Розробка методу розв’язання багатокритеріальної задачі про найкоротший маршрут з нечіткими вихідними даними

The object of this study is the optimization of road freight transportation routes under conditions of martial law or emergencies. The paper addresses the task of building a model and devising a method for solving the multi-criteria shortest path problem, taking into account the uncertainty of input data and the multiplicity of optimization criteria. The input data consists of communication lengths, their safety level, and road surface quality, which are represented by elements of fuzzy sets with corresponding membership functions, as well as a road network graph. The introduction of a system of rules, according to which the communication optimal by three criteria is chosen, has made it possible to formulate a generalized fuzzy optimization criterion for the edges of the graph, represented by the membership function of the fuzzy goal. This criterion is used as the weight of the edges in the devised method for solving the problem and makes it possible to simultaneously take into account the uncertainty of the input data and several optimization criteria. The method for solving the problem is based on a modified Dijkstra’s algorithm. For fuzzy data processing, fuzzy logical inference is used to form a generalized optimization criterion, and the Bellman-Zadeh approach is used for the optimization problem. The results of solving the problem are the optimal route, its length, safety level, and road surface quality. For the considered road network, the length of the optimal route (41 km) is not the shortest, compared to other methods (ranging from 19 km to 50 km), but the safety level of the route is high (0.75). This is due to the values of the weight coefficients of the optimization criteria. The application of this method for optimizing freight transportation routes under conditions of martial law could improve the efficiency and reliability of transport systems under conditions of uncertainty