Approach to defining the maximum amount of flow in dynamic fuzzy network with the given vitality degree

Present paper is devoted to defining the maximum amount of flow in dynamic graph with bounds of flow not equal to zero with the given vitality degree. The approach takes into account fuzziness of the network's parameters, values and measurements. The considered approach allows taking into account profitability of transportation via setting the bounds of flow not equal to zero. Peculiarity of present task is in considering the reliability of transportation, expressed by the vitality parameter and considering arcs with the required vitality. Considered graph is described as fuzzy lower and upper-capacitated network with vitality degrees and crisp values of the time-parameters. All parameters of the considered network can vary over time. These methods can be applied in the real railways, roads and air roads solving the task of the optimal cargo transportation.