A TOPSIS Method For Multi-Attribute Group Decision Making Based on Hesitant Fuzzy Linguistic q-Rung Orthopair Fuzzy Sets and Its Application in Credit Evaluation

Abstract Exploring the determination method of membership degree and non-membership degree with higher richness of linguistic elicitation is an important issue in the application research of q -rung orthopair fuzzy sets ( q -ROFSs) in multi-attribute group decision-making (MAGDM). Firstly, the definition of hesitant fuzzy linguistic element normalized score function (HFLENSF) was proposed by using the linguistic scale function which can realize the transformation between qualitative information and quantitative data, and the mapping from hesitant fuzzy linguistic term set (HFLTS) to [0,1] interval was realized. Secondly, based on the HFLENSF, the definition of hesitant fuzzy linguistic q -rung orthopair fuzzy set (HFL q -ROFS) was then proposed, so that the HFLTS was reasonably introduced into the q -ROFS. Thirdly, the HFL q -ROFS was applied to MAGDM, and a TOPSIS method for MAGDM based on HFL q -ROFS was constructed. Finally, the proposed method was applied to the credit evaluation of the listed companies in strategic emerging industries in China, and taking q = 3 as an example, an application example analysis was carried out. The application example analysis results show that the ranking of alternatives obtained by the proposed method is completely consistent with that of the TOPSIS method for MAGDM based on linguistic Fermatean fuzzy set, but the discrimination degree of the former for alternatives is 2.2257, which is higher than 2.0889 of the latter, which proves the feasibility and effectiveness of the proposed method. This study enriches the theoretical framework of q -ROFSs and expands the applicability and methodology of q -ROFSs in MAGDM.