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In this letter, we propose two relay selection schemes in cognitive relay networks. According to the proposed schemes, the number of relays involved in the opportunistic relaying is determined by the partial channel state information (CSI) of primary user link and partial CSI between the relays and the primary user receiver, so as to maintain the primary user's outage probability below a predetermined value. The exact outage probabilities of the secondary user are derived over Rayleigh fading channels. Finally, simulation results validate our analysis.