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Symmetry 2018, 10(5), 154; https://doi.org/10.3390/sym10050154

The Cosine Measure of Single-Valued Neutrosophic Multisets for Multiple Attribute Decision-Making

1
Department of Computer Science, Shaoxing University, 508 Huancheng West Road, Shaoxing 312000, China
2
Department of Electrical and Information Engineering, Shaoxing University, 508 Huancheng West Road, Shaoxing 312000, China
*
Author to whom correspondence should be addressed.
Received: 29 April 2018 / Revised: 7 May 2018 / Accepted: 10 May 2018 / Published: 11 May 2018
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Abstract

Based on the multiplicity evaluation in some real situations, this paper firstly introduces a single-valued neutrosophic multiset (SVNM) as a subclass of neutrosophic multiset (NM) to express the multiplicity information and the operational relations of SVNMs. Then, a cosine measure between SVNMs and weighted cosine measure between SVNMs are presented to measure the cosine degree between SVNMs, and their properties are investigated. Based on the weighted cosine measure of SVNMs, a multiple attribute decision-making method under a SVNM environment is proposed, in which the evaluated values of alternatives are taken in the form of SVNMs. The ranking order of all alternatives and the best one can be determined by the weighted cosine measure between every alternative and the ideal alternative. Finally, an actual application on the selecting problem illustrates the effectiveness and application of the proposed method. View Full-Text
Keywords: single valued neutrosophic set (SVNS); neutrosophic multiset (NM); single valued neutrosophic multiset (SVNM); cosine measure; multiple attribute decision-making single valued neutrosophic set (SVNS); neutrosophic multiset (NM); single valued neutrosophic multiset (SVNM); cosine measure; multiple attribute decision-making
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Fan, C.; Fan, E.; Ye, J. The Cosine Measure of Single-Valued Neutrosophic Multisets for Multiple Attribute Decision-Making. Symmetry 2018, 10, 154.

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