This study focuses on the false feedback of spectrum information and the malicious behavior that forcibly occupies spectrum resources in cognitive radio networks. A credible spectrum sensing and allocation model based on fuzzy theory is proposed. The spectrum sensing behavior and spectrum utilization behavior are taken as two evaluation factors. On the basis of subjectivity and uncertainty of trust, this study adopts the fuzzy comprehensive evaluation method to construct the trust evaluation of nodes. In cooperative spectrum sensing, comprehensive evaluation results can be used to identify malicious nodes and eliminate false feedback information. In spectrum allocation, the degree of lattice closeness among fuzzy sets is used to define and calculate the difference between the actual comprehensive evaluation set and the ideal comprehensive evaluation. The difference is calculated to quantify the credibility of non-malicious nodes and to determine the allocation of spectrum resources to nodes using the multi-objective optimization algorithm. These techniques can control the malicious behaviors of nodes and encourage cooperative behavior among nodes. Consequently, the joint design of spectrum sensing at the physical layer and spectrum allocation at the media access control layer is realized. Simulation results and analysis indicate that under malicious attacks, the proposed model has sound performance in terms of system sensing, throughput, and fair spectrum allocation compared with existing models. Copyright © 2013 John Wiley & Sons, Ltd.