A Chi-square Distance-based Similarity Measure of Single-valued Neutrosophic Set and Applications

  • Haiping Ren
  • Shixiao Xiao
  • Hui Zhou


The aim of this paper is to propose a new similarity measure of singlevalued neutrosophic sets (SVNSs). The idea of the construction of the new similarity measure comes from Chi-square distance measure, which is an important measure in the applications of image analysis and statistical inference. Numerical examples are provided to show the superiority of the proposed similarity measure comparing with the existing similarity measures of SVNSs. A weighted similarity is also put forward based on the proposed similarity. Some examples are given to show the effectiveness and practicality of the proposed similarity in pattern recognition, medical diagnosis and multi-attribute decision making problems under single-valued neutrosophic environment.


[1] Atanassov, K. T.(1986); Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1), 87–96, 1986.

[2] Atanassov, K.; Gargov, G. (1989); Interval-valued intuitionistic fuzzy sets, Fuzzy Sets and Systems, 31(3), 343–349, 1989.

[3] Boran, F. E; Akay, D. (2014); A biparametric similarity measure on intuitionistic fuzzy sets with applications to pattern recognition, Information Sciences, 255, 45–57, 2014.

[4] Bozic, M.; Ducic, N.; Djordjevic, G.; Slavkovic, R. (2017); Optimization of Wheg Robot Running with Simulation of Neuro-Fuzzy Control, International Journal of Simulation Modelling, 16(1), 19–30, 2017.

[5] Chaira, T.; Panwar, A. (2014); An Atanassov's intuitionistic fuzzy kernel clustering for medical image segmentation, International Journal of Computational Intelligence Systems, 7(2), 360–370, 2014.

[6] Dalman H.; Gazel N.; Sivri M. (2016); A fuzzy set-based approach to multi-objective multiitem solid transportation problem under uncertainty, International Journal of Fuzzy Systems, 18(4), 716–729, 2016.

[7] Das, S.; Guha, D.; Dutta, B. (2016); Medical diagnosis with the aid of using fuzzy logic and intuitionistic fuzzy logic, Applied Intelligence, 45(3), 850–867, 2016.

[8] De S. K.; Biswas, R.; Roy, A. R. (2001); An application of intuitionistic fuzzy sets in medical diagnosis, Fuzzy Sets & Systems, 117(2), 209–213, 2001.

[9] Dubois, D.; Prade, H.; Esteva, F. (2015); Fuzzy set modelling in case-based reasoning, International Journal of Intelligent Systems, 13(4), 345–373, 2015.

[10 Gau, W. L.; Buehrer, D. J.(1993); Vague sets, IEEE Transactions on Systems Man & Cybernetics, 23(2), 610–614, 1993.

[11] Huang, H. (2016); New distance measure of single-valued neutrosophic sets and its application, International Journal of Intelligent Systems, 31(10), 1021–1032, 2016.

[12] Hung, W. L.; Yang, M. S. (2007); Similarity measures of intuitionistic fuzzy sets based on Lp metric, International Journal of Approximate Reasoning, 46(1), 120–136, 2007.

[13] Hwang, C. M.; Yang, M. S. (2013); New construction for similarity measures between intuitionistic fuzzy sets based on lower, upper and middle fuzzy sets, International Journal of Fuzzy Systems, 15(3), 371–378, 2013.

[14] Kar, A. K. (2015); A hybrid group decision support system for supplier selection using analytic hierarchy process, fuzzy set theory and neural network, Journal of Computational Science, 6,23–33, 2015

[15] Karaaslan, F. (2017); Correlation coefficients of single valued neutrosophic refined soft sets and their applications in clustering analysis, Neural Computing & Applications, 28(9), 2781–2793,2017.

[16] Le, H. S.; Phong, P. H. (2016); On the performance evaluation of intuitionistic vector similarity measures for medical diagnosis, Journal of Intelligent & Fuzzy Systems, 31(3), 1–12, 2016.

[17] Li D. F.; Cheng C. T. (2012); New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions, Pattern Recognition Letters, 23(1), 221–225, 2002.

