Multi-criteria Group Decision-Making Based on Interval Neutrosophic Uncertain Linguistic Variables and Choquet Integral

Background/IntroductionThe interval neutrosophic uncertain linguistic variables (INULVs) can be better at handling the uncertainty of the decision-makers’ cognition in multi-criteria group decision-making (MCGDM) problems. Most MCGDM methods with INULVs are based on the supposition that all criteria are independent; however, they may be correlative in real decisions. The Choquet integral can process MCGDM problems with correlated criteria, which fail to aggregate INULVs. So, it is necessary and meaningful to propose the MCGDM method with INULVs based on the Choquet integral by considering the correlations between the attributes.MethodsBy combining INULVs with the Choquet integral, we propose the interval neutrosophic uncertain linguistic Choquet averaging (INULCA) operator and the interval neutrosophic uncertain linguistic Choquet geometric (INULCG) operator. These two operators reflect the existing correlation between two adjacent coalitions. In order to globally consider the correlations between elements or their ordered positions, the generalized Shapley INULCA (GS-INULCA) operator and the generalized Shapley INULCG (GS-INULCG) operator are further proposed. Furthermore, some models based on the grey relational analysis (GRA) method for determining the optimal fuzzy measures on the expert set and the criteria set are respectively built.ResultsBased on the proposed operators and built models, a method is developed to cope with the MCGDM problems with INULVs, and the validity and advantages of the proposed method are analyzed by comparison with some existing approaches.ConclusionsThe method proposed in this paper can effectively handle the MCGDM problems in which the attribute information is expressed by INULVs, the attributes’ and experts’ weights are partly known, and the experts and attributes are interactive.