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Article title APPROACH TO THE MAXIMUM TWO-COMMODITY FLOW DETERMINING IN A FUZZY NETWORK
Authors E. M. Gerasimenko
Section SECTION II. ARTIFICIAL INTELLIGENCE AND FUZZY SYSTEMS
Month, Year 04, 2018 @en
Index UDC 519.178
DOI
Abstract This article is devoted to solving the problem of the maximum two-commodity flow finding in a fuzzy transportation network. The task of determining the volume of a multi-commodity flow passing through the transportation network is an important task in transport planning and optimization of traffic. This article describes a variation of this task, in particular, the problem of determining the flow of two commodities in a transportation network. The main difficulty of this task is the fact that the max-flow min- cut theorem is not fulfilled for such tasks, however, it is performed to find the flow of two commodities in the undirected transportation network. A feature of this task is the ability of the first flow to block the flow of the second product in such a way that we may not get the optimal result. The central part of this task is the parameters of the transportation network, presented in a fuzzy form, such as the arc capacities of its arcs. The developed method uses a modified search path method for augmented paths, allowing to take into account fuzzy network parameters assigned to the arcs of the graph. The described method can be applied when planning the transportation of two types of goods, each of which has its own source and sink, for example, in the case of passenger and freight trains or cars and trucks. The method of operating with fuzzy numbers is considered, which does not lead to a “blurring” of the boundaries of the resulting number and allows operating with fuzzy boundaries at the last iterations, while at the previous preceding iterations they are performed with calculations only with centers of fuzzy numbers.

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Keywords Two-commodity flow; fuzzy graph; fuzzy double path..
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