Fuzzy Correspondence Matrix for Air-Transportation Models

A new decision-support method is proposed for air-transportation planning using uncertainties in the form of fuzzy numbers. It allows the determination of such changes in the transport graph so that they are more in line with the current needs of the population and the available fleet of aircraft. This is especially true in the context of the current significant transformation of traffic flows and available types of aircraft in modern realities. The problem is solved by restoring the fuzzy matrix of correspondence according to data on air transportation for previous periods. It is often not known what proportion of passengers are compelled to move between given points, using large transport hubs as intermediate ones. To determine the truth of the correspondence matrix, a number of optimization models are constructed to determine the membership function of the fuzzy number of passengers carried. Algorithms and software for searching for the fuzzy correspondence and fuzzy ranking of potentially promising routes are created. The possibilities of the method are shown using the example of the problem of choosing new routes between airports.