Existence results of a perturbed variational inequality with a fuzzy mapping

This paper is devoted to the existence of a perturbed variational inequality with a fuzzy mapping in a finite dimensional space. We introduce two perturbation methods for a fuzzy mapping: in one method it is perturbed by a nonlinear mapping, and in the other it is perturbed by a vector. Under suitable coercivity conditions, we show that the perturbed variational inequality with a fuzzy mapping has a solution when perturbed by both of the methods mentioned above. The main results presented in this paper generalize and improve some known results.