Abstract
The power Heronian aggregation (PHA) operator can use the advantages of power average and the Heronian mean operator, which together could take into account the interrelationship of the aggregated arguments, and therefore alleviate the effects caused by unreasonable data through considering the support degree between input arguments. However, PHA operators cannot be used to process single-valued neutrosophic numbers (SVNNs), which is significant for extending it to SVNNs. We propose some new PHA operators for SVNNs and introduce a novel MAGDM method on the basis of the proposed operators. Firstly, the definition, properties, comparison method, and operational rules of SVNNs are introduced briefly. Then, some PHA operators are proposed, such as the single-valued neutrosophic power Heronian aggregation (SVNPHA) operator, the single-valued neutrosophic weighted power Heronian aggregation (SVNWPHA) operator, single-valued neutrosophic geometric power Heronian aggregation (SVNGPHA) operator, single-valued neutrosophic weighted geometric power Heronian aggregation (SVNWGPHA) operator. Furthermore, we discuss some properties of these new aggregation operators and several special cases. Moreover, the method to solve the MAGDM problems with SVNNs is proposed, based on the SVNWPHA and SVNWGPHA operators. Lastly, we verified the application and effectiveness of the proposed method by using an example for the MAGDM problem.
Highlights
In real decision-making, multiple-attribute group decision-making (MAGDM) methods are extensively used to rank alternatives for relevant attributes
To verify the effectiveness and explain the advantage of the proposed method relating to the single-valued neutrosophic weighted power Heronian aggregation (SVNWPHA) and SVNWGPHA operators, we can plan to compare it with the method proposed by Li, Liu and Chen [33], which is based on the NNIGWHM operator; the method proposed by Yang and
Owing to the limitations of human thinking and the complexity of decision-making problems, the decision information involved in MAGDM problems is often incomplete, indeterminate, and inconsistent
Summary
In real decision-making, multiple-attribute group decision-making (MAGDM) methods are extensively used to rank alternatives for relevant attributes. Based on the use of Hamming distance, Stanujkić [18] proposed a extend WASPAS method with single-valued intuitionistic fuzzy numbers, and application it in website evaluation. Heronian mean (HM) operator for SVNSs. Yang and Li [34] extended the PA operator to SVNSs and developed some single-valued neutrosophic power weighted average (SVNPWA) operators. Liu proposed some power Heronian aggregation (PHA) operators through combining the PA operator and HM operator to IVIFNs [40] and Linguistic Neutrosophic Sets (LNSs) [41]. Propose a novel MAGDM method based on the SVNWPHA and SVNWGPHA operators for SVNNs. Demonstrate the application and effectiveness of the developed methods.
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