In this thesis, we consider a pair of primary link (PU link) and a pair of cognitive link (CR link) in a fading channel. The PU link and CR link share spectrum simultaneously with different priorities, establishing the spectrum sharing network. The PU link has a higher priority to utilize spectrum with respect to the CR link. A desired quality of service (QoS) is given as a threshold on the PU link when it utilizes spectrum. The CR link utilizes spectrum only when the PU link is assured with the desired QoS or recognized as idle, not utilizing spectrum. Under this constraint, the CR link utilizes spectrum with an opportunistic power scale to assure the desired QoS on the PU link. To optimize the spectrum usage, we propose a fuzzy-based optimal power control strategy for the CR link using Mamdani fuzzy control. With the proposed control strategy, the CR link can estimate an optimal power scale for the spectrum sharing network.To illustrate the proposed fuzzy-based optimal power control strategy and its advantages, we approach the spectrum sharing network in two different propagation environments: without path loss and with path loss. In the propagation environment without path loss, we assume all channel state information (CSI) on each transmission side is available to the others, including the PU’s signal-to-noise (PU’s SNR) and PU’s interference channel gain . These two variables are used as fuzzy antecedents to estimate a corresponding power scale. In the propagation environment with path loss, we analyze the spectrum sharing network from the geometric point of view. We assume all CSI on each side is available to the others, including the PU’s SNR, PU’s interference channel gain and relative distance is fixed and normalized to 1, we use PU’s SNR and relative distance as fuzzy antecedents to calculate a corresponding power scale.