On the uniqueness of the expression for the Choquet integral with linear core in classification

The Choquet integral has been applied in data mining, such as nonlinear multiregressions and nonlinear classifications. Adopting signed efficiency measures in the Choquet integral makes the models more powerful. Another idea for generalizing the above-mensioned models is to use a linear core in the Choquet integral. This has been successfully used in nonlinear multiregression. However, there is a uniqueness problem for presenting the Choquet integral in classification models such that it is difficult to explain the exact contribution rate from each individual attributes, as well as their combinations, towards the target. In this work, an additional restriction on the parameters is given to guarantee the uniqueness of the expression.