Abstract
The aim of this paper is to introduce some new operators for aggregating single-valued neutrosophic (SVN) information and to apply them to solve the multi-criteria decision-making (MCDM) problems. Single-valued neutrosophic set, as an extension and generalization of an intuitionistic fuzzy set, is a powerful tool to describe the fuzziness and uncertainty, and Muirhead mean (MM) is a well-known aggregation operator which can consider interrelationships among any number of arguments assigned by a variable vector. In order to make full use of the advantages of both, we introduce two new prioritized MM aggregation operators, such as the SVN prioritized MM (SVNPMM) and SVN prioritized dual MM (SVNPDMM) under SVN set environment. In addition, some properties of these new aggregation operators are investigated and some special cases are discussed. Furthermore, we propose a new method based on these operators for solving the MCDM problems. Finally, an illustrative example is presented to testify the efficiency and superiority of the proposed method by comparing it with the existing method.
Highlights
Multicriteria decision-making (MCDM) is one of the hot topics in the decision-making field to choose the best alternative to the set of the feasible one
Apart from these, we verify that the methods proposed in this paper have advantages with respect to existing operators as follows: (1) some of the existing aggregation operators (AOs) can be taken as a special case of the proposed operators under neutrosophic sets (NSs) environment, (2) they consider the interrelationship among all arguments, (3) they are more adaptable and feasible than the existing AOs based on the parameter vector, (4) the presented approach considers the preferences of the decision maker in terms of risk preference as well as risk aversion
Muirhead mean aggregation operator is more flexible by using a variable and considering the multiple interrelationships between the pairs of the input arguments
Summary
Multicriteria decision-making (MCDM) is one of the hot topics in the decision-making field to choose the best alternative to the set of the feasible one. It is important to deal with how to consider the relationship between input arguments Keeping all these features in mind, and by taking the advantages of the SVNS, we combine the prioritized aggregation and MM and propose prioritized MM (PMM) operator by considering the advantages of both. Apart from these, we verify that the methods proposed in this paper have advantages with respect to existing operators as follows: (1) some of the existing AOs can be taken as a special case of the proposed operators under NSs environment, (2) they consider the interrelationship among all arguments, (3) they are more adaptable and feasible than the existing AOs based on the parameter vector, (4) the presented approach considers the preferences of the decision maker in terms of risk preference as well as risk aversion.
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