The main goal of this paper is to investigate the leader-following formation control of multi-robot systems. The problem of collision avoidance is considered as well. According to the graph-theoretic concepts and locally distributed information, an interval type-2 neural fuzzy formation controller is designed with the capability of on-line learning. The learning rules of controller parameters can be derived from the gradient descent method. To avoid collisions between robots, a fuzzy separation controller is proposed such that the local minimum problem can be solved. Both static and dynamic leaders are discussed for performance validations. Simulation and experimental results indicate that the proposed fuzzy formation and separation control can provide better formation responses compared to conventional consensus formation and potential-based collision-avoidance algorithms.