Decision Analysis on Choquet Integral-Based Multi-Criteria Decision-Making with Imprecise Information

The uncertain multi-criteria decision-making problem is investigated, where the information about criteria weights and criteria evaluations is imprecise and there exist interactions between criteria. In real-life multi-criteria decision-making problems, there often exist positive or negative interactions between criteria, and it is also difficult to obtain the precise information about criteria weights and criteria evaluations. However, most of the existing multi-criteria decision-making methods only focus on one of these two issues, which often co-exist in practice. To address such a gap in the existing research, Choquet integral is firstly employed to aggregate the imprecise information of alternatives to reflect the interactions between criteria. Based on the regret values between pairs of alternatives with imprecise information, four types of best alternative concepts are defined from the perspectives of optimism and pessimism, respectively, and four corresponding optimal models are established to identify such best alternatives. By comparing the proposed methods with the existing ones, it is showed that the proposed methods not only give a complete decision analysis, but also have better distinguishability by considering the interactions between criteria. These methods are then extended to identify the worst alternatives.