Abstract
The neutrosophic cubic set (NCS) is a hybrid structure, which consists of interval neutrosophic sets (INS) (associated with the undetermined part of information associated with entropy) and single-valued neutrosophic set (SVNS) (associated with the determined part of information). NCS is a better tool to handle complex decision-making (DM) problems with INS and SVNS. The main purpose of this article is to develop some new aggregation operators for cubic neutrosophic numbers (NCNs), which is a basic member of NCS. Taking the advantages of Muirhead mean (MM) operator and power average (PA) operator, the power Muirhead mean (PMM) operator is developed and is scrutinized under NC information. To manage the problems upstretched, some new NC aggregation operators, such as the NC power Muirhead mean (NCPMM) operator, weighted NC power Muirhead mean (WNCPMM) operator, NC power dual Muirhead mean (NCPMM) operator and weighted NC power dual Muirhead mean (WNCPDMM) operator are proposed and related properties of these proposed aggregation operators are conferred. The important advantage of the developed aggregation operator is that it can remove the effect of awkward data and it considers the interrelationship among aggregated values at the same time. Furthermore, a novel multi-attribute decision-making (MADM) method is established over the proposed new aggregation operators to confer the usefulness of these operators. Finally, a numerical example is given to show the effectiveness of the developed approach.
Highlights
One of the drawbacks of real multi-attribute decision-making (MADM) problems is expressing attribute values in fuzzy and indeterminate DM environments
We develop the weighted NC power Muirhead mean (WNCPMM) operator, which has the capacity of taking the weights of neutrosophic numbers (NCNs)
If Q = 1a, 1a, . . . ., 1a, NC power Muirhead mean (NCPMM) operators degenerate into the following form: NC power dual MM operator (NCPDMM)
Summary
One of the drawbacks of real MADM problems is expressing attribute values in fuzzy and indeterminate DM environments. Operator [31,32] developed by Yager [31] which can aggregate the input information by giving the weighted vector based on support degree among the input arguments. Discussions on some basic properties and related cases with respect to the parameter vector will be dealt at length The advantages of these proposed aggregation operators are to capture the interrelationship among input arguments by the MM operator, and simultaneously eliminate the effect of awkward data. A novel approach to solve MADM problems based on these proposed aggregation operators will be developed.
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