: Academic press, 1976.

J. Malczewski. GIS and multicriteria decision analysis. New York: John Willey and Sons, 1999.

I.N. Rozenberg, and T.A. Starostina, Solving of location problems under fuzzy data with using GIS. Moscow: Nauchniy Mir, 2006.

A. Bozhenyuk, and I. Rozenberg. “Allocation of service centers in the GIS with the largest vitality degree,” in: Proceedings of the IPMU 2012, Part II, Communications in Computer and Information Science, CCIS 298, Berlin Heidelberg: Springer-Verlag, 2012. pp: 98-106.

V. Bozheniuk, A. Bozhenyuk, and S. Belyakov, “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: Atlantis Press, 2015, pp. 1006–1011.

A. Bozhenyuk, S. Belyakov, E. Gerasimenko, and M. Savelyeva. “Fuzzy Optimal Allocation of Service Centers for Sustainable Transportation Networks Service”, Intelligent Systems Reference Library, Vol. 113, 2017, pp. 415-437.

J.N.Monderson, and P.S. Nair. Fuzzy Graphs and Fuzzy Hypergraphs. Heidelberg; New-York: Physica-Verl., 2000. 383 p. L.S. Bershtein, and A.V. Bozhenyuk. “Fuzzy Graphs and Fuzzy Hypergraphs”. In: Dopico, J., de la Calle, J., Sierra, A. (eds.) Encyclopedia of Artificial Intelligence, Information SCI, Hershey, New York, 2008, pp. 704-709.

A. Rosenfeld. “Fuzzy graph,” in: L.A.Zadeh, K.S.Fu, M.Shimura (Eds.), Fuzzy sets and their applications to cognitive and decision process, New York: Academic Press, 1975, pp. 77 -95.

R.T Yeh, and S.Y. Bang. “Fuzzy relations fuzzy graphs and their applications to clustering analysis,” in: L.A.Zadeh, K.S.Fu, M.Shimura (Eds.), Fuzzy sets and their applications, Academic Press, 1975, pp. 125 – 149.

A. Bozhenyuk, I. Rozenberg and D. Yastrebinskaya. “Finding of Service Centers in GIS Described by Second Kind Fuzzy Graphs”, World Applied Sciences Journal, Vol. 22(Special Issue on Techniques and Technologies), 2013, pp. 82-86.

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