Projection Model for Fusing the Information of Pythagorean Fuzzy Multicriteria Group Decision Making Based on Geometric Bonferroni Mean.

As a new generalization of fuzzy sets, Pythagorean fuzzy sets (PFSs) can availably handle uncertain information more flexibly in the process of decision making. Through synthesizing the Bonferroni mean and the geometric mean, the geometric Bonferroni mean (GBM) captures the interrelationship of the input arguments. Considering the interrelationship among the input arguments, we introduce GBM into Pythagorean fuzzy situations and expand its applied fields. Under the Pythagorean fuzzy environment, we develop the Pythagorean fuzzy geometric Bonferroni mean and weighted Pythagorean fuzzy geometric Bonferroni mean (WPFGBM) operators describing the interrelationship between arguments and some special properties of them are also investigated. Then, we employ the WPFGBM operator to fuse the information in the Pythagorean fuzzy multicriteria group decision making (PFMCGDM) problem, which can obtain much more information in the process of group decision making. With the aid of the projection model, we present its extension and further design a new method for the application of PFMCGDM. Finally, an example is given to elaborate on the performance of our proposed method. (C) 2017 Wiley Periodicals, Inc.