A fuzzy proportional-integral-derivative (PID) controller is designed using time-delay estimation (TDE). In this paper, we show that, in a discrete-time domain, the fuzzy PID controller is a superset of a time-delay controller (TDC). In other words, with certain fuzzy parameter conditions, the discrete fuzzy PID controller is equivalent to the discrete TDC. Tuning the fuzzy PID controller can be started by exploiting the TDC: a simple, efficient and effective controller. The initial fuzzy parameters can be obtained with equivalence relationships between the fuzzy PID controller and the TDC. Furthermore, the performance of the fuzzy PID controller can be enhanced by using the non-linear control surface described by various fuzzy parameters. To this end, a fuzzy TDC is proposed using the TDE and the desired fuzzy error dynamics, and a conversion formula from the fuzzy TDC to the fuzzy PID controller is derived in a discrete-time domain. The effectiveness of the proposed method is verified through experiments on a PUMA-type robot manipulator.