Spline approximation of fuzzy functions
MATH'05 Proceedings of the 8th WSEAS International Conference on Applied Mathematics
On the suitability of the Bandler-Kohout subproduct as an inference mechanism
IEEE Transactions on Fuzzy Systems
Mathematical aspects of fuzzy control
WILF'03 Proceedings of the 5th international conference on Fuzzy Logic and Applications
WILF'05 Proceedings of the 6th international conference on Fuzzy Logic and Applications
International Journal of Fuzzy System Applications
Design and Analysis of an Improved Approximated Fuzzy Logic Controller for Shunt Active Power Filter
International Journal of Fuzzy System Applications
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Mamdani (1975) controller was successfully used in many applications. One of its interpretations is that it uses a fuzzy relation as an approximation of the desirable input-output correspondence. We analyze mathematical properties of Mamdani controller and notice that it has lower computational complexity when compared to the residuum-based controller. However, we show that in standard situations, both these fuzzy controllers do not represent the rule base properly in the sense of finding a solution to the related system of fuzzy relational equations. First, we consider the premises and consequents as typical inputs and outputs, and we want their correspondence to be kept. Next, we require that each normal input produces an output that bears nontrivial information. These two conditions appear to be almost contradictory to the previous controllers. We suggest a generalization of Mamdani controller which allows us to satisfy these requirements. The theory and experiments suggest that it performs better without any change of rule base and without a substantial increase of complexity