Evgeniya Gerasimenko

Flows Finding in Networks in Fuzzy Conditions

The following chapter deals with flow problems in transportation networks in terms of fuzziness. Literature review considering flows and basic problem statements is given. The task of maximum flow finding in transportation network with lower flow bounds in fuzzy conditions is described and solved. The necessity of considering dynamic transportation networks is explained. The task of maximum flow finding with lower flow bounds in fuzzy conditions in dynamic network is solved. Peculiarity of the considered task is in fuzzy and transit nature of the network parameters.

Determining the minimum cost flow in fuzzy dynamic network with GIS «ObjectLand»

Present paper deals with the problem of the minimum cost flow finding in fuzzy dynamic network with nonzero lower flow bounds. The necessity of the fuzzy logic tools application is explained. The method and basic rules of the minimum cost determining in fuzzy conditions are considered. Numerical example and practical implementation of the presented method are provided.

Flows in Networks Under Fuzzy Conditions

This book offers a comprehensive introduction to fuzzy methods for solving flow tasks in both transportation and networks. It analyzes the problems of minimum cost and maximum flow finding with fuzzy nonzero lower flow bounds, and describes solutions to minimum cost flow finding in a network with fuzzy arc capacities and transmission costs. After a concise introduction to flow theory and tasks, the book analyzes two important problems. The first is related to determining the maximum volume for cargo transportation in the presence of uncertain network parameters, such as environmental changes, measurement errors and repair work on the roads. These parameters are represented here as fuzzy triangular, trapezoidal numbers and intervals. The second problem concerns static and dynamic flow finding in networks under fuzzy conditions, and an effective method that takes into account the networks transit parameters is presented here. All in all, the book provides readers with a practical reference guide to state-of-the art fuzzy methods for solving flow tasks and offers a valuable resource for all researchers and postgraduate students in the fields of network theory, fuzzy models and decision-making.

Algorithm for Monitoring Minimum Cost in Fuzzy Dynamic Networks

Abstract The present paper examines the task of minimum cost flow finding in a fuzzy dynamic network with lower flow bounds. The distinguishing feature of this problem statement lies in the fuzzy nature of the network parameters, such as flow bounds, transmission costs and transit times. The arcs of the considered network have lower bounds. Another feature of this task is that fuzzy flow bounds, costs and transit times can vary depending on the flow departure time. Algorithm, which implements the solution of considered problem, is proposed.

Fuzzy Optimal Allocation of Service Centers for Sustainable Transportation Networks Service

In this chapter questions of defining of service centers optimum allocation in transportation network are observed. It is supposed that transportation network is described by a fuzzy graph. In this case a task of definition of optimum allocation of the service centers can be transformed into the task of definition of base fuzzy set, antibase fuzzy set and vitality fuzzy set of fuzzy graph. The method of definition of these sets is considered in this chapter. The numerical example of optimum allocation of the service centers finding in the railway network in the form of the fuzzy graph is considered.

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

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.

Approach to the Minimum Cost Flow Determining in Fuzzy Terms Considering Vitality Degree

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.

Maximum and Minimum Cost Flow Finding in Networks in Fuzzy Conditions

The problems of the maximum and the minimum cost flow finding with zero and nonzero lower flow bounds are relevant, since they allow solving the problems of economic planning, logistics, transportation management, etc. In the area of transportation networks flow tasks enable to find the cargo transportation of the maximum volume between given points taking into account restrictions on the arc capacities of the cargo transmission paths, choose the routes of the optimal cost with the set lower flow bounds, which can be found after the profitability analysis of the cargo transportation along the particular road section. In considering these tasks it is necessary to take into account the inherent uncertainty of the network parameters, since environmental factors, measurement errors, repair work on the roads, the specifics of the constantly changing structure of the network influence the upper and lower flow bounds and transportation costs.

Flow Tasks in Networks in Crisp Conditions

The flow tasks arising in the study of transportation networks are relevant due to their wide practical application.

Flow Tasks Solving in Dynamic Networks with Fuzzy Lower, Upper Flow Bounds and Transmission Costs

Tasks, considered in the first chapter of the present book, assume instant flow transition along the arcs of the graph. The present paper deals with dynamic networks, i.e. such a networks, in which flow spends certain time passing along the arcs of the graph.