© The Institution of Engineering and Technology
An effective approach is developed to establish affine Takagi-Sugeno (T-S) fuzzy model for a given nonlinear system from its input–output data. Firstly, the fuzzy c-regression model (FCRM) clustering technique is applied to partition the product space of the given input–output data into hyper-plan-shaped clusters. Each cluster is essentially a basis of the fuzzy rule that describes the system behaviour, and the number of clusters is just the number of fuzzy rules. Particularly, a novel cluster validity criterion for FCRM is set up to choose the appropriate number of clusters (rules). Once the number of clusters is determined, the consequent parameters of each IF-THEN rule are directly obtained from the functional cluster representatives (affine linear functions). The antecedent fuzzy sets of each IF-THEN fuzzy rule are acquired by projecting the fuzzy partitions matrix U onto the axes of individual antecedent variable to obtain point-wise defined fuzzy sets and to approximate these point-wise defined fuzzy sets by normal bell-shaped membership functions. Additionally, a check and repartition algorithm is suggested to prevent the inappropriate premise structure where separate regions of data shared the same regression model. Finally, the gradient descent algorithm is included to adjust the fuzzy model precisely. An affine T-S fuzzy model with compact IF-THEN rules could thus be generated systematically. Several simulation examples are provided to demonstrate the accuracy and effectiveness of the affine T-S fuzzy modelling algorithm.
References
-
-
1)
-
C.T. Chao ,
Y.J. Chen ,
C.C. Teng
.
Simplification of fuzzy neural system using similarity analysis.
IEEE Trans. Syst., Man Cybern., Part B
,
2 ,
344 -
354
-
2)
-
Rovatti, R.: `Takagi-sugeno models as approximators in Sobolev norms: the SISO case', Proc. 5th IEEE Conf. on Fuzzy Systems, 1996, New Orleans, p. 1060–1066.
-
3)
-
W. Pedrycz
.
An identification algorithm in fuzzy relational systems.
Fuzzy Sets Syst.
,
153 -
167
-
4)
-
C.W. Xu ,
Y.Z. Lu
.
Fuzzy model identification and self-learning for dynamic systems.
IEEE Trans. Syst., Man Cybern.
,
683 -
689
-
5)
-
X.L. Xie ,
G.A. Beni
.
A validity measure for fuzzy clustering.
IEEE Trans. Pattern Anal. Machine Intell.
,
8 ,
841 -
846
-
6)
-
C.T. Lin ,
C.S.G. Lee
.
Reinforcement structure/parameter learning of neural-network based fuzzy logic control system.
IEEE Trans. Fuzzy Syst.
,
1 ,
43 -
63
-
7)
-
N.R.and Pal ,
J.C. Bezdek
.
On cluster validity for the fuzzy c-means model.
IEEE Trans. Fuzzy Syst.
,
3 ,
370 -
379
-
8)
-
C.C. Chuang ,
S.F. Su ,
S.S. Chen
.
Robust TSK fuzzy modeling for function approximation with outliers.
IEEE Trans. Fuzzy Syst.
,
6 ,
810 -
821
-
9)
-
T. Takagi
.
Fuzzy identification of systems and its applications to modeling and control.
IEEE Trans. Syst., Man Cybern.
,
116 -
132
-
10)
-
Fantuzzi, C., Rovatti, R.: `On the approximation capability of the homogeneous takagi-sugeno model', Proc. 5th IEEE Conf. on Fuzzy Systems, 1996, New Orleans, p. 1067–1072.
-
11)
-
R. Kruse ,
J. Gebhardt ,
F. Klawonn
.
(1994)
Foundations of fuzzy systems.
-
12)
-
J.Q. Chen ,
Y.G. Xi ,
Z.J. Zhang
.
A clustering algorithm for fuzzy model identification.
Fuzzy Sets Syst.
,
3 ,
319 -
329
-
13)
-
J.M. Leski
.
Fuzzy c-varieties/elliptotypes clustering in reproducing kernel Hilbert space.
Fuzzy Sets Syst.
,
2 ,
259 -
280
-
14)
-
L.X. Wang
.
(1994)
Adaptive fuzzy systems and control: design and stability analysis.
-
15)
-
M.Y. Chen ,
D.A. Linkens
.
Rule-base self-generation and simplification for data-driven fuzzy models.
Fuzzy Sets Syst.
,
2 ,
243 -
265
-
16)
-
A. Flores-Sintas ,
J.M. Cadenas ,
F. Martin
.
Partition validity and defuzzification.
Fuzzy Sets Syst.
,
3 ,
433 -
447
-
17)
-
E. Kim ,
M. Park ,
S. Ji ,
M. Park
.
