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Nowadays IEEE 802.11 WLANs are widely deployed; in spite of this, the issue of designing an efficient and practical Access Point selection schemes that can provide the best throughput performance in a variety of link conditions is still open. In this paper we present a Cognitive AP selection scheme that allows the mobile station to learn from its past experience how to select the best AP. In our proposal the mobile station collects measurements regarding the past link conditions and throughput performance, and a cognitive engine based on a Neural Network trained on this data drives the AP selection process. Our performance evaluation shows that the proposed scheme has very good performance in a variety of scenarios, as opposed to other algorithms previously proposed in the literature which perform well only in specific cases and cannot address the non-idealities typical under real conditions.