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Symmetry 2018, 10(5), 144; https://doi.org/10.3390/sym10050144

Symmetry Measures of Simplified Neutrosophic Sets for Multiple Attribute Decision-Making Problems

1,2
,
2
and
1,*
1
School of Mechatronic Engineering and Automation, Shanghai University, 149 Yanchang Road, Shanghai 200072, China
2
Department of Electrical and Information Engineering, Shaoxing University, 508 Huancheng West Road, Shaoxing 312000, Zhejiang, China
*
Author to whom correspondence should be addressed.
Received: 27 March 2018 / Revised: 29 April 2018 / Accepted: 4 May 2018 / Published: 5 May 2018
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Abstract

A simplified neutrosophic set (containing interval and single-valued neutrosophic sets) can be used for the expression and application in indeterminate decision-making problems because three elements in the simplified neutrosophic set (including interval and single valued neutrosophic sets) are characterized by its truth, falsity, and indeterminacy degrees. Under a simplified neutrosophic environment, therefore, this paper firstly defines simplified neutrosophic asymmetry measures. Then we propose a normalized symmetry measure and a weighted symmetry measure of simplified neutrosophic sets and develop a simplified neutrosophic multiple attribute decision-making method based on the weighted symmetry measure. All alternatives can be ranked through the weighted symmetry measure between the ideal solution/alternative and each alternative, and then the best one can be determined. Finally, an illustrative example on the selection of manufacturing schemes (alternatives) in the flexible manufacturing system demonstrates the applicability of the proposed method in a simplified (interval and single valued) neutrosophic setting, and then the decision-making method based on the proposed symmetry measure is in accord with the ranking order and best choice of existing projection and bidirectional projection-based decision-making methods and strengthens the resolution/discrimination in the decision-making process corresponding to the comparative example. View Full-Text
Keywords: asymmetry measure; symmetry measure; simplified neutrosophic set; decision making asymmetry measure; symmetry measure; simplified neutrosophic set; 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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Tu, A.; Ye, J.; Wang, B. Symmetry Measures of Simplified Neutrosophic Sets for Multiple Attribute Decision-Making Problems. Symmetry 2018, 10, 144.

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