Providing fairness is one of the most important requirements of a rate assignment strategy. Many fairness criteria have been proposed by different researchers. A fuzzy-based rate allocation strategy is proposed which can provide a wide range of fairness criteria (such as proportional, minimum potential delay, and max min) in the network. The algorithm is superior to conventional algorithms in convergence speed. Stability analysis is performed using suitable Lyapunov functions. In this algorithm, users can adjust their gain parameters in the rate allocation algorithm, using a fuzzy controller based on some information that is received from network. The stability of the algorithm is also investigated in the presence of propagation delays. As simulation results show, the proposed rate allocation method, while maintaining stability, outperforms the conventional ones in the rate of convergence.