A generalized Shapley index-based interval-valued Pythagorean fuzzy PROMETHEE method for group decision-making

Zhen Hua*, Xiaochuan Jing

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


Multi-criteria group decision-making (MCGDM) problems, where correlations commonly exist among input arguments, are becoming increasingly complex. However, most of the existing consensus-reaching methods for MCGDM problems fail to adequately consider the effects of these interactions among criteria and experts, which may bring about inaccurate results. Therefore, this paper establishes a novel MCGDM framework based on the generalized Shapley value to solve the consensus-reaching problem with interval-valued Pythagorean fuzzy sets (IVPFS). First, experts’ evaluations are collected using IVPFS, which offers a more flexible way to express this vague information. Second, the interval-valued Pythagorean fuzzy Choquet integral operator and the interval-valued Pythagorean fuzzy Shapley aggregation operator are developed to fuse the decision information with complementary, redundant, or independent characteristics. Third, an integrated consensus-reaching algorithm is established to improve group consensus by iteratively updating the evaluations until the group consensus level reaches the preset threshold. Then, the classical PROMETHEE method is extended using the generalized Shapley value within an IVPFS context to derive a more scientific ranking result. Finally, a case study for a sustainable supplier evaluation problem is presented to validate the proposed method. The results and comparative analysis show that the proposed method can represent experts’ evaluations more flexibly, integrate inputs with interrelationships more effectively, and improve group consensus more efficiently.

Original languageEnglish
Pages (from-to)6629-6652
Number of pages24
JournalSoft Computing
Issue number10
Publication statusPublished - May 2023
Externally publishedYes


  • Consensus-reaching process (CRP)
  • Fuzzy measure
  • Interval-valued Pythagorean fuzzy set (IVPFS)
  • Multi-criteria group decision-making (MCGDM)
  • The generalized Shapley index


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