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This research deals with the soft computing methodology of fuzzy cognitive map (FCM). Here a mathematical description of FCM is presented and a new methodology based on fuzzy logic techniques for developing the FCM is examined. The capability and usefulness of FCM in modeling complex systems and the application of FCM to modeling and describing the behavior of a heat exchanger system is presented. The applicability of FCM to model the supervisor of complex systems is discussed and the FCM-supervisor for evaluating the performance of a system is constructed; simulation results are presented and discussed.