Mathematical aspects of fuzzy control

Authors:
Paolo Amato;Antonio Di Nola;Mirko Navara
Affiliations:
Soft Computing, Si-Optics and Post Silicon Technologies Corporate R&D, STMicroelectronics, Arzano, NA, Italy;Department of Mathematics and Informatics, University of Salerno, Baronissi, Salerno, Italy;Center for Machine Perception, Department of Cybernetics, Faculty of Electrical Engineering, Czech Technical University, Praha, Czech Republic
Venue:
WILF'03 Proceedings of the 5th international conference on Fuzzy Logic and Applications
Year:
2003

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Abstract

In recent decades, fuzzy controllers were successfully applied to many tasks. Their use was based more on engineering intuition than on deep mathematical treatment. Here we collect several criteria that a fuzzy controller should satisfy in order to represent the meaning of the rule base. Surprisingly, these conditions are often ignored and violated. Sometimes this is caused only by wrong design, but there are cases when the principle of the controller does not admit to satisfy these criteria. We discuss them in more detail and formulate conclusions for selection of an appropriate type of fuzzy controller.