Abstract
An algorithm is presented to determine the minimum cost flow in a fuzzy network taking into account vitality degree. Algorithm consists in iteratively finding the paths of the minimum cost with vitality degrees no less than required one and pushing the flows along these paths. Network’s parameters are presented in a fuzzy form due to the impact of environment factors and human activity. The proposed algorithm is based on the introduced rules of the residual network building. The numerical example is given that operated data from geoinformation system “ObjectLand” that contains information about railway system of Russian Federation. Initial data in a fuzzy form allow turning to the fuzzy graph with nodes presented by stations and arcs – by paths among them.
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References
Busacker, R.G., Gowen, P.: A procedure for determining a family of minimum-cost network flow patterns. Technical report 15, Operations Research Office, John Hopkins University (1961)
Ganesan, K., Veeramani, P.: Fuzzy linear programs with trapezoidal fuzzy numbers. Ann Oper. Res. 143, 305–315 (2006)
Kovács, P.: Minimum-cost flow algorithms: An experimental evaluation. EGRES Technical report, № 4 (2013)
Bozhenyuk, A.V., Rozenberg, I.N., Rogushina, E.M.: Approach of maximum flow determining for fuzzy transportation network. Izvestiya SFedU. Eng. Sci. 5(118), 83–88 (2011)
Bozhenyuk, A., Gerasimenko, E.: Flows finding in networks in fuzzy conditions. In: Kahraman, C., Öztayşi, B. (eds.) Supply Chain Management Under Fuzziness. STUDFUZZ, vol. 313, pp. 269–291. Springer, Heidelberg (2014). doi:10.1007/978-3-642-53939-8_12
Yi, T., Murty, K.G.: Finding Maximum Flows in Networks with Nonzero Lower Bounds Using Preflow Methods. Technical report, IOE Dept., University of Michigan, Ann Arbor, Mich., (1991)
Bozhenyuk A.V., Gerasimenko E.M.: Maximum dynamic flow finding task with the given vitality degree. In: Proceedings of the 2nd International Workshop on Soft Computing Applications and Knowledge Discovery (SCAKD 2016), Moscow, Russia, 18 July 2016, pp. 75–86 (2016)
Belyakov, S.L., Bozhenyuk, A.V., Ginis, L.A., Gerasimenko, E.M.: Fuzzy Methods of Control by Streams in Geoinformation Systems. Southern Federal University, Taganrog (2013)
ObjectLand/Geoinformation system. http://www.objectland.ru/
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This work has been supported by the Russian Foundation for Basic Research, Project № 16-01-00090 a.
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Kureichik, V., Gerasimenko, E. (2017). Approach to the Minimum Cost Flow Determining in Fuzzy Terms Considering Vitality Degree. In: Silhavy, R., Senkerik, R., Kominkova Oplatkova, Z., Prokopova, Z., Silhavy, P. (eds) Artificial Intelligence Trends in Intelligent Systems. CSOC 2017. Advances in Intelligent Systems and Computing, vol 573. Springer, Cham. https://doi.org/10.1007/978-3-319-57261-1_20
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DOI: https://doi.org/10.1007/978-3-319-57261-1_20
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