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Method of Maximum Two-Commodity Flow Search in a Fuzzy Temporal Graph

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Advances in Fuzzy Logic and Technology 2017 (EUSFLAT 2017, IWIFSGN 2017)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 641))

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Abstract

This paper is devoted to the task of the two-commodity maximum flow finding in a fuzzy temporal graph. Arcs of the network are assigned by the fuzzy arc capacities and crisp transit times. All network’s parameters can vary over time, therefore, it allows to consider network as dynamic one. The task is to maximize total flow passing through the network, considering temporal nature of the network. Such methods can be applied in the real railways, roads, when it is necessary to take into account the commodities of two types solving the task of the optimal cargo transportation, for example, passenger and cargo trains or motor cars and lorries Method of operating fuzzy numbers for flow tasks is proposed that doesn’t lead to the blurring of the resulting number.

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Acknowledgments

This work has been supported by the Russian Foundation for Basic Research, Project №. 16-01-00090 a, and the Ministry of Education and Science of the Russian Federation under Project No. 213.01-11/2014-48 (Base part, State task 2014/174).

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Authors and Affiliations

  1. Southern Federal University, Taganrog, Russia

    Alexander Bozhenyuk & Evgeniya Gerasimenko

  2. Public Corporation “Research and Development, Institute of Railway Engineers”, Moscow, Russia

    Igor Rozenberg

Authors
  1. Alexander Bozhenyuk
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  2. Evgeniya Gerasimenko
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  3. Igor Rozenberg
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Corresponding author

Correspondence to Alexander Bozhenyuk .

Editor information

Editors and Affiliations

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

    Janusz Kacprzyk

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

    Eulalia Szmidt

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

    Sławomir Zadrożny

  4. Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Krassimir T. Atanassov

  5. WIT - Warsaw School of Information Technology, Warsaw, Poland

    Maciej Krawczak

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Bozhenyuk, A., Gerasimenko, E., Rozenberg, I. (2018). Method of Maximum Two-Commodity Flow Search in a Fuzzy Temporal Graph. In: Kacprzyk, J., Szmidt, E., Zadrożny, S., Atanassov, K., Krawczak, M. (eds) Advances in Fuzzy Logic and Technology 2017. EUSFLAT IWIFSGN 2017 2017. Advances in Intelligent Systems and Computing, vol 641. Springer, Cham. https://doi.org/10.1007/978-3-319-66830-7_23

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  • DOI: https://doi.org/10.1007/978-3-319-66830-7_23

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66829-1

  • Online ISBN: 978-3-319-66830-7

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