## 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.

Original language | English |
---|---|

Pages (from-to) | 317-321 |

Number of pages | 5 |

Journal | Soft Computing |

Volume | 11 |

Issue number | 4 |

Early online date | 20 Apr 2006 |

DOIs | |

Publication status | Published - Feb 2007 |

Externally published | Yes |

## Keywords

- Decision tree
- Information entropy
- Information fusion
- Non linear integral
- Partition