In this article we study efficiency and weakly efficiency in fuzzy vector optimization. After formulating the problem, we introduce two new concepts of generalized convexity for fuzzy vector mappings based on the generalized Hukuhara differentiability, pseudoinvexity-I and pseudoinvexity-II. We prove that pseudoinvexity is the necessary and sufficient condition for a stationary point to be a solution of a fuzzy vector optimization problem. We give conditions to insure that a fuzzy vector mapping is invex and pseudoinvex (I and II). Moreover, we present some examples to illustrate the results. Lastly, we use these results to study the class of problems which have uncertainty and inaccuracies in the objective function coefficients of mathematical programming models.