User equilibrium in traffic assignment problem with fuzzy N-A incidence matrix

Abstract The user equilibrium in traffic assignment problem is to choose the minimum-cost path between every origin–destination pair and through this process, those utilized paths will have equal costs. In other words, giving cost and demand function for transportation between every origin–destination pair, the solution of the problem is to provide the minimum cost of which the flow is generated. In this study, we consider this problem when the N–A incidence matrix for transportation is fuzzy, in the sense that, which arcs are chosen into the desired path for traveling is uncertain. Therefore, we apply the method and concept of the theory of variational inequality with fuzzy convex cone to establish a user equilibrium pattern. Finally, the proposed method is demonstrated with a numerical example.