A Copula Approach to Model Validation

Abstract

Two types of the multiple-output Choquet integral models are defined. Vector-valued Choquet＜BR＞integral models are vector-valued functions calculated by m times Choquet integral calculations with respect to the m-th fuzzy measure of a fuzzy measure vector. Logical set-function-valued Choquet integral models are set-functionvalued functions that can be used in classification. The set function shows singleton, overlap, and unclassifiable degrees. The sum value of the set function is equal to 1. A method for transformation from vector-valued Choquet integral models to logical set-function-valued Choquet integral models is proposed.