TITLE:
Hesitant Fuzzy Linguistic Pythagorean Fuzzy Sets and Its Application in Credit Evaluation of Enterprise
AUTHORS:
Mu Zhang, Yan Li
KEYWORDS:
Pythagorean Fuzzy Set, Hesitant Fuzzy Linguistic Term Set, Hesitant Fuzzy Linguistic Element, Linguistic Scale Function, Multiple-Attribute Group Decision-Making, TOPSIS Method, Enterprise Credit Evaluation
JOURNAL NAME:
Applied Mathematics,
Vol.17 No.8,
August
12,
2026
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 Pythagorean fuzzy sets (PFSs) 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, and the mapping from hesitant fuzzy linguistic term set (HFLTS) to [0, 1] interval was realized. Based on the HFLENSF, the definition of hesitant fuzzy linguistic Pythagorean fuzzy set (HFLPFS) was then proposed. Thus, the HFLTS was reasonably introduced into the PFS. Secondly, the HFLPFS was applied to MAGDM, and a TOPSIS method for MAGDM based on HFLPFS was constructed. Finally, the proposed method was applied to the credit evaluation of the listed companies in strategic emerging industries in China, and an application example analysis was carried out. The application example analysis results show that the ranking of alternatives obtained by the proposed method is consistent with that obtained by the TOPSIS method for MAGDM based on linguistic Pythagorean fuzzy set (LPFS), but the discrimination degree of the former for alternatives is 3.8724, which is higher than 3.5188 of the latter, which proves the feasibility and effectiveness of the proposed method. This study enriches the theoretical framework of Pythagorean fuzzy sets, and expands the applicability and methodology of Pythagorean fuzzy sets in MAGDM.