Abstract
As a generalization of the intuitionistic fuzzy set (IFS), a Pythagorean fuzzy set has more flexibility than IFS in expressing uncertainty and fuzziness in the process of multiple criteria group decision-making (MCGDM). Meanwhile, the prominent advantage of the Muirhead mean (MM) operator is that it can reflect the relationships among the various input arguments through changing a parameter vector. Motivated by these primary characters, in this study, we introduced the MM operator into the Pythagorean fuzzy context to expand its applied fields. To do so, we presented the Pythagorean fuzzy MM (PFMM) operators and Pythagorean fuzzy dual MM (PFDMM) operator to fuse the Pythagorean fuzzy information. Then, we investigated their some properties and gave some special cases related to the parameter vector. In addition, based on the developed operators, two MCGDM methods under the Pythagorean fuzzy environment are proposed. An example is given to verify the validity and feasibility of our proposed methods, and a comparative analysis is provided to show their advantages.
Highlights
Multi-criteria group decision-making (MCGDM), a sub-field of decision-making, is a common and important activity in the real world, and is especially useful in the fields of engineering, economic, management, and the military
The main reason is that the Pythagorean fuzzy weighted MM (PFWMM) operator highlights the impact of overall arguments, but arguments, but the Pythagorean fuzzy dual weighted MM (PFDWMM) operator emphasizes the role of individual arguments
For the PFWMM operator, when the the PFWMM operator, when the parameter vector Q has only one real number and the rest are 0, parameter vector Q has only one real number and the rest are 0, we discover that the larger the real we discover that the larger theQ, real parameter the greater the value ofThe the more score
Summary
Multi-criteria group decision-making (MCGDM), a sub-field of decision-making, is a common and important activity in the real world, and is especially useful in the fields of engineering, economic, management, and the military. Garg [8] introduced the Einstein operational laws into the Pythagorean fuzzy environment to develop two generalized averaging aggregation operators, and utilized these operators to solve MCDM problems. Liang et al [14] proposed the Pythagorean fuzzy weighted geometric Bonferroni mean operator and applied it to handle MCGDM problems with Pythagorean fuzzy information. According to the above analysis, we know that the existing aggregation operators of Pythagorean fuzzy cannot capture the relationships between any number of input arguments in the information fusion process. Inspired by the ideal characteristics of the MM operator, the present paper aims at developing some new aggregation operators of Pythagorean fuzzy to solve MCGDM problems in which we consider the interrelationship among any number of input arguments.
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