Optimization of Jobs in GIS by Coloring of Fuzzy Temporal Graph

  • Alexander Bozhenyuk
  • Stanislav Belyakov
  • Janusz Kacprzyk
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 896)


The article proposes to consider the optimization of works in GIS as a task of coloring a fuzzy graph. The concept of fuzzy chromatic set of the second type is introduced and discussed in this paper as invariant fuzzy temporal graph. Fuzzy temporal graph is a graph in which the degree of connectivity of the vertices is changed in discrete time. Fuzzy chromatic set of the second type determines the greatest reparability degree of vertices of temporal fuzzy graph, when each of them can be assigned a specified number of colors at any discrete time. The example of finding the chromatic set of the second type is considered too.


Fuzzy temporal graph Invariant Fuzzy subgraph Graph coloring Fuzzy chromatic set Degree of reparability 



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), and the Russian Foundation for Basic Research, Project № 18-01-00023a.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Alexander Bozhenyuk
    • 1
  • Stanislav Belyakov
    • 1
  • Janusz Kacprzyk
    • 2
  1. 1.Southern Federal UniversityTaganrogRussia
  2. 2.Systems Research Institute Polish Academy of SciencesWarsawPoland

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