Abstract
Pythagorean fuzzy sets accommodate more uncertainties than the intuitionistic fuzzy sets and hence it is one of the most important concepts to describe the fuzzy information in the process of decision making. Under this environment, the main objective of the work is to develop some new operational laws and their corresponding weighted aggregation operators. For it, we define some new neutral addition and scalar multiplication operational laws by incorporating the features of a neutral character towards the membership degrees of the set and the probability sum. Some properties of the proposed laws are investigated. Then, associated with these operational laws, we define some novel Pythagorean fuzzy weighted, ordered weighted and hybrid neutral averaging aggregation operators for Pythagorean fuzzy information, which can neutrally treat the membership and non-membership degrees. The various relations and the characteristics of the proposed operators are discussed. Further, in order to ease with the possible application, we present an algorithm to solve the multiple attribute group decision-making problems under the Pythagorean fuzzy environment. Finally, a practical example is provided to illustrate the approach and show its superiority, advantages by comparing their performance with some several existing approaches.
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