Abstract
On account of the indeterminacy and subjectivity of decision makers (DMs) in complexity decision-making environments, the evaluation information over alternatives presented by DMs is usually fuzzy and ambiguous. As the generalization of intuitionistic fuzzy sets (IFSs), the Pythagorean fuzzy set (PFS) is more useful in expressing fuzzy and ambiguous information. Meanwhile, in order to consider human hesitance, dual hesitant Pythagorean fuzzy sets (DHPFSs) are presented, which can be more valid for handling real multiple attribute decision-making (MADM) problems. To fuse the information in DHPFSs more effectively, in this article, some dual hesitant Pythagorean fuzzy Heronian mean operators, which can consider the relationships between arguments being fused, are defined and studied. Evidently, the new proposed operators can obtain more exact results than other existing methods. In addition, some important properties of these Heronian mean (HM) operators are discussed. Subsequently, the defined aggregation operators are used in MADM with dual hesitant Pythagorean fuzzy numbers (DHPFNs), and the MADM model is developed. In accordance with the defined operators and the built model, the dual hesitant Pythagorean fuzzy generalized weighted Heronian mean (DHPFGWHM) operator and dual hesitant Pythagorean fuzzy generalized geometric weighted Heronian mean (DHPFGGWHM) operator are applied to deal with the green supplier selection in supply chain management, and the availability and superiority of the proposed operators are analyzed by comparing them with some existing approaches. The method presented in this paper can effectively solve the MADM problems in which the decision-making information is expressed by DHPFNs and the attributes are interactive.
Highlights
In practical decision making environments, it is difficult for decision makers (DMs) to give evaluated information with exact real numbers
In accordance with the defined operators and the built model, the dual hesitant Pythagorean fuzzy generalized weighted Heronian mean (DHPFGWHM) operator and dual hesitant Pythagorean fuzzy generalized geometric weighted Heronian mean (DHPFGGWHM) operator are applied to deal with the green supplier selection in supply chain management, and the availability and superiority of the proposed operators are analyzed by comparing them with some existing approaches
In a complicated decision-making environment, the decision maker’s risk attitude is an important factor to think about, and our methods can do this by altering the parameters ξ and ζ, whereas the dual hesitant Pythagorean fuzzy weighted average (DHPFWA) and dual hesitant Pythagorean fuzzy weighted geometric (DHPFWG) operators presented by Wei and Lu [53] do not have the ability to dynamically adjust to the parameters according to the decision maker’s risk attitude, meaning it is difficult to solve risk multiple attribute decision making in real practice
Summary
In practical decision making environments, it is difficult for decision makers (DMs) to give evaluated information with exact real numbers. To express fuzzy information more Liu et al [27] have developed the concepts of hesitant intuitionistic fuzzy linguistic elements (HLFLEs) and have defined some weighted aggregation operators. In practical MADM problems, some relationships do exist between arguments being fused, and it is obvious that the dual hesitant Pythagorean fuzzy Hamacher aggregation operators defined by Wei and Lu [53] do not take the relationships between the arguments being fused into consideration.
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