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Searching Method of Fuzzy Internally Stable Set as Fuzzy Temporal Graph Invariant

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Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations (IPMU 2018)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 853))

Abstract

In this paper we consider the problem of finding the invariant of a fuzzy temporal graph, namely, a fuzzy internally stable set. Fuzzy temporal graph is a generalization of a fuzzy graph on the one hand, and a temporal graph on the other hand. In this paper, a temporal fuzzy graph is considered, in which the connectivity degree of vertices varies in discrete time. The notion of maximum internally stable subset of fuzzy temporal graph is considered. A method and an algorithm for finding all maximal internally stable sets are proposed which makes it possible to find a fuzzy internally stable set. The example of definition of internal stable fuzzy set is considered as well.

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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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Authors and Affiliations

  1. Southern Federal University, Nekrasovskiy Str., 44, 347928, Taganrog, Russia

    Alexander Bozhenyuk, Stanislav Belyakov & Margarita Knyazeva

  2. Public Corporation “Research and Development Institute of Railway Engineers”, Nizhegorodskaya Str., 27/1, 109029, Moscow, Russia

    Igor Rozenberg

Authors
  1. Alexander Bozhenyuk
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  2. Stanislav Belyakov
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  3. Margarita Knyazeva
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  4. Igor Rozenberg
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Corresponding author

Correspondence to Alexander Bozhenyuk .

Editor information

Editors and Affiliations

  1. Universidad de Cádiz, Cádiz, Cadiz, Spain

    Jesús Medina

  2. Universidad de Málaga, Málaga, Málaga, Spain

    Manuel Ojeda-Aciego

  3. Universidad de Granada, Granada, Spain

    José Luis Verdegay

  4. Universidad de Granada, Granada, Spain

    David A. Pelta

  5. Universidad de Málaga, Málaga, Málaga, Spain

    Inma P. Cabrera

  6. LIP6, Université Pierre et Marie Curie, CNRS, Paris, France

    Bernadette Bouchon-Meunier

  7. Iona College, New Rochelle, New York, USA

    Ronald R. Yager

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Bozhenyuk, A., Belyakov, S., Knyazeva, M., Rozenberg, I. (2018). Searching Method of Fuzzy Internally Stable Set as Fuzzy Temporal Graph Invariant. In: Medina, J., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations. IPMU 2018. Communications in Computer and Information Science, vol 853. Springer, Cham. https://doi.org/10.1007/978-3-319-91473-2_43

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  • DOI: https://doi.org/10.1007/978-3-319-91473-2_43

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-91472-5

  • Online ISBN: 978-3-319-91473-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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