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• [P463] Necessary and Sufficient Conditions for General SISO Mamdani Fuzzy Systems on a Given Accuracy
  Author(s): Jin Yang
  
  

  Abstract
  Given a prescribed accuracy, necessary and sufficient conditions are investigated for general single input/single output (SISO) Mamdani fuzzy systems as approximators of continuous functions defined on compact domain. Since general SISO Mamdani fuzzy systems are monotonic on subintervals, necessary conditions for fuzzy systems on a given accuracy have been established firstly with the extreme of the desired continuous function. Simultaneously, a dynamically constructive method is proposed to show the conditions are sufficient. Furthermore, it is shown that existing results concerning necessary conditions are only special cases of ours. The necessary and sufficient conditions can not only be used practically to determine input/output fuzzy sets, and fuzzy rules for fuzzy systems, but also provide guidance on the membership function design. Finally, simulation examples are given to illustrate the conclusions and analyze the strength as well as the limitation of the fuzzy systems as function approximators: the number of fuzzy rules increases with the number of extreme whose swings are larger than the accuracy, not associated with the function¡¯s formulation.

  
   

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