Q-indeterminate correlation coefficient between simplified neutrosophic indeterminate sets and its multicriteria decision-making method
Owing to the indeterminacy, incompleteness, and inconsistency of decision makers’ arguments/cognitions regarding complicated decision-making problems, the truth, falsity, and indeterminacy degrees given by decision makers may imply the partial certainty and partial uncertainty information. In this case, a simplified neutrosophic set (SNS) cannot express the uncertainty degrees of the truth, falsity, indeterminacy arguments. To depict the hybrid information of SNS and neutrosophic (indeterminate) numbers (NNs) together, this study presents a simplified neutrosophic indeterminate set (SNIS) to describe the uncertainty degrees of the truth, falsity, indeterminacy, and then based on the de-neutrosophication technology using the parameterized SNSs of SNISs we introduce the q-indeterminate correlation coefficients of SNISs with a parameter q ∈ [0, 1]. Next, a simplified neutrosophic indeterminate multicriteria decision-making method using the qindeterminate correlation coefficients of SNISs is established along with decision makers’ risk attitudes, such as the small risk for q = 0, the moderate risk for q = 0.5, and the large risk for q = 1, to carry out multicriteria decision-making problems in SNIS setting. Eventually, the proposed decision-making approach is applied in an example of selecting a satisfactory slope design scheme for an open pit mine to indicate the practicality and flexibility in SNIS setting.
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Atanassov, K. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20, 87–96. https://doi.org/10.1016/S0165-0114(86)80034-3
Broumi, S., & Smarandache, F. (2013). Correlation coefficient of interval neutrosophic set. Applied Mechanics and Materials, 436, 511–517. https://doi.org/10.4028/www.scientific.net/AMM.436.511
Hanafy, I. M., Salama, A. A., & Mahfouz, K. (2012). Correlation of neutrosophic data. International Refereed Journal of Engineering and Science, 1(2), 39–43.
Hu, K. L., Fan, E., Ye, J., Pi, J. T., Zhao, L. P., & Shen, S. G. (2018). Element-weighted neutrosophic correlation coefficient and its application in improving CAMShift tracker in RGBD video. Information, 9(5), 126. https://doi.org/10.3390/info9050126
Li, C. Q., Ye, J., Cui, W. H., & Du, S. Q. (2019). Slope stability assessment method using the arctangent and tangent similarity measure of neutrosophic numbers. Neutrosophic Sets and Systems, 27, 98–103.
Peng, J. J., Wang, J. Q., Zhang, H. Y., & Chen, X. H. (2014). An outranking approach for multi-criteria decision-making problems with simplified neutrosophic sets. Applied Soft Computing, 25, 336–346. https://doi.org/10.1016/j.asoc.2014.08.070
Peng, J. J., Wang, J. Q., Wang, J., Zhang, H. Y., & Chen, X. H. (2016). Simplified neutrosophic sets and their applications in multi-criteria group decision-making problems. International Journal of Systems Science, 47(10), 2342–2358. https://doi.org/10.1080/00207721.2014.994050
Read, J., & Stacey, P. (2009). Guidelines for open pit slope design. CSIRO Publishing. https://doi.org/10.1071/9780643101104
Şahin, R., & Liu, P. (2017). Correlation coefficient of single-valued neutrosophic hesitant fuzzy sets and its applications in decision making. Neural Computing and Applications, 28(6), 1387–1395. https://doi.org/10.1007/s00521-015-2163-x
Salama, A. A., Khaled, O. M., & Mahfouz, K. M. (2014). Neutrosophic correlation and simple linear regression. Neutrosophic Sets and Systems, 5, 3–8.
Shi, L. L. (2016). Correlation coefficient of simplified neutrosophic sets for bearing fault diagnosis. Shock and Vibration, Article ID 5414361. https://doi.org/10.1155/2016/5414361
Smarandache, F. (1998). Neutrosophy: neutrosophic probability, set, and logic. American Research Press.
Smarandache, F. (2013). Introduction to neutrosophic measure, neutrosophic integral, and neutrosophic probability. Sitech & Education Publisher.
Smarandache, F. (2014). Introduction to neutrosophic statistics. Sitech & Education Publishing.
Wang, H., Smarandache, F., Zhang, Y. Q., & Sunderraman, R. (2005). Interval neutrosophic sets and logic: Theory and applications in computing. Hexis.
Wang, H., Smarandache, F., Zhang, Y. Q., & Sunderraman, R. (2010). Single valued neutrosophic sets. Multispace and Multistructure, 4, 410–413.
Wu, X. H., Wang, J. Q., Peng, J. J., & Chen, X. H. (2016). Crossentropy and prioritized aggregation operator with simplified neutrosophic sets and their application in multi-criteria decision-making problems. International Journal of Fuzzy Systems, 18(6), 1104–1116. https://doi.org/10.1007/s40815-016-0180-2
Xue, H. L., Yu, M. R., & Chen, C. F. (2019). Research on novel correlation coefficient of neutrosophic cubic sets and its applications. Mathematical Problems in Engineering, Article ID 7453025. https://doi.org/10.1155/2019/7453025
Ye, J. (2013a). Multicriteria decision-making method using the correlation coefficient under single-valued neutrosophic environment. International Journal of General Systems, 42(4), 386–394. https://doi.org/10.1080/03081079.2012.761609
Ye, J. (2013b). Another form of correlation coefficient between single valued neutrosophic sets and its multiple attribute decision-making method. Nuetrosophic Sets and Systems, 1, 8–12.
Ye, J. (2014a). Improved correlation coefficients of single valued neutrosophic sets and interval neutrosophic sets for multiple attribute decision making. Journal of Intelligent & Fuzzy Systems, 27(5), 2453–2462. https://doi.org/10.3233/IFS-141215
Ye, J. (2014b). A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets. Journal of Intelligent & Fuzzy Systems, 26, 2459–2466. https://doi.org/10.3233/IFS-130916
Ye, J. (2016). Correlation coefficients of interval neutrosophic hesitant fuzzy sets and their multiple attribute decision making method. Informatica, 27(1), 179–202. https://doi.org/10.15388/Informatica.2016.81
Ye, J. (2017a). Correlation coefficient between dynamic single valued neutrosophic multisets and its multiple attribute decision making method. Information, 8(2), 41. https://doi.org/10.3390/info8020041
Ye, J. (2017b). Bidirectional projection method for multiple attribute group decision making with neutrosophic numbers. Neural Computing and Applications, 28, 1021–1029. https://doi.org/10.1007/s00521-015-2123-5
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338– 353. https://doi.org/10.1016/S0019-9958(65)90241-X
Zhang, H. Y., Ji, P., Wang, J. Q., & Chen, X. H. (2015). An improved weighted correlation coefficient based on integrated weight for interval neutrosophic sets and its application in multi-criteria decision-making problems, International Journal of Computational Intelligence Systems, 8(6), 1027–1043. https://doi.org/10.1080/18756891.2015.1099917
Zhou, L. P., Dong, J. Y., & Wan, S. P. (2019). Two new approaches for multi-attribute group decision-making with interval-valued neutrosophic Frank aggregation operators and incomplete weights. IEEE Access, 7, 102727–102750. https://doi.org/10.1109/ACCESS.2019.2927133