In recent past, cognitive radio has come out to as a promising solution to the spectrum scarcity problem. It tends to increase the spectrum utilization by making use of underutilized frequencies with the help of dynamic spectrum allocation technique. In this paper, we present one such scheme for bandwidth allocation to cognitive radio. Our proposal helps the channel distributor to decide the quantity of bandwidth that can be allocated to an unlicensed user at any given time. Fuzzy rules are used to optimize the bandwidth allocation based on three antecedents as: arrival rate of both licensed and unlicensed users and the availability of unoccupied number of channels within the system. The scheme is independent of the service times for user's requests and thus may be applicable to any service distribution type.