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Relay selection is a technique that can considerably increase the performance of cooperative communications. In this paper, we propose a new relay selection algorithm using fuzzy logic aiming at both network lifetime and end-to-end throughput. The new algorithm operates in a distributed way, running independently at each node, not requiring a central entity for complex coordination. The method considers the channel state of the relay-destination link and the residual energy of its battery. It is shown that the proposed scheme can transmit a larger amount of information during the network lifetime with respect to both the opportunistic (which focuses on throughput) and random (which focuses on lifetime) selection algorithms, increasing the network utility.