A Choquet Integral Model with Multiple Outputs and Its Application to Classifications

Abstract

A Choquet integral model with multiple outputs is proposed. For an input pair (x₁,..., x_n) and m fuzzy measures μ_j, the output values y₁,..., y_m are calculated by the extended Choquet integral with respect to the j-th fuzzy measure μ_j. By imposing the constrains that the sum of μ(A)=1 for all A, the sum of the output values, ∑y_j is founded to be 1. By using this model, it is possible to categorize objects with fuzzy inputs into m classes. We show an example where objects are categorized as class1, class2, contradiction class, and rest-unknown class.