A Chi-square Distance-based Similarity Measure of Single-valued Neutrosophic Set and Applications
Keywords:
Chi-square distance measure, similarity measure, multi-attribute decision making, single-valued neutrosophic setAbstract
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.References
Atanassov, K. T.(1986); Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1), 87-96, 1986. https://doi.org/10.1016/S0165-0114(86)80034-3
Atanassov, K.; Gargov, G. (1989); Interval-valued intuitionistic fuzzy sets, Fuzzy Sets and Systems, 31(3), 343-349, 1989. https://doi.org/10.1016/0165-0114(89)90205-4
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. https://doi.org/10.1016/j.ins.2013.08.013
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. https://doi.org/10.2507/IJSIMM16(1)2.363
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. https://doi.org/10.1080/18756891.2013.865830
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. https://doi.org/10.1007/s40815-015-0081-9
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. https://doi.org/10.1007/s10489-016-0792-0
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. https://doi.org/10.1016/S0165-0114(98)00235-8
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. https://doi.org/10.1109/21.229476
Huang, H. (2016); New distance measure of single-valued neutrosophic sets and its application, International Journal of Intelligent Systems, 31(10), 1021-1032, 2016. https://doi.org/10.1002/int.21815
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. https://doi.org/10.1016/j.ijar.2006.10.002
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 https://doi.org/10.1016/j.jocs.2014.11.002
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. https://doi.org/10.1007/s00521-016-2209-8
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. https://doi.org/10.1007/s40815-016-0195-8
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. https://doi.org/10.1007/s10044-014-0378-6
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. https://doi.org/10.2507/IJSIMM16(1)5.368
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 https://doi.org/10.1016/j.eswa.2015.09.045
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. https://doi.org/10.1080/00207721.2014.994050
Perlibakas, V. (2004); Distance measures for PCA-based face recognition, Pattern Recognition Letters, 25(6), 711-724, 2004. https://doi.org/10.1016/j.patrec.2004.01.011
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. https://doi.org/10.1016/j.asoc.2015.12.005
Torra V. (2010); Hesitant fuzzy sets, International Journal of Intelligent Systems, 25(6), 529-539, 2010. https://doi.org/10.1002/int.20418
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. https://doi.org/10.1007/s00500-014-1569-1
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. https://doi.org/10.1142/S0218488508005406
Xu Z. S.; Zhao N. (2016); Information fusion for intuitionistic fuzzy decision making: an overview, Information Fusion, 28, 10-23, 2016. https://doi.org/10.1016/j.inffus.2015.07.001
Ye, J.(2015); The generalized Dice measures for multiple attribute decision making under simplified neutrosophic environments, Intelligent & Fuzzy Systems, 31(1), 663-671, 2015. https://doi.org/10.3233/IFS-162179
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. https://doi.org/10.1016/j.cmpb.2015.10.002
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. https://doi.org/10.1007/s00500-015-1818-y
Published
Issue
Section
License
ONLINE OPEN ACCES: Acces to full text of each article and each issue are allowed for free in respect of Attribution-NonCommercial 4.0 International (CC BY-NC 4.0.
You are free to:
-Share: copy and redistribute the material in any medium or format;
-Adapt: remix, transform, and build upon the material.
The licensor cannot revoke these freedoms as long as you follow the license terms.
DISCLAIMER: The author(s) of each article appearing in International Journal of Computers Communications & Control is/are solely responsible for the content thereof; the publication of an article shall not constitute or be deemed to constitute any representation by the Editors or Agora University Press that the data presented therein are original, correct or sufficient to support the conclusions reached or that the experiment design or methodology is adequate.