Abstract
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.
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References
Malczewski, J.: GIS and Multicriteria Decision Analysis. Wiley, New York (1999)
Longley, P., Goodchild, M., Maguire, D., Rhind, D.: Geographic Information Systems and Science. Wiley, New York (2001)
Goodchild, M.: Modelling error in objects and fields. In: Goodchild, M.F., Gopal, S. (eds.) Accuracy of Spatial Databases, pp. 107–113. Taylor & Francis, Basingstoke (1989)
Zhang, J., Goodchild, M.: Uncertainty in Geographical Information. Taylor & Francis, New York (2002)
Belyakov, S., Belyakova, M., Bozhenyuk, A., Rozenberg, I.: Transformation of elements of geoinformation models in the synthesis of solutions. Adv. Intell. Syst. Comput. 679, 526–535 (2018). https://doi.org/10.1007/978-3-319-68321-8_55
Bershtein, L., Bozhenyuk, A.: The using of temporal graphs as the models of complicity systems. Izvestiya UFY. Technicheskie nayuki. TTI UFY, Taganrog 4(105), 198–203 (2010)
Bershtein, L., Bozhenyuk, A., Rozenberg, I.: Definition method of strong connectivity of fuzzy temporal graphs. Vestnik RGUPS, Rostov-on-Don 3(43), 15–20 (2011)
Bozhenyuk, A., Belyakov, S., Rozenberg, I.: Coloring method of fuzzy temporal graph with the greatest separation degree. Adv. Intell. Syst. Comput. 450, 331–338 (2016). https://doi.org/10.1007/978-3-319-33609-1_30
Monderson, J., Nair, P.: Fuzzy Graphs and Fuzzy Hypergraphs. Springer, Heidelberg (2000)
Bershtein, L., Bozhenyuk, A., Rozenberg, I.: Fuzzy coloring of fuzzy hypergraph. Adv. Soft Comput. 33, 703–711 (2006). https://doi.org/10.1007/3-540-31182-3_65
Bozhenyuk, A., Belyakov, S., Knyazeva, M., Rozenberg, I.: Searching method of fuzzy internally stable set as fuzzy temporal graph invariant. Commun. Comput. Inf. Sci. 583, 501–510 (2018). https://doi.org/10.1007/978-3-319-91473-2_43
Bershtein, L., Bozhenuk, A.: Maghout method for determination of fuzzy independent, dominating vertex sets and fuzzy graph kernels. Int. J. Gen. Syst. 1(30), 45–52 (2001). https://doi.org/10.1080/03081070108960697
Acknowledgments
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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Bozhenyuk, A., Belyakov, S., Kacprzyk, J. (2019). Optimization of Jobs in GIS by Coloring of Fuzzy Temporal Graph. In: Aliev, R., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Sadikoglu, F. (eds) 13th International Conference on Theory and Application of Fuzzy Systems and Soft Computing — ICAFS-2018. ICAFS 2018. Advances in Intelligent Systems and Computing, vol 896. Springer, Cham. https://doi.org/10.1007/978-3-030-04164-9_8
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