[1]SUN Fu-chun,YANG Jin,LIU Hua-ping.Preconditions for SISO Mamdani fuzzy systems to perform as function approximators[J].CAAI Transactions on Intelligent Systems,2009,4(4):288-294.
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Preconditions for SISO Mamdani fuzzy systems to perform as function approximators

CAAI Transactions on Intelligent Systems[ISSN 1673-4785/CN 23-1538/TP] Volume: 4 Number of periods: 2009 4 Page number: 288-294 Column: 学术论文—人工智能基础 Public date: 2009-08-25
Title:
Preconditions for SISO Mamdani fuzzy systems to perform as function approximators
Author(s):
SUN Fu-chun;  YANG Jin;  LIU Hua-ping
State Key Laboratory of Intelligent Technology and System, Tsinghua University, Beijing 100084, China
Keywords:
fuzzy systems;  necessary conditions;  fuzzy rules;  approximation accuracy
CLC:
TP18
DOI:
-
Abstract:
It has been proven that fuzzy systems are universal approximators. However, a large number of rules are usually needed for high accuracy. Knowledge of conditions necessary for a fuzzy system to have a given level of accuracy can provide guidance for design of an optimal system, such as selection of optimal input/output fuzzy sets and fuzzy rules. The necessary conditions for a singleinput singleoutput (SISO) Mamdani fuzzy system to operate as a function approximator subject to a given precision were discussed. Since the general SISO Mamdani fuzzy system is monotonic at subintervals, its optimal configuration is when the number of division points is not less than the number of times its monotonicity changes. Thus by analyzing the local characteristics of the object function under the fuzzy system, necessary conditions for a SISO Mamdani fuzzy systems were obtained in accordance with the extrema of the object function. Furthermore, it was shown that the necessary conditions found in prior documents are only a special case of those described here. Finally, simulation examples were given to verify our conclusions and analyze the performance as well as the limitations of a fuzzy system as a function approximator. 
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