Methods for Maximum and Minimum Cost Flow Determining in Fuzzy Conditions

This article considers the problems of maximum flow and minimum cost flow determining in fuzzy network. Parameters of fuzzy networks are fuzzy arc capacities in the case of maximum flow finding and transmission costs of one flow unit in the case of minimum cost flow finding. These parameters are represented as fuzzy triangular numbers. Conventional rules of operating with fuzzy triangular numbers lead to a strong "blurring" of their borders, resulting in loss of self-descriptiveness of calculations with them. The following technique of addition and subtraction of fuzzy triangular numbers is proposed in the presented paper: the centers are added (subtracted) by the conventional methods and the borders of the deviations are calculated using linear combinations of the borders of adjacent values. The fact that the limits of uncertainty of fuzzy triangular numbers should increase with the increasing of central values is taken into account. To illustrate the proposed method numerical examples are presented.