The tree can be pruned, by transforming a node into a leaf node, if the performance loss is low. This procedure facilitates the tree interpretation. Pruning is based on the performance of the tree equivalent FIS.
Note: the pruned tree may have a better performance than the full tree. as tree building is based on a purity criterion and not directly on a performance criterion.
Fuzzy decision trees proposed in FisPro are based on a fuzzy implementation of the ID3 algorithm .
The fuzzy decision tree generation procedure in FisPro needs both a current FIS configuration file and a current data file. The tree building is based on one output only, even if the FIS has several outputs. This output is user chosen.
Four cases are possible:
For a crisp output with the classification option, classes are determined from data, and discrete MFs corresponding to the class labels are assigned to the output. The maximum number of classes is 100.
With the classification option, the majority class is assigned to each node, without it, the average of the node attracted example output is assigned to it.
In the fuzzy output case, the tree summary gives the fuzzy proportions of the node attracted example output for each MF.
If rules are present in the FIS configuration file, they are ignored.
The Generate tree option opens a pop up windows allowing to choose:
The relative entropy favors the variables with an unequal distribution of examples (not classes) between the MFs. It also favors the variables with a small number of MFs.
Pruning consists in a recursive node removal, from tree bottom to top. The removal is done if the equivalent FIS performance does not decrease, or decreases only a little.
The relative loss of performance (compared to the performance of the full tree) has a default value of 0.1. It is user editable. The default validation file used for computing the performance is the current data file. Other files can be used, in particular the active or inactive data file created by the use of the Data-table menu option.
Pruning can be done by removing a full split, or by removing node after node.
The procedure creates one tree or two (if pruning was selected). It opens two windows for each tree:
The user can select the informations to display for all nodes: number of items attracted by the node, node entropy, majority class and sample number class distribution (classification case), or else mean and standard deviation (regression case). The part of the tree displayed in the window can be exported or printed.
The initial tree location is done automatically but the user can also select tree branches and maually move them to improve the location. The scale and font are editable.
result.fistree file describes a fuzzy tree (full or pruned tree): The first column gives the FIS equivalent name (full tree or prunded tree). Then we have the indices described in section 2:
Then follow some indices specific to fuzzy trees:
This submenu allows to view an existing tree. Two possibilities are offered.