Pythagorean fuzzy multiple criteria decision analysis based on Shapley fuzzy measures and partitioned normalized weighted Bonferroni mean operator

Pythagorean fuzzy sets are powerful techniques for modeling vagueness in practice. The aim of this article is to investigate an effective means to aggregate uncertain information and then employ it into settling multiple criteria decision making (MCDM) problems within the Pythagorean fuzzy circumstances. To capture the nature of the reality, some special cases should be comprehensively considered. First, though correlation commonly exist among criteria, a deep insight should also be provided into some realistic situations, in which not all the criteria are interrelated to others. Besides, it is more reasonable to take the importance of the input arguments into consideration. Effected by aforementioned point, this article explores a Pythagorean fuzzy partitioned normalized weighted Bonferroni mean (PFPNWBM) operator with the combination of partitioned Bonferroni mean (BM) and normalized weighted BM operators considering Shapley fuzzy measure. Subsequently, in the context of partially known weight information, models are established to identify the optimal Shapley fuzzy measure. Moreover, integrated the PFPNWBM operator with the optimal Shapley fuzzy measure identification model, a Pythagorean fuzzy MCDM approach is designed. Finally, an illustrative example and detailed analyses are performed to demonstrate its feasibility and reliability.