Fuzzy decision trees have been used for classification problems and I want to know if there is a paper on FDTs for regression problems.
In the attached article, a fuzzy decision tree is constructed by allowing the possibility of partial membership of a point in the nodes that make up the tree structure. This extension of its expressive capabilities transforms the decision tree into a powerful functional approximant that incorporates features of connectionist methods, while remaining easily interpretable. Fuzzification is achieved by superimposing a fuzzy structure over the skeleton of a CART decision tree.
In the attached article, a fuzzy decision tree is constructed by allowing the possibility of partial membership of a point in the nodes that make up the tree structure. This extension of its expressive capabilities transforms the decision tree into a powerful functional approximant that incorporates features of connectionist methods, while remaining easily interpretable. Fuzzification is achieved by superimposing a fuzzy structure over the skeleton of a CART decision tree.
This is a good question with lots of paths to follow in looking for an answer.
A good place to start in answering this question is
T.A. Runkler, J.C. Bezdek, Function approximation with polynomial membership functions and alternating cluster estimation, Fuzzy Sets and Systems 101 (2), 1999, 207-218:
http://www.sciencedirect.com/science/article/pii/S016501149800164X
In this article, nonlinear functions are approximated with local linear models.
More to the point, consider
Decision trees as classifers are introduced in chapter 3, starting on page 30. Fuzzy decision trees are examined in Section 3.3.5, starting on page 45. Fuzzy decision trees help overcome a significant disadvantage of decision trees, namely, sharp decision boundaries.
See, also,
J. Hauth, Grey-box modelling for nonlinear systems, Ph.D. thesis, Technischen Universitat Kaiserslautern, 2008:
http://web.maths.unsw.edu.au/~peterdel-moral/grey-box-modelling.pdf
This thesis is especially good in its detailed analysis of decision trees. Constructive approximation theory is considered in terms of function approximation and its application, starting on page 210.
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