Fuzzy resolution on the infeasibility of user equilibrium in traffic assignment problem

The user equilibrium in traffic assignment problem is to choose the minimum cost path between every origin-destination pair. In this study, we consider the infeasible user equilibrium in traffic assignment problem. That is, there does not exist any solution of the problem. We are interested in the minimum degree of relaxation needed so that the problem can exist with at least one solution. Therefore, we apply the method and concept of the theory of fuzzy resolution on the infeasibility of variational inequality to solve the infeasible user equilibrium problem.