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

  • Alexander BozhenyukEmail author
  • Evgeniya Gerasimenko
  • Igor Rozenberg
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 641)

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.

Keywords

Fuzzy dynamic graph Two-commodity fuzzy flow 

Notes

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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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Alexander Bozhenyuk
    • 1
    Email author
  • Evgeniya Gerasimenko
    • 1
  • Igor Rozenberg
    • 2
  1. 1.Southern Federal UniversityTaganrogRussia
  2. 2.Public Corporation “Research and Development, Institute of Railway Engineers”MoscowRussia

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