Generalized vector complementarity problem in fuzzy environment

This paper is devoted to introduce and study a new class of generalized vector complementarity problems ((GVCP), for short) and generalized vector variational inequalities ((GVVI), for short) in fuzzy environment. Under suitable conditions, we prove the equivalence between (GVCP) and (GVVI) in Banach spaces. Then, without any monotonicity assumption, we apply KKM-technique to establish an existence theorem of solutions for (GVVI). Finally, we show that the solution set of (GVCP) is nonempty and closed.