Abstract
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.
Highlights
Fuzzy decision-making has been studied and applied extensively [1,2,3]
To model interaction among hesitant Pythagorean fuzzy values and interaction between membership and non-membership at the same time, we develop some hesitant Pythagorean fuzzy interaction Bonferroni mean operator including the hesitant Pythagorean fuzzy interaction Bonferroni mean (HPFIBM) operator, the hesitant Pythagorean fuzzy interaction weighted Bonferroni mean (HPFIWBM) operator, the hesitant Pythagorean fuzzy interaction geometric Bonferroni mean (HPFIGBM) operator and the hesitant Pythagorean fuzzy interaction weighted geometric Bonferroni mean (HPFIWGBM) aggregation operator
Q ≥ 0 with p + q > 0, the hesitant Pythagorean fuzzy interaction weighted Bonferroni mean (HPFIWBM) aggregation operator can be defined as HPFIWBMp,q ( f1, f2, . . . , fn)
Summary
Fuzzy decision-making has been studied and applied extensively [1,2,3]. Pythagorean fuzzy set [4,5] is the extension of intuitionistic fuzzy set [6]. N) be a collection of HPFEs. For any p, q ≥ 0 with p + q > 0, the hesitant Pythagorean fuzzy interaction weighted Bonferroni mean (HPFIWBM) aggregation operator can be defined as HPFIWBMp,q N) be a collection of HPFEs. For any p, q ≥ 0 with p + q > 0, the hesitant Pythagorean fuzzy interaction geometric Bonferroni mean (HPFIGBM) aggregation operator can be defined as HPFIGBMp,q N) be a collection of HPFEs. For any p, q ≥ 0 with p +q > 0, the hesitant Pythagorean fuzzy interaction geometric weight Bonferroni mean (HPFIGWBM) aggregation operator can be defined as HPFIGWBMp,q
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