Approximation theory of fuzzy systems based upon genuine many-valued implications - MIMO cases

It is proved that the single input and single output (SISO) fuzzy systems based upon genuine many-valued implications are universal approximators. It is shown theoretically that fuzzy control systems based upon genuine many-valued implications are equivalent to those based upon t-norm implications, the general approach to construct fuzzy systems is given. It is also shown that defuzzifier based upon center of areas is not appropriate to the fuzzy systems based upon genuine many-valued implications.

[1]  Xiao-Jun Zeng,et al.  Approximation theory of fuzzy systems-MIMO case , 1995, IEEE Trans. Fuzzy Syst..

[2]  D. Dubois,et al.  Fuzzy sets in approximate reasoning. I, Inference with possibility distributions , 1991 .

[3]  A. Kandel,et al.  Applicability of some fuzzy implication operators , 1989 .

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

[5]  D. Dubois,et al.  Fuzzy sets in approximate reasoning, part 2: logical approaches , 1991 .

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

[7]  D. Dubois,et al.  Fuzzy sets in approximate reasoning, part 1: inference with possibility distributions , 1999 .

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

[9]  Fengming Song,et al.  Constructive theory for fuzzy systems , 1997, Fuzzy Sets Syst..

[10]  Guojun Wang,et al.  On the Logic Foundation of Fuzzy Reasoning , 1999, Inf. Sci..

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

[12]  Li Yong-ming,et al.  Approximation capability of fuzzy input-output systems based on similarity measures , 2000, Proceedings of the 3rd World Congress on Intelligent Control and Automation (Cat. No.00EX393).

[13]  M. Sc,et al.  Sufficient Conditions on Uniform Approximation of Multivariate Functions by General Takagi-Sugeno Fuzzy Systems with Linear Rule Consequent , 1998 .

[14]  Bart Kosko,et al.  Fuzzy Systems as Universal Approximators , 1994, IEEE Trans. Computers.

[15]  LangJérôme,et al.  Fuzzy sets in approximate reasoning, part 2 , 1991 .

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

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

[18]  Ramon López de Mántaras,et al.  Approximate Reasoning Models , 1990 .

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

[20]  Juan Luis Castro,et al.  Fuzzy logic controllers are universal approximators , 1995, IEEE Trans. Syst. Man Cybern..

[21]  Francisco Herrera,et al.  Applicability of the fuzzy operators in the design of fuzzy logic controllers , 1997, Fuzzy Sets Syst..

[22]  Chuen-Chien Lee,et al.  Fuzzy logic in control systems: fuzzy logic controller. I , 1990, IEEE Trans. Syst. Man Cybern..

[23]  Senén Barro,et al.  Reasoning with truth values on compacted fuzzy chained rules , 1998, IEEE Trans. Syst. Man Cybern. Part B.

[24]  前田 博,et al.  Didier Dubois and Henri Prade Fuzzy sets in approximate reasoning, Part 1 : Inference with possibility distributions Fuzzy Sets and Systems, vol.40,pp143-202,1991 , 1995 .

[25]  J. B. Kiszka,et al.  The influence of some fuzzy implication operators on the accuracy of a fuzzy model-part II , 1985 .

[26]  Abraham Kandel,et al.  Investigations on the applicability of fuzzy interference , 1992 .