Volume 15 , Issue 2 , PP: 62-76, 2021 | Cite this article as | XML | PDF | Full Length Article
Ngan Thi Roan 1 * , Florentin Smarandache 2
Doi: https://doi.org/10.54216/IJNS.150201
As an instance of a neutrosophic set, a single-valued neutrosophic set (SVNS) can be used to handle uncertainty, inaccuracy, indeterminacy, and inconsistency. In this paper, a new not-so-sophisticated distance measure between two SVNSs is defined by considering the cross-assessment between characteristic functions for the forward and backward differences. Furthermore, a single-valued neutrosophic similarity measure, a single-valued neutrosophic entropy measure, and their basic properties are presented and proven. In addition, an application to medical diagnosis is shown to illustrate the effective applicability of the proposals.
Single-Valued Neutrosophic Distance, similarity measure, entropy measure, medical diagnosis
  ,
[1] L. A. Zadeh, Fuzzy Sets, Informtion and Control , vol 8, pp. 338 – 353, 1965.
[2] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, vol 20, pp. 87–96, 1986.
[3] F. Smarandache, A unifying field in logics. neutrosophy: neutrosophic probability, set and logic, Rehoboth: American Research Press, 1999.
[4] F. Taş, S. Topal, F. Smarandache, Clustering neutrosophic data sets and neutrosophic valued metric spaces, Symmetry, vol 10(10), 430, 2018.
[5] S. Topal, S. Broumi, A. Bakali, M. Talea, F. Smarandache, A python tool for implementations on bipolar neutrosophic matrices, Infinite Study, 2019.
[6] S. Topal, A. Çevik, F. Smarandache, A New Group Decision Making Method With Distributed Indeterminacy Form Under Neutrosophic Environment: An Introduction to Neutrosophic Social Choice Theory, IEEE Access, vol 8, pp. 42000-42009, 2020.
[7] S. Topal, F. Tas, S. Broumi, O. A. Kirecci, Applications of Neutrosophic Logic of Smart Agriculture via Internet of Things. International Journal of Neutrosophic Science, vol 12(2), pp. 105-115, 2020
[8] H. Wang, F. Smarandache, Y. Q. Zhang, R. Sunderraman, Single valued neutrosophic sets, Multispace Multistruct, vol 4, pp. 410–413, 2010.
[9] H. L. Huang, New distance measure of single‐valued neutrosophic sets and its application, International Journal of Intelligent Systems, vol 31(10), pp. 1021-1032, 2016.
[10] S. Ridvan, Multi-criteria neutrosophic decision making method based on score and accuracy funtions under neutrosophic environment, Eprint Arxiv, 2014.
[11] J. Ye, A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets, Journal of Intelligent & Fuzzy Systems, vol 26, pp. 2459–2466, 2014.
[12] J. Ye, Single valued neutrosophic cross-entropy for multicriteria decision making problems, Applied Mathematical Modelling, vol 38, pp. 1170–1175, 2014.
[13] H. Zhang, J. Wang, X. Chen, Interval neutrosophic sets and their application in multicriteriadecision making problems, International Journal of Intelligent Systems, vol 31(5), pp. 1–15, 2014.
[14] A. A. Salama, M. Fazaa, M. Yahya, M. Kazim, A suggested diagnostic system of corona virus based on the neutrosophic systems and deep learning, International Journal of Neutrosophic Science, vol 9, 54, 2020.
[15] F. Smarandache, D. Stanujkic, D. Karabasevic, G. Popovic, A novel approach for assessing the reliability of data contained in a single valued neutrosophic number and its application in multiple criteria decision making, International Journal of Neutrosophic Science, vol 11(1), 22, 2020.
[16] J. Ding, W. Bai, C. Zhang, A New Multi-Attribute Decision Making Method with Single-Valued Neutrosophic Graphs, International Journal of Neutrosophic Science, vol 11(2) , pp. 76-86, 2020.
[17] R. T. Ngan, L. H. Son, M. Ali, δ-equality of intuitionistic fuzzy sets: a new proximity measure and applications in medical diagnosis, Applied Intelligence, vol 48(2), pp. 499-525, 2018.
[18] R. T. Ngan, L. H. Son, B. C. Cuong, M. Ali, H-max distance measure of intuitionistic fuzzy sets in decision making, Applied Soft Computing, vol 69, pp. 393-425, 2018.
[19] R. T. Ngan, L. H. Son, M. Ali, D. E. Tamir, N. D. Rishe, A. Kandel, Representing complex intuitionistic fuzzy set by quaternion numbers and applications to decision making, Applied Soft Computing, vol 87, 105961, 2020.
[20] L. H. Son, R. T. Ngan, M. Ali, H. Fujita, M. Abdel-Basset, N. L. Giang, G. Manogaran, M. K. Priyan, A new representation of intuitionistic fuzzy systems and their applications in critical decision making, IEEE Intelligent Systems, vol 35(1), pp. 6-17, 2019.
[21] F. Smarandache, N. T. Roan, S. C. Arnau, M. A. Díaz, J. M. M. Rubio, P. Lopez, F. Andujar, L. H. Son, V. V. Manh, The picture fuzzy distance measure in controlling network power consumption, Journal of Fuzzy Extension & Applications, vol 1(3), 148, 2020.
[22] S. Broumi, F. Smarandache, Several similarity measures of neutrosophic sets, Infinite Study, 2013.
[23] J. Ye, Vector similarity measures of simplified neutrosophic sets and their application in multicriteria decision making, Infinite Study, 2014.
[24] J. Ye, Clustering methods using distance-based similarity measures of single-valued neutrosophic sets, Journal of Intelligent Systems, vol 23(4), pp. 379-389, 2014.
[25] A. Aydoğdu, On similarity and entropy of single valued neutrosophic sets, General mathematics notes, vol 29(1), pp. 67-74, 2015.
[26] R. T. Ngan, L. H. Son, B. C. Cuong, A New Entropy of Dynamical Systems in Complex Intuitionistic Fuzzy Environment, Proceeding of the 11th International Conference on Internet (ICONI 2019), Hanoi, Vietnam, pp. 61-65, 2019.
[27] B. C. Cuong, V. Kreinovich, Picture Fuzzy Sets-a new concept for computational intelligence problems, In 2013 third world congress on information and communication technologies (WICT 2013), IEEE, pp. 1-6, 2013.