Correlation Coefficients of Refined-Single Valued Neutrosophic Sets and Their Applications in Multiple Attribute Decision-Making

Changxing Fan

doi:10.20965/jaciii.2019.p0421

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JACIII Vol.23 No.3 pp. 421-426

doi: 10.20965/jaciii.2019.p0421

(2019)

Paper:

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Correlation Coefficients of Refined-Single Valued Neutrosophic Sets and Their Applications in Multiple Attribute Decision-Making

Changxing Fan

Department of Computer Science, Shaoxing University
508 Huancheng West Road, Shaoxing, Zhejiang 312000, China

Received:

July 21, 2018

Accepted:

October 19, 2018

Published:

May 20, 2019

Keywords:

refined-SVNSs, correlation coefficients, decision making, SVNSs

Abstract

The paper presents the correlation coefficient of refined-single valued neutrosophic sets (Refined-SVNSs) based on the extension of the correlation of single valued neutrosophic sets (SVNSs), and then a decision making method is proposed by the use of the weighted correlation coefficient of Refined-SVNSs. Through the weighted correlation coefficient between the ideal alternative and each alternative, we can rank all alternatives and the best one of all alternatives can be easily identified as well. Finally, to prove this decision making method proposed in this paper is useful to deal with the actual application, we use an example to illustrate it.

Cite this article as:

C. Fan, “Correlation Coefficients of Refined-Single Valued Neutrosophic Sets and Their Applications in Multiple Attribute Decision-Making,” J. Adv. Comput. Intell. Intell. Inform., Vol.23 No.3, pp. 421-426, 2019.

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References

[1] F. Smarandache, “Neutrosophy: Neutrosophic probability, set, and logic,” American Research Press, 1998.
[2] H. Wang, F. Smarandache, Y. Q. Zhang, and R. Sunderraman, “Interval neutrosophic sets and logic: Theory and applications in computing,” Hexis, 2005.
[3] F. Smarandache, “A unifying field in logics. In Neutrosophy: Neutrosophic Probability, Set and Logic,” American Research Press, 1999.
[4] F. Smarandache, “Neutrosophy. Neutrosophic probability, set, and logic. Analytic synthesis and synthetic analysis,” American Research Press, p.105, 1998.
[5] H. Wang, F. Smarandache, Y. Q. Zhang, and R. Sunderraman, “Single valued neutrosophic sets,” Multispace and Multistructure, Vol.4, pp. 410-413, 2010.
[6] F. Smarandache, “n-Valued Refined Neutrosophic Logic and Its Applications in Physics,” Progress in Physics, Vol.4, pp. 143-146, 2013.
[7] J. Ye, “A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets,” J. of Intelligent and Fuzzy Systems, Vol.26, pp. 2459-2466, 2014.
[8] J. Ye and F. Smarandache, “Similarity Measure of Refined Single-Valued Neutrosophic Sets and Its Multicriteria Decision Making Method,” Neutrosophic Sets and Systems, Vol.12, pp. 41-44, 2016.
[9] J. Ye, “Similarity measures between interval neutrosophic sets and their applications in multi criteria decision-making,” J. of Intelligent and Fuzzy Systems, Vol.26, pp. 165-172, 2014.
[10] J. Ye, “Multi criteria decision-making method using the correlation coefficient under single-valued neutrosophic environment,” Int. J. of General Systems, Vol.42, pp. 386-394, 2013.
[11] S. Ye and J. Ye, “Dice similarity measure between single valued neutrosophic multisets and its application in medical diagnosis,” Neutrosophic Sets and System, Vol.6, pp. 49-54, 2014.
[12] H.-Y. Zhang, J.-Q. Wang, and X.-H. Chen, “Interval neutrosophic sets and their application in multicriteria decision making problems,” The Scientific World J., 2014.
[13] J. Ye, “Improved cosine similarity measures of simplified neutrosophic sets for medical diagnoses,” Artificial Intelligence in Medicine, Vol.63, No.3, pp. 171-179, 2015.
[14] J. Ye, “Another Form of Correlation Coefficient between Single Valued Neutrosophic Sets and Its Multiple Attribute Decision Making Method,” Neutrosophic Sets and Systems, Vol.1, pp. 8-13, 2013.
[15] C. X. Fan and J. Ye, “The Cosine Measure of Refined-Single Valued Neutrosophic Sets and Refined-Interval Neutrosophic Sets for Multiple Attribute Decision-Making,” J. Intell. Fuzzy Syst., Vol.33, pp. 2281-2289, 2017.
[16] S. Broumi, M.Talea, F. Smarandache, and A. Bakali, “Single Valued Neutrosophic Graphs: Degree, Order and Size,” IEEE Int. Conf. on Fuzzy Systems (FUZZ), pp. 2444-2451, 2016.
[17] S. Broumi, A. Bakali, M. Talea, and F. Smarandache, “Isolated Single Valued Neutrosophic Graphs,” Neutrosophic Sets and Systems, Vol.11, pp. 74-78, 2016.
[18] S. Broumi, F. Smarandache, M. Talea, and A. Bakali, “Decision-Making Method Based on the Interval Valued Neutrosophic Graph,” 2016 Future Technologies Conf. (FTC), pp. 44-50, 2016.
[19] S. Broumi, A. Bakali, M. Talea, F. Smarandache, and L. Vladareanu, “Computation of Shortest Path Problem in a Network with SV-Trapezoidal Neutrosophic Numbers,” Proc. of the 2016 Int. Conf. on Advanced Mechatronic Systems, pp. 417-422, 2016.
[20] S. Broumi, A. Bakali, M. Talea, F. Smarandache, and L. Vladareanu, “Applying Dijkstra Algorithm for Solving Neutrosophic Shortest Path Problem,” Proc. of the 2016 Int. Conf. on Advanced Mechatronic Systems, No.30, pp. 412-416, 2016.
[21] C. X. Fan, E. Fan, and J. Ye, “The Cosine Measure of Single-Valued Neutrosophic Multisets for Multiple Attribute Decision-Making,” Symmetry, Vol.10, Issue 5, doi:10.3390/sym10050154, 2018.
[22] J. Ye and F. Smarandache, “Similarity Measure of Refined Single-Valued Neutrosophic Sets and Its Multicriteria Decision Making Method,” Neutrosophic Sets and Systems, Vol.12, pp. 41-44, 2016.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.

