On Nov. 4 2008, the Federal Communications Commission adopted rules for unlicensed use of television white spaces. The IEEE 802.22 Wireless Regional Area Networks (WRAN) standard is the first IEEE standard utilizing cognitive radio (CR) technology to exploit the television white space. A decision engine that is able to respond to the changes in the radio environment is necessary to efficiently exploit underutilized spectrum resources and avoid interfering with the licensed systems (e.g., TV services). This paper discusses the development of a case-based reasoning cognitive engine (CBR-CE) for the IEEE 802.22 WRAN applications. The performance of the CBR-CE is evaluated under various radio scenarios and compared to that of several multi objective search based algorithms, including the hill climbing search (HCS) and the genetic algorithm (GA). The simulation results show that the developed CBR-CE can achieve comparable utility with faster adaptation than the search based cognitive engines after appropriate training / learning. The learning process of the CBR is also simulated and discussed.