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Symmetry 2017, 9(8), 153; doi:10.3390/sym9080153

Vector Similarity Measures between Refined Simplified Neutrosophic Sets and Their Multiple Attribute Decision-Making Method

1
Key Laboratory of Rock Mechanics and Geohazards, 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: 17 July 2017 / Revised: 29 July 2017 / Accepted: 8 August 2017 / Published: 11 August 2017
(This article belongs to the Special Issue Neutrosophic Theories Applied in Engineering)
View Full-Text   |   Download PDF [275 KB, uploaded 11 August 2017]

Abstract

A refined single-valued/interval neutrosophic set is very suitable for the expression and application of decision-making problems with both attributes and sub-attributes since it is described by its refined truth, indeterminacy, and falsity degrees. However, existing refined single-valued/interval neutrosophic similarity measures and their decision-making methods are scarcely studied in existing literature and cannot deal with this decision-making problem with the weights of both attributes and sub-attributes in a refined interval and/or single-valued neutrosophic setting. To solve the issue, this paper firstly introduces a refined simplified neutrosophic set (RSNS), which contains the refined single-valued neutrosophic set (RSVNS) and refined interval neutrosophic set (RINS), and then proposes vector similarity measures of RSNSs based on the Jaccard, Dice, and cosine measures of simplified neutrosophic sets in vector space, and the weighted Jaccard, Dice, and cosine measures of RSNSs by considering weights of both basic elements and sub-elements in RSNS. Further, a decision-making method with the weights of both attributes and sub-attributes is developed based on the weighted Jaccard, Dice, and cosine measures of RSNSs under RSNS (RINS and/or RSVNS) environments. The ranking order of all the alternatives and the best one can be determined by one of weighted vector similarity measures between each alternative and the ideal solution (ideal alternative). Finally, an actual example on the selecting problem of construction projects illustrates the application and effectiveness of the proposed method. View Full-Text
Keywords: refined simplified neutrosophic set; refined single-valued neutrosophic set; refined interval neutrosophic set; vector similarity measure; decision-making refined simplified neutrosophic set; refined single-valued neutrosophic set; refined interval neutrosophic set; vector similarity measure; 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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Chen, J.; Ye, J.; Du, S. Vector Similarity Measures between Refined Simplified Neutrosophic Sets and Their Multiple Attribute Decision-Making Method. Symmetry 2017, 9, 153.

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