This research aims to address the problem of multimodal transport under an environment characterized by uncertainty by developing an optimization model based on multi-objective programming within the framework of fuzzy set theory. The transportation problem is one of the fundamental problems in the field of operations research because of its important role in improving the efficiency of resource allocation and reducing the costs of logistics operations, however, many parameters associated with this problem such as transportation costs and shipping times are often characterized by a degree of ambiguity and inaccuracy. To deal with this problem, trigonometric fuzzy numbers were used to represent uncertain parameters in the transport network.
The research proposes a mathematical model based on the integration of multi-objective optimization techniques with Fuzzy Logic with the aim of balancing several conflicting criteria, most notably reducing the total cost of transportation and reducing the transportation time. The center of gravity method of blur removal has also been applied in order to convert blurry values into sharp ones that can be used in solving the mathematical model. In order to test the efficiency of the proposed model, it was applied to a numerical example representing a transport network consisting of several sources and several destinations with the use of more than one means of transport. The results have shown that the proposed model provides more realistic and flexible solutions compared to traditional models based on deterministic data, and also contributes to improving the efficiency of decision-making in multimodal transport systems.