Affiliations: Department of Genetics, Cell Biology, and Anatomy, University of Nebraska Medical Center, Omaha, NE, USA | Department of Mathematics, University of Nebraska at Omaha, Omaha, NE, USA
Note: [] Corresponding author. Naomi Kochi, Department of Genetics, Cell Biology, and Anatomy, University of Nebraska Medical Center, Omaha, NE 68198, USA. Tel.: +1 402 554 2734; Fax: +1 402 554 2975; E-mail: nkochi@unomaha.edu
Abstract: There are different nonlinear integrals that could be used as an aggregation tool in information fusion and data mining. The Choquet integral with respect to fuzzy measures is one of them. We present some methods to identify fuzzy measures based on the Choquet integral in this paper. An iterative method introduced by Grabisch is discussed with some counterexamples. Furthermore, after removing some restrictions which are used in Grabisch's model, we introduce an algebraic method and a genetic algorithm to identify fuzzy measures and present some experimental results on both artificial and real-world data sets to show their effectiveness.
Keywords: Fuzzy measures, the Choquet integral, genetic algorithms, least square method
