Necessary conditions for general MISO fuzzy systems as universal approximators

We investigate necessary conditions for general multiple-input single-output (MISO) fuzzy systems as universal approximators with as minimal system configuration as possible. The general MISO fuzzy systems employ almost arbitrary continuous input fuzzy sets, arbitrary singleton output fuzzy sets, arbitrary fuzzy rules, product fuzzy logic AND and the generalized defuzzifier containing the popular centroid defuzzifier as a special case. Our necessary conditions are developed under the practically sensible assumption that only a finite set of extrema of the multivariate continuous function to be approximated is available. We first show a decomposition property of the general fuzzy systems. Utilizing this property, we derive some necessary conditions for the fuzzy systems to be universal approximators with minimal system configuration. The conditions expose the strength as well as limitation of the fuzzy approximation, which are described in this paper.

[1]  James J. Buckley,et al.  Universal fuzzy controllers , 1992, Autom..

[2]  B. Kosko.  Fuzzy systems as universal approximators , 1992, [1992 Proceedings] IEEE International Conference on Fuzzy Systems.

[3]  Dimitar P. Filev,et al.  A generalized defuzzification method via bad distributions , 1991, Int. J. Intell. Syst..

[4]  Bart Kosko,et al.  Fuzzy function approximation with ellipsoidal rules , 1996, IEEE Trans. Syst. Man Cybern. Part B.

[5]  Vladik Kreinovich,et al.  Fuzzy control as a universal control tool , 1996, Fuzzy Sets Syst..

[6]  Xiao-Jun Zeng,et al.  Approximation theory of fuzzy systems-SISO case , 1994, IEEE Trans. Fuzzy Syst..

[7]  F. Lewis,et al.  Function approximation by fuzzy systems , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[8]  Joos Vandewalle,et al.  Fuzzy systems as universal approximators : Constructive theory , 1997 .

[9]  Hao Ying,et al.  Sufficient conditions on general fuzzy systems as function approximators , 1994, Autom..

[10]  J. Buckley.  Sugeno type controllers are universal controllers , 1993 .

[11]  L X Wang,et al.  Fuzzy basis functions, universal approximation, and orthogonal least-squares learning , 1992, IEEE Trans. Neural Networks.

[12]  Juan Luis Castro,et al.  Fuzzy systems with defuzzification are universal approximators , 1996, IEEE Trans. Syst. Man Cybern. Part B.

[13]  Guanrong Chen,et al.  Necessary Conditions for Some Typical Fuzzy Systems as Universal Approximators , 1997, Autom..

[14]  Xiao-Jun Zeng,et al.  Approximation accuracy analysis of fuzzy systems as function approximators , 1996, IEEE Trans. Fuzzy Syst..

[15]  Chuen-Chien Lee.  FUZZY LOGIC CONTROL SYSTEMS: FUZZY LOGIC CONTROLLER - PART I , 1990 .

[16]  Kevin M. Passino,et al.  Fuzzy systems for function approximation with applications to failure estimation , 1994, Proceedings of 1994 9th IEEE International Symposium on Intelligent Control.

[17]  L. Wang,et al.  Fuzzy systems are universal approximators , 1992, [1992 Proceedings] IEEE International Conference on Fuzzy Systems.