Interval-valued intuitionistic pure linguistic entropy weight method and its application to group decision-making

In recent years, the problem of complex multi-attribute group decision-making (MAGDM) in uncertain environments has received increasing attention. In evaluating MAGDM problems, obtaining the objective attribute weights is very important. Considering the excellent performance of intuitive fuzzy linguistic sets in dealing with uncertain information, this paper introduces a new interval-valued intuitionistic pure linguistic entropy weight (IVIPLEW) method for determining attribute weights and evaluating MAGDM problems. The IVIPLEW method considers the cases of missing values, and uses the conventional interval-valued intuitionistic pure linguistic (IVIPL) expectations to supplement the missing values. This method of dealing with missing values not only considers the expectations of experts, but also prevents fluctuations in linguistic variables from impacting the decision results. This paper establishes an analysis framework that allows the IVIPLEW method to be applied to MAGDM problems, and presents a practical case study that illustrates the practicality and effectiveness of IVIPLEW. The results are quite satisfactory. The effectiveness of the proposed method is demonstrated through a comparison with the IVIPL information aggregation method. Furthermore, the robustness of the IVIPLEW method is verified through a sensitivity analysis. The results presented in this paper show that the IVIPLEW method is applicable to a wide range of MAGDM problems.