Statistics-based approach for large-scale group decision-making under incomplete Pythagorean fuzzy information with risk attitude

As loss in decision sample information occurs during large-scale group decision-making (LSGDM), this paper proposes a statistical estimation approach for handling Pythagorean fuzzy information under the risk attitude of decision-makers (DMs). The DMs are partitioned by risk attitudes (hesitancy degrees) into subgroups. A five-number summary for the subgroups from the incomplete decision information given by the DMs is obtained. The Cornish–Fisher expansion is then applied to estimate the mean, standard variance, and skewness of the decision sample information from the five-number summary. The confidence interval constructed by the skewness is used to obtain the interval-valued Pythagorean fuzzy number (IVPFN) evaluation information of the subgroups. An optimization model based on minimizing the conflicts between the subgroups and the overall group is used to derive the weights of the subgroups. A sorting function of the IVPFNs is used to rank the alternatives. A case study on green credit and a comparison analysis are applied to validate the proposed method.