Applying a complexity-based Choquet integral to evaluate students' performance
The weighted arithmetic mean and the regression methods are the most often used operators to aggregate criteria in decision making problems with the assumption that there are no interactions among criteria. When interactions among criteria exist, the discrete Choquet integral is proved to be an adequate aggregation operator by further taking into accounts the interactions. In this study, we propose a complexity-based method to construct fuzzy measures needed by the discrete Choquet integral and a real data set is analyzed. The advantage of the complexity-based method is that no population probability is to be estimated such that the error of estimating the population probability is reduced. Four methods, including weighted arithmetic method, regress ion-based method, the discrete Choquet integral with the entropy-based method, and our proposed discrete Choquet integral with the complexity-based method, are used in this study to evaluate the students' performance based on a Basic Competence Test. The results show that the students' overall performance evaluated by our proposed discrete Choquet integral with the complexity-based method is the best among the four methods when the interactions among criteria exist. (C) 2008 Elsevier Ltd. All rights reserved.
discrete choquet integral fuzzy measure entropy complexity