A new class of fuzzy constrained multi-objective games with fuzzy payoffs (FCMGFPs) is considered in this paper. First, Berge's maximum theorem for the fuzzy-vector-valued function is obtained. Based on this theorem and the Fan-Glicksberg fixed point theorem, the existence theorem of the fuzzy Pareto-Nash equilibrium for the FCMGFP is established. Second, the abstract rationality function for the FCMGFP is given by using a nonlinear scalarization function of interval vectors. Finally, a series of results, such as structural stability ( $(\gamma ,ϵ)$-stability) and robustness to $ϵ$-equilibrium ( $(\gamma ,ϵ)$-robustness), are obtained.