[18] Li D. F.; Ren H. P. (2015); Multi-attribute decision making method considering the amount and reliability of intuitionistic fuzzy information, Journal of Intelligent & Fuzzy Systems, 28(4), 1877–1883, 2015.

[19] Liu, P. D. (2016); The aggregation operators based on archimedean t-conorm and t-norm for single-valued neutrosophic numbers and their application to decision making, International Journal of Fuzzy Systems, 18(5), 1–15, 2016.

[20] Meng, F.; Chen, X. (2016); Entropy and similarity measure of AtanassovAZs intuitionistic fuzzy sets and their application to pattern recognition based on fuzzy measures, Pattern Analysis and Applications, 19(1), 11–20, 2016.

[21] Mousavi, M.; Yap, H. J.; Musa, S. N.; Dawal, S. Z. M. (2017); A Fuzzy Hybrid GA-PSO Algorithm for Multi-Objective AGV Scheduling in FMS, International Journal of Simulation Modelling, 16(1), 58–71, 2017.

[22] Nguyen, H. (2016); A novel similarity/dissimilarity measure for intuitionistic fuzzy sets and its application in pattern recognition, Expert Systems with Applications, 45, 97–107, 2016

[23] 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, 2016.

[24] Perlibakas, V. (2004); Distance measures for PCA-based face recognition, Pattern Recognition Letters, 25(6), 711–724, 2004.

[25] Pramanik, S.; Pramanik, S.; Giri, B. C. (2015); TOPSIS method for multi-attribute group decision-making under single-valued neutrosophic environment, Neural Computing & Applications, 27(3), 727–737, 2015.

[26] Smarandache, F. (1999); A Unifying Field in Logics. Neutrosophy: Neutrosophic Probability, Set and Logic, American Research Press, 1999.

[27] Tavana, M.; Zareinejad, M.; Caprio, D. D.; Kavianic M. A. (2016); An integrated intuitionistic fuzzy AHP and SWOT method for outsourcing reverse logistics, Applied Soft Computing, 40, 544–557, 2016.

[28] Torra V. (2010); Hesitant fuzzy sets, International Journal of Intelligent Systems, 25(6), 529–539, 2010.

[29] Vasavi, C.; Kumar G. S.; Murty, M. S. N.(2016); Generalized differentiability and integrability for fuzzy set-valued functions on time scales, Soft Computing, 20(3), 1093–1104, 2016.

[30] Wang, H. B.; Smarandache, F.; Zhang Y. Q.; Sunderraman R. (2010); Single valued neutrosophic sets, Multispace and Multistructure, 4, 410–413, 2010.

[31] Xu, Z. S.; Chen, J. (2008); An overview of distance and similarity measures of intuitionistic fuzzy sets, International Journal of Uncertainty, Fuzziness and Knowlege-Based Systems, 16(4), 529–555, 2008.

[32] Xu Z. S.; Zhao N. (2016); Information fusion for intuitionistic fuzzy decision making: an overview, Information Fusion, 28, 10–23, 2016.

[33] Ye, J.(2015); The generalized Dice measures for multiple attribute decision making under simplified neutrosophic environments, Intelligent & Fuzzy Systems, 31(1), 663–671, 2015.

[34] Ye J.; Fu, J. (2016); Multi-period medical diagnosis method using a single valued neutrosophic similarity measure based on tangent function, Comput Methods Programs Biomed, 123, 142–149, 2016.

[35] Ye, J. (2017); Single-valued neutrosophic similarity measures based on cotangent function and their application in the fault diagnosis of steam turbine, Soft Computing, 21(3), 1–9, 2017.
How to Cite
REN, Haiping; XIAO, Shixiao; ZHOU, Hui. A Chi-square Distance-based Similarity Measure of Single-valued Neutrosophic Set and Applications. INTERNATIONAL JOURNAL OF COMPUTERS COMMUNICATIONS & CONTROL, [S.l.], v. 14, n. 1, p. 78-89, feb. 2019. ISSN 1841-9844. Available at: <http://univagora.ro/jour/index.php/ijccc/article/view/3430>. Date accessed: 13 july 2020. doi: https://doi.org/10.15837/ijccc.2019.1.3430.


Chi-square distance measure, similarity measure, multi-attribute decision making, single-valued neutrosophic set