Hesitant Pythagorean fuzzy interaction aggregation operators and their application in multiple attribute decision-making

The aim of this paper is to develop hesitant Pythagorean fuzzy interaction aggregation operators based on the hesitant fuzzy set, Pythagorean fuzzy set and interaction between membership and non-membership. The new operation laws can overcome shortcomings of existing operation laws of hesitant Pythagorean fuzzy values. Several new hesitant Pythagorean fuzzy interaction aggregation operators have been developed including the hesitant Pythagorean fuzzy interaction weighted averaging operator, the hesitant Pythagorean fuzzy interaction weighted geometric averaging operator and the generalized hesitant Pythagorean fuzzy interaction weighted averaging operator. Using the Bonferroni mean, some hesitant Pythagorean fuzzy interaction Bonferroni mean operators have been developed including the hesitant Pythagorean fuzzy interaction Bonferroni mean operator, the hesitant Pythagorean fuzzy interaction weighted Bonferroni mean (HPFIWBM) operator, the hesitant Pythagorean fuzzy interaction geometric Bonferroni mean operator and the hesitant Pythagorean fuzzy interaction geometric weight Bonferroni mean (HPFIGWBM) operator. Some properties have been studied. A new multiple attribute decision-making method based on the HPFIWBM operator and the HPFIGWBM operator has been presented. Numerical example is presented to illustrate the new method.