This paper is mainly concerned with a class of variational inequality whose underlying set is defined by chance constraints in finite-dimensional Euclidean spaces. To solve it, the inverse uncertainty distribution function in uncertainty theory is used to convert the underlying set into a parameter-dependent set under some conditions, say \(\alpha \) -dependent set, where \(\alpha \in (0,1]\) is a confidence level. Then an \(\alpha \) -dependent gap function based on the \(\alpha \) -dependent set is brought to light and an equivalence between it and the solution to the variational inequality is unveiled. Furthermore, a descent algorithm (exact line search) is executed to find the solution to the gap function which is also a solution to the variational inequality under investigation. As to close the paper, a traffic network equilibrium problem, a special case of Nash equilibrium problem, is applied to demonstrate the method in detail.
