In this paper, a novel spectrum association approach for cognitive radio networks (CRNs) is proposed. Based on a measure of both inference and confidence as well as on a measure of quality-of-service, the association between secondary users (SUs) in the network and frequency bands licensed to primary users (PUs) is investigated. The problem is formulated as a matching game between SUs and PUs. In this game, SUs employ a soft-decision Bayesian framework to detect PUs' signals and, eventually, rank them based on the logarithm of the a posteriori ratio. A performance measure that captures both the ranking metric and rate is further computed by the SUs. Using this performance measure, a PU evaluates its own utility function that it uses to build its own association preferences. A distributed algorithm that allows both SUs and PUs to interact and self-organize into a stable match is proposed. Simulation results show that the proposed algorithm can improve the sum of SUs' rates by up to 20 % and 60 % relative to the deferred acceptance algorithm and random channel allocation approach, respectively. The results also show an improved convergence time.