Abstract
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 fuzzy base 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 fuzzy base set for second kind fuzzy graphs is considered. The example of finding optimum allocation centers in second kind fuzzy graph is considered too.
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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 2.918.2017/4.6), and the Russian Foundation for Basic Research, Project № 15-07-00185a.
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References
Clarke, K.: Analytical and Computer Cartography. Prentice-Hall, New Jersey (1995)
Longley, P., Goodchild, M., Maguire, D., Rhind, D.: Geographic Information Systems and Science. Wiley, New York (2001)
Zhang, J., Goodchild, M.: Uncertainty in Geographical Information. Taylor & Francis, New York (2002)
Goodchild, M.: Modelling error in objects and fields. In: Goodchild, M., Gopal, S. (eds.) Accuracy of Spatial Databases, pp. 107–113. Taylor & Francis, Basingstoke (1989)
Kaufmann, A.: Introduction a la theorie des sous-ensemles flous. Masson, Paris (1977)
Christofides, N.: Graph Theory. An Algorithmic Approach. Academic Press, London (1976)
Malczewski, J.: GIS and Multicriteria Decision Analysis. Willey, New York (1999)
Rozenberg, I., Starostina, T.: Solving of Location Problems Under Fuzzy Data with Using GIS. Nauchniy Mir, Moscow (2006)
Bozhenyuk, A., Rozenberg, I.: 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, vol. 298, pp. 98–106. Springer, Heidelberg (2012)
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)
Bozhenyuk, A., Belyakov, S., Gerasimenko, E., Savelyeva, M.: Fuzzy optimal allocation of service centers for sustainable transportation networks service. Intell. Syst. Ref. Libr. 113, 415–437 (2017)
Monderson, J., Nair, P.: Fuzzy Graphs and Fuzzy Hypergraphs. Physica-Verl, Heidelberg, New York (2000)
Bershtein, L., Bozhenyuk, A.: Fuzzy graphs and fuzzy hypergraphs. In: Dopico, J., de la Calle, J., Sierra, A. (eds.) Encyclopedia of Artificial Intelligence, pp. 704–709. Information SCI, Hershey, New York (2008)
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)
Yeh, R., Bang, S.: Fuzzy relations fuzzy graphs and their applications to clustering analysis. In: Zadeh, L.A., Fu, K.S., Shimura, M. (eds.) Fuzzy Sets and Their Applications, pp. 125–149. Academic Press (1975)
Bozhenyuk, A., Rozenberg, I., Yastrebinskaya, D.: Finding of service centers in GIS described by second kind fuzzy graphs. World Appl. Sci. J. 22, 82–86 (2013). (Special Issue on Techniques and Technologies)
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Bozhenyuk, A., Belyakov, S., Knyazeva, M., Rozenberg, I. (2018). Optimal Allocation Centers in Second Kind Fuzzy Graphs with the Greatest Base Degree. In: Abraham, A., Kovalev, S., Tarassov, V., Snasel, V., Vasileva, M., Sukhanov, A. (eds) Proceedings of the Second International Scientific Conference “Intelligent Information Technologies for Industry” (IITI’17). IITI 2017. Advances in Intelligent Systems and Computing, vol 679. Springer, Cham. https://doi.org/10.1007/978-3-319-68321-8_32
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