Fuzzy decision trees.
 
Alberto Suárez (1,2)   and James F. Lutsko (2)
 
 (1)  Escuela Técnica Superior de Informática
Universidad Autónoma de Madrid
Cra. de Colmenar Viejo Km. 15
28048 Madrid
Spain
 
e-mail: alberto.suarez@ii.uam.es
phone: +34-1-3975543
fax: +34-1-3975277
 
 (2)  Expert Systems  Applications and  Development Group.
Katholieke Universiteit Leuven.
de Croylaan 46
     B-3001 Heverlee-Leuven
     Belgium
 
 



 
    Attributes
Dependent variable
x1 = a2;       x2 = (a20.5)2   
      y = a + noise 
   
Size  of tree 
RMS / s(noise)
Crisp tree
RMS / s(noise)
Fuzzy tree
4
1.2738
0.9975
5
1.2029
1.0677
6
1.0639
1.0241
5
1.0872
1.0027
5
1.1875
1.0462
5
1.2583
1.0270
6
1.1410
1.0962
5
1.3566
1.1658
6
1.2511
1.0462
6
1.2054
1.0374
 
                                Table I. Results for 10 realizations of the data. Results are normalized by the standard deviation of the noise in the original data. Therefore, a result of a normalized RMS in the neighborhood of 1 indicates a good quality fit. Table I shows how fuzzification improves the performance of the tree upon fuzzification. More detailed results for other regression and
classification problems will be presented.
 

Bibliography
 

[1]  L. Zadeh. Fuzzy sets. Information and Control, 8:338-353, 1965.
 
[2]   J. Bedzek. Fuzzy Models for Pattern Recognition, S. Pal ed.  IEE Press, NY, 1992.

[3]  L.  Breiman, J. H.. Friedman, R. A. Olshen, and C.J. Stone. Classification and Regression Trees. Chapman & Hall, NY, 1984.

[4] J.R. Quinlan. Induction of decision trees. Machine Learning, 1(1):81-106, 1986.
 
[5]   V. Cherkassky and F.Mulier. Statistical and neural network techniques for nonparametric
  regression. In Selecting Models from Data, P. Cheeseman R.W. Oldford eds. pages 383--392, Springer-Verlag, NY, 1994.
 
 
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