A mass assignment based ID3 algorithm for decision tree induction

A mass assignment based ID3 algorithm for learning probabilistic fuzzy decision trees is introduced. Fuzzy partitions are used to discretize continuous feature universes and to reduce complexity when universes are discrete but with large cardinalities. Furthermore, the fuzzy partitioning of classification universes facilitates the use of these decision trees in function approximation problems. Generally the incorporation of fuzzy sets into this paradigm overcomes many of the problems associated with the application of decision trees to real-world problems. The probabilities required for the trees are calculated according to mass assignment theory applied to fuzzy labels. The latter concept is introduced to overcome computational complexity problems associated with higher dimensional mass assignment evaluations on databases.