Nonadditive robust ordinal regression with nonadditivity index and multiple goal linear programming

Nonadditive robust ordinal regression (NAROR) is a widely adopted approach to analyze and reveal the dominance relationships among all decision alternatives based on nonadditive measures, called capacities. In this paper, we first investigate some advantages of the nonadditivity index as an explicit interaction index, as compared with the traditional probabilistic simultaneous interaction indices, and show that nonadditivity index can serve as an equivalent representation of a capacity. Then we enhance the NAROR method by using nonadditivity index as well as multiple-goal linear programming, where the former is used to replace the traditional interaction index to more naturally represent the decision maker's preferences, and the latter aims to replace the 0 to 1 mixed integer programming to enhance the ability to detect and adjust contradictory and redundant preference information. The updated NAROR's steps are constructed and discussed in detail and illustrated with a practical example.