Multiple Criteria Nonlinear Programming Classification with the Non-additive Measure

Multiple criteria linear/nonlinear programming has well been used for decision making problems, such as classification and prediction. In these applications, usually only contributions from the attributes towards a certain target, such as classification, are considered (using weighted sum), while the impact from the interactions among attributes is simply ignored, resulting a model of linear aggregation of attributes. However, interaction among attributes could be a very important factor for more accurate classification. Taking interaction among attributes into consideration, in this paper we review the concept of the Choquet integral, and apply the Choquet integral with respect to non-additive measure as the attributes aggregation tool for multiple criteria nonlinear programming. We have applied our method in credit cardholders’ behaviors classification problems. The experimental results on two real life data sets show the significant improvement of using the non-additive measure in data mining.