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.


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

Full Text:



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

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

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.

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.

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.

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.

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.

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.

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

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

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

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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

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.

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

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.

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

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.

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

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.

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

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.

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

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

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.

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.

DOI: https://doi.org/10.15837/ijccc.2019.1.3430

Copyright (c) 2019 Haiping Ren, Shixiao Xiao, Hui Zhou

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

CC-BY-NC  License for Website User

Articles published in IJCCC user license are protected by copyright.

Users can access, download, copy, translate the IJCCC articles for non-commercial purposes provided that users, but cannot redistribute, display or adapt:

  • Cite the article using an appropriate bibliographic citation: author(s), article title, journal, volume, issue, page numbers, year of publication, DOI, and the link to the definitive published version on IJCCC website;
  • Maintain the integrity of the IJCCC article;
  • Retain the copyright notices and links to these terms and conditions so it is clear to other users what can and what cannot be done with the  article;
  • Ensure that, for any content in the IJCCC article that is identified as belonging to a third party, any re-use complies with the copyright policies of that third party;
  • Any translations must prominently display the statement: "This is an unofficial translation of an article that appeared in IJCCC. Agora University  has not endorsed this translation."

This is a non commercial license where the use of published articles for commercial purposes is forbiden. 

Commercial purposes include: 

  • Copying or downloading IJCCC articles, or linking to such postings, for further redistribution, sale or licensing, for a fee;
  • Copying, downloading or posting by a site or service that incorporates advertising with such content;
  • The inclusion or incorporation of article content in other works or services (other than normal quotations with an appropriate citation) that is then available for sale or licensing, for a fee;
  • Use of IJCCC articles or article content (other than normal quotations with appropriate citation) by for-profit organizations for promotional purposes, whether for a fee or otherwise;
  • Use for the purposes of monetary reward by means of sale, resale, license, loan, transfer or other form of commercial exploitation;

    The licensor cannot revoke these freedoms as long as you follow the license terms.

[End of CC-BY-NC  License for Website User]

INTERNATIONAL JOURNAL OF COMPUTERS COMMUNICATIONS & CONTROL (IJCCC), With Emphasis on the Integration of Three Technologies (C & C & C),  ISSN 1841-9836.

IJCCC was founded in 2006,  at Agora University, by  Ioan DZITAC (Editor-in-Chief),  Florin Gheorghe FILIP (Editor-in-Chief), and  Misu-Jan MANOLESCU (Managing Editor).

Ethics: This journal is a member of, and subscribes to the principles of, the Committee on Publication Ethics (COPE).

Ioan  DZITAC (Editor-in-Chief) at COPE European Seminar, Bruxelles, 2015:

IJCCC is covered/indexed/abstracted in Science Citation Index Expanded (since vol.1(S),  2006); JCR2018: IF=1.585..

IJCCC is indexed in Scopus from 2008 (CiteScore2018 = 1.56):

Nomination by Elsevier for Journal Excellence Award Romania 2015 (SNIP2014 = 1.029): Elsevier/ Scopus

IJCCC was nominated by Elsevier for Journal Excellence Award - "Scopus Awards Romania 2015" (SNIP2014 = 1.029).

IJCCC is in Top 3 of 157 Romanian journals indexed by Scopus (in all fields) and No.1 in Computer Science field by Elsevier/ Scopus.


 Impact Factor in JCR2018 (Clarivate Analytics/SCI Expanded/ISI Web of Science): IF=1.585 (Q3). Scopus: CiteScore2018=1.56 (Q2);

SCImago Journal & Country Rank

Editors-in-Chief: Ioan DZITAC & Florin Gheorghe FILIP.