A Multiple Attribute Decision-Making Method Based On Free Double Hierarchy Hesitant Fuzzy Linguistic Information Considering the Prioritized and Interactive Attributes

As the development and extension of hesitant fuzzy linguistic term sets (HFLTSs), free double hierarchy hesitant fuzzy linguistic term sets (FDHHFLTSs) can describe the evaluation information in more detail. In addition, in practical multiple attribute decision-making (MADM) problems, priority relations and interaction relations usually exist among attributes, and the prioritized interactive Choquet (PIC) operator based on generalized prioritized measure-guided aggregation (GPMGA) operator and Choquet integral (CI) operator is an effective tool for dealing with decision-making problems with priority relations and interaction relations. Under the above contexts, we improve the PIC operator and propose the FDHHFLPIC operator which can aggregate the evaluation information under free double hesitant fuzzy linguistic environment and take both priority and interaction relations into account. Furthermore, we propose an approach based on the FDHHFLPIC operators to address the real MADM problem, and the proposed method considering the different relations between attributes in decision-making process. Finally, two numerical examples are given to demonstrate the effectiveness and advantages of the proposed method which can consider priority relations and interaction relations under the FDHHFLTSs.