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Fuzzy Clique Set Determination Method as an Example of Fuzzy Temporal Graph Invariant

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14th International Conference on Theory and Application of Fuzzy Systems and Soft Computing – ICAFS-2020 (ICAFS 2020)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1306))

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Abstract

The paper investigates the problem of the invariant determination in graphs that have fuzzy-estimated parameters and temporal characteristics. The basic idea is to find fuzzy clique set in such graphs. Fuzzy temporal graph capture the notion of temporal characteristics and uncertainty while processing some operations on it. In this paper the idea of temporality in such graph models is treated in the way that adjacency of the vertices may change over time periods. Cliques normally refer to subgraphs in a graph such that vertices in each subgraph are pairwise adjacent. Adjacency may be uncertain due to some features of the network and may vary in time. In the problem of maximum clique determination the idea is to search the clique with most vertices within a graph. So the fuzzy adjacency here can be interpreted in terms of immediate likelihood of vertex to capture or to share whatever is flowing though the graph network. The idea of maximum clique subset for the fuzzy graph with fuzzy-estimated characteristics is presented in this paper. A method for determination of all maximum clique sets is proposed, as well as a fuzzy clique set is determined. The illustrative examples are given as well.

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Acknowledgments

The reported study was funded by RFBR according to the research project N 20-01-00197.

Author information

Authors and Affiliations

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

    Alexander Bozhenyuk & Margarita Knyazeva

  2. RWTH Aachen University, Templergraben 55, 52056, Aachen, Germany

    Vitalii Bozheniuk

  3. Systems Research Institute Polish Academy of Sciences, Newelska 6, 01-447, Warsaw, Poland

    Janusz Kacprzyk

Authors
  1. Alexander Bozhenyuk
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  2. Vitalii Bozheniuk
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  3. Janusz Kacprzyk
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  4. Margarita Knyazeva
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Corresponding author

Correspondence to Alexander Bozhenyuk .

Editor information

Editors and Affiliations

  1. Department of Control Systems, Azerbaijan State Oil and Industry University, Baku, Azerbaijan

    Rafik A. Aliev

  2. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Janusz Kacprzyk

  3. Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, Canada

    Witold Pedrycz

  4. Department of Electrical and Computer Engineering, University of Texas at San Antonio, San Antonio, TX, USA

    Mo Jamshidi

  5. Azerbaijan State Oil and Industry University, Baku, Azerbaijan

    Mustafa Babanli

  6. Department of Mechatronics, Near East University, Mersin, Turkey

    Fahreddin M. Sadikoglu

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Bozhenyuk, A., Bozheniuk, V., Kacprzyk, J., Knyazeva, M. (2021). Fuzzy Clique Set Determination Method as an Example of Fuzzy Temporal Graph Invariant. In: Aliev, R.A., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Babanli, M., Sadikoglu, F.M. (eds) 14th International Conference on Theory and Application of Fuzzy Systems and Soft Computing – ICAFS-2020 . ICAFS 2020. Advances in Intelligent Systems and Computing, vol 1306. Springer, Cham. https://doi.org/10.1007/978-3-030-64058-3_1

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