A new approach to fuzzy modeling.
IEEE Trans. Fuzzy Syst.
,
3 ,
328 -
337
-
18)
-
J.A. Dickerson ,
B. Kosko
.
Fuzzy function approximation with ellipsoidal rules.
IEEE Trans. Syst., Man Cybern.
,
4 ,
542 -
560
-
19)
-
J. Fan ,
W. Xie ,
J. Pei
.
Subsethood measure: new definitions.
Fuzzy Sets Syst.
,
2 ,
201 -
209
-
20)
-
R.J. Hathaway ,
J.C. Bezdek
.
Switching regression models and fuzzy clustering.
IEEE Trans. Fuzzy Syst.
,
3 ,
195 -
204
-
21)
-
E. Ruspini
.
Numerical method for fuzzy clustering.
Inf. Sci.
,
319 -
350
-
22)
-
R.M. Tong
.
The evaluation of fuzzy models derived from experimental data.
Fuzzy Sets Syst.
,
1 -
12
-
23)
-
I. Gath ,
A.B. Geva
.
Unsupervised optimal fuzzy clustering.
IEEE Trans. Pattern Anal. Machine Intell
,
7 ,
773 -
781
-
24)
-
A.F.G. Skarmeta ,
M. Delgado ,
M.A. Vila
.
About the use of fuzzy clustering techniques for fuzzy model identification.
Fuzzy Sets Syst.
,
3 ,
179 -
188
-
25)
-
Y. Lin ,
G.A. Cunningham
.
A new approach to fuzzy-neural modeling.
IEEE Trans. Fuzzy Syst.
,
2 ,
190 -
198
-
26)
-
L. Wang ,
R. Langari
.
Building Seugeno-tpye models using fuzzy discretisation and orthogonal parameter estimation techniques.
IEEE Trans. Fuzzy Syst.
,
454 -
458
-
27)
-
J. Bezdek
.
(1981)
Pattern recognition with fuzzy objective function algorithms.
-
28)
-
G. Tsekouras ,
H. Sarimveis ,
E. Kavakli ,
G. Bafas
.
A hierarchical fuzzy-clustering approach to fuzzy modeling.
Fuzzy Sets Syst.
,
2 ,
245 -
266
-
29)
-
Gustafson, E.E., Kessel, W.C.: `Fuzzy clustering with a fuzzy covariance matrix', Proc. IEEE CDC, 1979, San Diego, p. 761–766.
-
30)
-
M. Sugeno ,
T. Yasukawa
.
A fuzzy-logic based approach to qualitative modeling.
IEEE Trans. Fuzzy Syst.
,
7 -
31
-
31)
-
R. Babuska
.
(1998)
Fuzzy modeling for control.
-
32)
-
M. Sugeno ,
K. Tanaka
.
Successive identification of a fuzzy model and its applications to prediction of a complex system.
Fuzzy Sets Syst.
,
315 -
334
-
33)
-
M. Sugeno ,
G.T. Kang
.
Structure identification of fuzzy model.
Fuzzy Sets Syst.
,
1 ,
15 -
33
-
34)
-
L.X. Wang
.
(1997)
A course in fuzzy systems and control.
-
35)
-
G.J. Klir ,
B. Yuan
.
(1995)
Fuzzy sets and fuzzy logic: theory and applications.
-
36)
-
G.E.P. Box ,
G.M. Jenkins
.
(1970)
Time series analysis, forecasting and control.
-
37)
-
A. Devillez ,
P. Billaudel ,
G.V. Lecolier
.
A fuzzy hybrid hierarchical clustering method with a new criterion able to find the optimal partition.
Fuzzy Sets Syst.
,
3 ,
323 -
338
-
38)
-
L. Ljung ,
T. Soderstrom
.
(1983)
Theory and practice of recursive identification.
-
39)
-
K. Hoffman ,
R. Kunze
.
(1971)
Linear algebra.
-
40)
-
J.C. Bezdek
.
Cluster validity with fuzzy set.
J. Cybern.
,
58 -
72
-
41)
-
F. Hoppner ,
F. Klawonn ,
R. Kruse ,
T. Runkler
.
(1999)
Fuzzy cluster analysis, methods for classification, data analysis and image recognition.
-
42)
-
T.W. Liao ,
A.K. Celmins ,
R.J. Hammell
.
A fuzzy c-means variant for the generation of fuzzy term sets.
Fuzzy Sets Syst.
,
2 ,
279 -
303
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta_20060415
Related content
content/journals/10.1049/iet-cta_20060415
pub_keyword,iet_inspecKeyword,pub_concept
6
6