Two MAGDM models based on hesitant fuzzy linguistic term sets with possibility distributions: VIKOR and TOPSIS

Hesitant fuzzy linguistic term sets (HFLTSs) with additional possibility distributions can represent a much broader range of linguistic data. This paper develops compromise solutions for multiple attribute group decision making (MAGDM) using HFLTS. Geodesic distance and possibility distribution based distance measures are introduced to calculate the consensus degrees and determine the participant importance weights for the aggregation. Two models are then proposed to derive a compromise solution for the MAGDM problems. The first model is based on the VIKOR method and is used to determine the compromise between group utility maximization and individual regret minimization. The second model is based on the TOPSIS method and seeks to identify the compromise between the distances from the ideal and anti-ideal solutions. For both models, several ideal solutions and separation measures are presented and some of the properties in the two models are proven. An example based on an assessment of a health-care waste disposal management system illustrates the feasibility and practicability of the two proposed models. A further comparative study highlights the distinct features and potential use of the presented models.