In cognitive radio networks, each cognitive transmission process typically requires two phases: the spectrum sensing phase and data transmission phase. In this paper, we investigate cognitive transmissions with multiple relays by jointly considering the two phases over Rayleigh fading channels. We study a selective fusion spectrum sensing and best relay data transmission (SFSS-BRDT) scheme in multiple-relay cognitive radio networks. Specifically, in the spectrum sensing phase, only the initial spectrum sensing results, which are received from the cognitive relays and decoded correctly at a cognitive source, are selected and used for fusion. In the data transmission phase, only the best relay is utilized to assist the cognitive source for data transmissions. Under the constraint of satisfying a required probability of false alarm of spectrum holes (for the protection of the primary user), we derive an exact closed-form expression of the spectrum hole utilization efficiency for the SF...