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Information 2017, 8(4), 117; doi:10.3390/info8040117

Cosine Measures of Linguistic Neutrosophic Numbers and Their Application in Multiple Attribute Group Decision-Making

Department of Electrical and Information Engineering, Shaoxing University, 508 Huancheng West Road, Shaoxing 312000, China
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Received: 21 August 2017 / Revised: 14 September 2017 / Accepted: 19 September 2017 / Published: 22 September 2017
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Abstract

The linguistic neutrosophic numbers (LNNs) can express the truth, indeterminacy, and falsity degrees independently by three linguistic variables. Hence, they are an effective tool for describing indeterminate linguistic information under linguistic decision-making environments. Similarity measures are usual tools in decision-making problems. However, existing cosine similarity measures have been applied in decision-making problems, but they cannot deal with linguistic information under linguistic decision-making environments. To deal with the issue, we propose two cosine similarity measures based on distance and the included angle cosine of two vectors between LNNs. Then, we establish a multiple attribute group decision-making (MAGDM) method based on the cosine similarity measures under an LNN environment. Finally, a practical example about the decision-making problems of investment alternatives is presented to demonstrate the effective applications of the proposed MAGDM method under an LNN environment. View Full-Text
Keywords: cosine similarity measure; linguistic neutrosophic number; multiple attribute group decision-making cosine similarity measure; linguistic neutrosophic number; multiple attribute group decision-making
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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MDPI and ACS Style

Shi, L.; Ye, J. Cosine Measures of Linguistic Neutrosophic Numbers and Their Application in Multiple Attribute Group Decision-Making. Information 2017, 8, 117.

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