Re: Fuzzy Trees

Christophe Marsala (Christophe.Marsala@lip6.fr)
Mon, 20 Apr 1998 16:55:13 +0200 (MET DST)

Will Dwinnell wrote:
>
> I agree. To take an analogy of the distinction between
> probabilistic automata and fuzzy automata, a fuzzy tree would
> allow several branches to be pursued simultaneously with varying
> degrees of membership.
>
> --
> Will Dwinnell
> Commercial Intelligence

A fuzzy decision tree (FDT) is not only a classical tree which would
allow several branches to be pursued simultaneously. A FDT is a decision
tree where edges are associated with fuzzy modalities. As a consequence,
when using this tree to classsify a new description, several pathes
would be pursued.
Moreover, when classifying a new description with this tree, it enables
us to take into account fuzzy modalities associated with this
description.
For instance, a test node of a FDT can be a test on the value of the
attribute "size" with two edges going out that node. Each edge is
associated with a fuzzy modality: "small" or "big". A new description to
classify can be associated with the fuzzy modality "near 2 meters" for
the attribute "size". Thus, this fuzzy modality of the description has
to be compared with the 2 fuzzy modalities of the edges in order to find
a degree a membership of this description to each path.

Fuzzy subset theory is used to construct FDT and to use them to classify
fuzzy descriptions.

If you want to know more about FDT: "Learning from Imperfect Data" by B.
Bouchon-Meunier, C. Marsala and M. Ramdani, in Fuzzy Information
Engineering: a Guided Tour of Applications, Dubois, Prade and Yager eds,
John Wileys and Sons, 1997, pp.139-148.

Best regards,
Christophe Marsala.