A Nonlinear Integral Defined on Partition and its Application to Decision Trees

  • Authors:

  • Xi-Zhao Wang;Su-Fang Zhang;Jun-Hai Zhai

  • Affiliations:

  • Department of Mathematics and Computer Science, Hebei University, 071002, Baoding City, Hebei Province, China;Department of Mathematics and Computer Science, Hebei University, 071002, Baoding City, Hebei Province, China;Department of Mathematics and Computer Science, Hebei University, 071002, Baoding City, Hebei Province, China

  • Venue:
  • Soft Computing - A Fusion of Foundations, Methodologies and Applications
  • Year:
  • 2006

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Abstract

Nonlinear integrals play an important role in information fusion. So far, all existing nonlinear integrals of a function with respect to a set function are defined on a subset of a space. In many of the problems with information fusion, such as decision tree generation in inductive learning, we often need to deal with the function defined on a partition of the space. Motivated by minimizing the classification information entropy of a partition while generating decision trees, this paper proposes a nonlinear integral of a function with respect to a nonnegative set function on a partition, and provides 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 decision trees.