Hesitant fuzzy linguistic TOPSIS method using a possibility-based comparison approach for multi-criteria decision-making with hesitant fuzzy linguistic term sets

The purpose of this study is to develop a hesitant fuzzy linguistic TOPSIS (The technique for order preference by similarity to ideal solution) method with a possibility-based comparison approach for addressing multi-criteria decision-making (MCDM) problems within the environment of hesitant fuzzy linguistic term sets (HFLTSs). This paper firstly analyses the existing comparison methods for HFLTSs and develops a new possibility degree formula which can address the issues in the previous ones. Then, based on the possibilities of the HFLTS binary relations, this paper defines the possibility-based outranking index to determine hesitant fuzzy linguistic positive ideal and negative ideal solutions. Subsequently, this paper introduces the concept of possibility-based comparison indices to establish a possibility-based closeness coefficient of each alternative relative to the ideal solutions. Based on a possibility-based comparison approach with the ideal solutions, this paper develops a hesitant fuzzy linguistic TOPSIS method for handling MCDM problems in which both the evaluative ratings of alternatives and the importance weights of criteria are expressed by HFLTSs. Finally, a numerical example is furnished to verify the feasibility and practicality of the proposed method and a comparative analysis with the existing methods is provided to illustrate the effectiveness and advantages of the proposed method.