Performance enhancement of secondary communication, while adhereing to the interference constraint of the primary network in an underlay sepctrum sharing environemnt, is an active area of research. In this paper, we propose a Fuzzy Rule Based System (FRBS) assisted relay selection and transmit power allocation (RSTPA) technique that provides the secondary users the ability to coexist with the primary users in an energyconstrainted dual-hop Cognitive Radio Network. In this proposal, FRBS selects the optimal combination of relays aiming to maximize the signal-to-noise ratio (SNR) received at the destination, while guaranteeing that interference threshold of the primary network is not exceeded. The proposed scheme has been investigated for well-defined range of certain parameters. Simulation results prove that FRBS can accurately select the best combination of relays and maximize the SNR. Its performance in terms of end-to-end SNR has been compared with another scheme in the literature for multiple relay selection.