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One of the great challenges nowadays when managing IP networks is to guarantee proper Quality of Service, using network infrastructure on optimized way. One of the proposed solutions is traffic engineering with MPLS. However, the characterization of the demands and of the network state are difficult tasks, considering that the demands and the data traffic are random, consequently, the network state changes dynamically and in a random way. In this work we propose a connection admission controller that uses fuzzy logic based on linguistic rules to treat the inaccurate information in IP over MPLS networks with the purpose of offering Quality of Service to the users. In accordance with the simulation results, we concluded that the use of fuzzy logic allows a large flexibility in the connection admission process and the possibility to include more network and traffic information when making a decision without increasing considerably the controller complexity.