Aggregate Operator Defined on Partition of Space and Its Application to ID3 Algorithm

Information fusion has been widely applied in many fields. Aggregate operator plays a key role in information fusion. So far, all existing aggregate operators are defined on a subset of a space (set). In many of the problems with information fusion, we often need to deal with the operator defined on a partition of the space. Motivated by minimizing the classification information entropy of a partition while generating decision tree using ID3 algorithm, in this paper, we propose a aggregate operator on a partition, investigate its properties and computation, and provide the conclusion that the sum of the weighted entropy of the union of several subsets is not less than the sum of the weighted entropy of a single subset. It is shown that selecting the entropy of a single attribute is better than selecting the entropy of the union of several attributes in generating rules by ID3 algorithm.