Pythagorean fuzzy heronian mean operators in multiple attribute decision making and their application to supplier selection

The Heronian mean and generalized Heronian mean provide two aggregation operators which consider the interdependent phenomena among the aggregated arguments. In this paper, the Heronian mean and generalized Heronian mean under Pythagorean fuzzy environments is studied. First, the generalized Pythagorean fuzzy Heronian mean (GPFHM) operator and generalized Pythagorean fuzzy weighted Heronian mean (GPFWHM) operator are proposed and some of their desirable properties and special cases are investigated in detail. Furthermore, we propose the Pythagorean fuzzy geometric Heronian mean (PFGHM) operator and Pythagorean fuzzy weighted geometric Heronian mean (PFWGHM) operator. Then, two approaches to multiple attribute decision making based on GPFWHM operator and PFWGHM operator are proposed. Finally, a practical example for supplier selection is given to verify the developed approach and to demonstrate its practicality and effectiveness.