Non-orthogonal multiple access (NOMA) is promising to further improve spectral efficiency (SE) and decrease transmit latency in fog radio access networks (F-RANs) through serving multi-users in the same frequency-time resource block simultaneously, while the complexity of user association is challenging to exploit the corresponding performance gains. In this paper, a performance analysis framework for the user association in NOMA based F-RANs is proposed and the closed-form analytical results are developed by using stochastic geometry tool. In particular, we propose two user association algorithms based on evolutionary game and reinforcement learning, respectively. The performance model jointly considering quality of service, delay cost, and power consumption is formulated as a payoff function, and the corresponding performance expressions are derived for these two user association algorithms. Numerical and simulation results demonstrate that the derived expressions are accurate, and the NOMA based F-RAN can provide over 50% performance gains on SE compared to the orthogonal multiple access scheme. Furthermore, these two proposed user association algorithms work well with high convergence, which can effectively enhance the overall performance and the fairness of users.