C-fuzzy decision trees

This paper introduces a concept and design of decision trees based on information granules - multivariable entities characterized by high homogeneity (low variability). As such granules are developed via fuzzy clustering and play a pivotal role in the growth of the decision trees, they will be referred to as C-fuzzy decision trees. In contrast with "standard" decision trees in which one variable (feature) is considered at a time, this form of decision trees involves all variables that are considered at each node of the tree. Obviously, this gives rise to a completely new geometry of the partition of the feature space that is quite different from the guillotine cuts implemented by standard decision trees. The growth of the C-decision tree is realized by expanding a node of tree characterized by the highest variability of the information granule residing there. This paper shows how the tree is grown depending on some additional node expansion criteria such as cardinality (number of data) at a given node and a level of structural dependencies (structurability) of data existing there. A series of experiments is reported using both synthetic and machine learning data sets. The results are compared with those produced by the "standard" version of the decision tree (namely, C4.5).