Models of many industrial complex systems are not completely identified yet, so controller design for these systems encounter some problems. These systems have worked satisfactorily, for many years, under the supervision of operators, but in some cases, it is necessary to make them automated. On the other hand, the cost of identification and designing computer-based controllers with common methods will be so high for them. Scince fuzzy controllers can be designed without knowing the mathematical model of the system, just based on rules extracted from experts experience, this kind of controllers has lots of applications in complex systems with high non-linearity and delay. That how we can convert the experts' experience to the the fuzzy rules, is an important issue in fuzzy identification and controller design. Rough sets theory is a new algorithm for extracting fuzzy rules directly out of observed data. To reduce the computation burden, this theory extracts the minimal set of relations between the previous and current mesurments and control actions. Both fuzzy and rough sets are able to face problems with uncertainity and can be good complement for each other. Lately reasearchers are working on combining these two sets which result in fuzzy-rough sets. So the way we combine the rough sets with other theories to face uncertainity is a valuable field of research. Additionally, using these new sets in system identification and controller design are useful applications of this study. In this thesis, controller rules and rule-base model of a sample system are extracted out of a huge amount of input-output data, using rough sets theory and its combination with fuzzy sets, i.e. fuzzy-rough sets. Additionally, it is shown that the performance of the resultant rule-base controller is improved in comparison with the former controller. Also it is more robust in facing disturbances. In this way the application of rough sets and its combination with fuzzy sets in identification and controller design is shown. Key Words Granular Computing, Rough Sets, System Identification, Controller.
