Non-additive robust ordinal regression: A multicriteria decision model based on hierarchical-level-bidirectional Choquet integral

Abstract

In contrast to the stable development of the traditional face to face teaching, distance education has become a considerable portion in higher education today and it is still rapidly growing. The mixed modes in education promote a great challenge for the professors and administrators to accurately and fairly evaluate the performance of students. Indeed, students’ performance evaluation is a multicriteria decision problem. To obtain a robust auxiliary decision support scheme compatible with the preferences of decision maker (DM), challenges often confronted in multicriteria decision analysis include dealing with complex structure of criteria, handling interaction between criteria and reducing the cognitive efforts of the DM. Based on the disaggregation–aggregation principle, complex preference is refined into smaller, manageable modules from two dimensions of alternative evaluation and criteria hierarchy. Then, a hierarchical-level-bidirectional Choquet integral preference method is developed to reproduce the refined preference and obtain the comprehensive evaluation of the alternatives. Further, a class of non-additive robust ordinal regression is performed by utilizing the characteristic indicators of the new Choquet integral and the preference relations given by the DM. Moreover, a representative preference method is put forward to rule out some preconceived possible relations, which enriches the necessary relations among alternatives. Finally, an illustrative example is provided to verify the practicability of the above multicriteria decision support methods.