[1] [1] F. Smarandache, “Neutrosophy: Neutrosophic probability, set, and logic,” American Research Press, 1998.

[2] [2] H. Wang, F. Smarandache, Y. Q. Zhang, and R. Sunderraman, “Interval neutrosophic sets and logic: Theory and applications in computing,” Hexis, 2005.

[3] [3] F. Smarandache, “A unifying field in logics. In Neutrosophy: Neutrosophic Probability, Set and Logic,” American Research Press, 1999.

[4] [4] F. Smarandache, “Neutrosophy. Neutrosophic probability, set, and logic. Analytic synthesis and synthetic analysis,” American Research Press, p.105, 1998.

[5] [5] H. Wang, F. Smarandache, Y. Q. Zhang, and R. Sunderraman, “Single valued neutrosophic sets,” Multispace and Multistructure, Vol.4, pp. 410-413, 2010.

[6] [6] F. Smarandache, “n-Valued Refined Neutrosophic Logic and Its Applications in Physics,” Progress in Physics, Vol.4, pp. 143-146, 2013.

[7] [7] J. Ye, “A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets,” J. of Intelligent and Fuzzy Systems, Vol.26, pp. 2459-2466, 2014.

[8] [8] J. Ye and F. Smarandache, “Similarity Measure of Refined Single-Valued Neutrosophic Sets and Its Multicriteria Decision Making Method,” Neutrosophic Sets and Systems, Vol.12, pp. 41-44, 2016.

[9] [9] J. Ye, “Similarity measures between interval neutrosophic sets and their applications in multi criteria decision-making,” J. of Intelligent and Fuzzy Systems, Vol.26, pp. 165-172, 2014.

[10] [10] J. Ye, “Multi criteria decision-making method using the correlation coefficient under single-valued neutrosophic environment,” Int. J. of General Systems, Vol.42, pp. 386-394, 2013.

[11] [11] S. Ye and J. Ye, “Dice similarity measure between single valued neutrosophic multisets and its application in medical diagnosis,” Neutrosophic Sets and System, Vol.6, pp. 49-54, 2014.

[12] [12] H.-Y. Zhang, J.-Q. Wang, and X.-H. Chen, “Interval neutrosophic sets and their application in multicriteria decision making problems,” The Scientific World J., 2014.

[13] [13] J. Ye, “Improved cosine similarity measures of simplified neutrosophic sets for medical diagnoses,” Artificial Intelligence in Medicine, Vol.63, No.3, pp. 171-179, 2015.

[14] [14] J. Ye, “Another Form of Correlation Coefficient between Single Valued Neutrosophic Sets and Its Multiple Attribute Decision Making Method,” Neutrosophic Sets and Systems, Vol.1, pp. 8-13, 2013.

[15] [15] C. X. Fan and J. Ye, “The Cosine Measure of Refined-Single Valued Neutrosophic Sets and Refined-Interval Neutrosophic Sets for Multiple Attribute Decision-Making,” J. Intell. Fuzzy Syst., Vol.33, pp. 2281-2289, 2017.

[16] [16] S. Broumi, M.Talea, F. Smarandache, and A. Bakali, “Single Valued Neutrosophic Graphs: Degree, Order and Size,” IEEE Int. Conf. on Fuzzy Systems (FUZZ), pp. 2444-2451, 2016.

[17] [17] S. Broumi, A. Bakali, M. Talea, and F. Smarandache, “Isolated Single Valued Neutrosophic Graphs,” Neutrosophic Sets and Systems, Vol.11, pp. 74-78, 2016.

[18] [18] S. Broumi, F. Smarandache, M. Talea, and A. Bakali, “Decision-Making Method Based on the Interval Valued Neutrosophic Graph,” 2016 Future Technologies Conf. (FTC), pp. 44-50, 2016.

[19] [19] S. Broumi, A. Bakali, M. Talea, F. Smarandache, and L. Vladareanu, “Computation of Shortest Path Problem in a Network with SV-Trapezoidal Neutrosophic Numbers,” Proc. of the 2016 Int. Conf. on Advanced Mechatronic Systems, pp. 417-422, 2016.

[20] [20] S. Broumi, A. Bakali, M. Talea, F. Smarandache, and L. Vladareanu, “Applying Dijkstra Algorithm for Solving Neutrosophic Shortest Path Problem,” Proc. of the 2016 Int. Conf. on Advanced Mechatronic Systems, No.30, pp. 412-416, 2016.

[21] [21] C. X. Fan, E. Fan, and J. Ye, “The Cosine Measure of Single-Valued Neutrosophic Multisets for Multiple Attribute Decision-Making,” Symmetry, Vol.10, Issue 5, doi:10.3390/sym10050154, 2018.

[22] [22] J. Ye and F. Smarandache, “Similarity Measure of Refined Single-Valued Neutrosophic Sets and Its Multicriteria Decision Making Method,” Neutrosophic Sets and Systems, Vol.12, pp. 41-44, 2016.