A Novel Similarity Measure Based on the Centre of Nine-point Circle of the Isosceles Triangular Fuzzy Numbers and Their Applications

Document Type : Research Paper

Author

School of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, Henan, P. R. China

Abstract

A new similarity/distance measure based on the centre of nine-point circle of the isosceles triangular fuzzy numbers is recommend in this paper. Extend the similarity/distance measure based on centroid, orthocenter, circumcenter, incenter and nine-point circle center of the isosceles triangles. It is proved that this general similarity/distance measure conforms to the properties of distance. Subsequently, some examples are presented to justify the superiority and validity of the proposed similarity/distance measure between IFSs based on the center of nine-point circle, which demonstrate that this measure overcomes the disadvantage of the existing similarity measures. The application of the proposed similarity measure to deal with pattern recognition problems is described, and the results are correlated with those reported in some prevailing studies. In addition, a clustering technique to classify objects based on the proposed similarity measure is discussed. Through a detailed comparative analysis of some existing measures, it is concluded that some of the existing measures fail to discriminate the results obtained under different circumstances, such as zero division or counter intuitive cases; in contrast, the proposed similarity measure successfully overcomes this weakness.

Keywords

Main Subjects

References

[1] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1) (1986), 87-96. https://doi.org/10.
1016/S0165-0114(86)80034-3
[2] K. T. Atanassov, Norms and metrics over intuitionistic fuzzy sets, Busefal, 55 (1993), 11-20. https://projects.
listic.univ-smb.fr/busefal/papers/55.zip/55_02.pdf
[3] K. T. Atanassov, G. Gargov, Interval-valued intuitionistic fuzzy sets, Fuzzy Sets and Systems, 31 (1989), 343-349.
https://doi.org/10.1016/0165-0114(89)90205-4
[4] G. Beliakov, M. Pagola, T. Wilkin, Vector valued similarity measures for Atanassov’s intuitionistic fuzzy sets,
Information Sciences, 280 (2014), 352-367. https://doi.org/10.1016/j.ins.2014.04.056
[5] F. E. Boran, D. Akay, A biparametric similarity measure on intuitionistic fuzzy sets with applications to pattern
recognition, Information Sciences, 255 (2014), 45-57. https://doi.org/10.1016/j.ins.2013.08.013
[6] G. Brindaban, C. Rituparna, D. Palash, G. Surabhi, Two new similarity measures for intuitionistic fuzzy sets and
its various applications, International Journal of Intelligent Systems, 37 (2021), 1-40. https://doi.org/10.1002/
int.22802
[7] S. M. Chen, Measures of similarity between vague sets, Fuzzy Sets and Systems, 74 (1995), 217-223. https://doi.
org/10.1016/0165-0114(94)00339-9
[8] S. M. Chen, S. H. Cheng, C. H. Chiou, Fuzzy multiattribute group decision making based on intuitionistic fuzzy
sets and evidential reasoning methodology, Information Fusion, 27 (2016), 215-227. https://doi.org/10.1016/j.
inffus.2015.03.002
[9] S. M. Chen, S. H. Cheng, T. C. Lan, A novel similarity measure between intuitionistic fuzzy sets based on the
centroid points of transformed fuzzy numbers with applications to pattern recognition, Information Sciences, 343
(2016), 15-40. https://doi.org/10.1016/j.ins.2016.01.040
[10] H. Garg, K. Kumar, An advanced study on the similarity measures of intuitionistic fuzzy sets based on the set
pair analysis theory and their application in decision making, Soft Computing, 22(15) (2018), 4959-4970. https:
//doi.org/10.1007/s00500-018-3202-1
[11] H. Garg, D. Rani, Novel distance measures for intuitionistic fuzzy sets based on various triangle centers of isosceles
triangular fuzzy numbers and their applications, Expert Systems With Applications, 191 (2022), 116228. https:
//doi.org/10.1016/j.eswa.2021.116228
[12] D. H. Hong, C. Kim, A note on similarity measures between vague sets and between elements, Information Sciences,
115 (1999), 83-96. https://doi.org/10.1016/S0020-0255(98)10083-X
[13] W. L. Hung, M. S. Yang, Similarity measures of intuitionistic fuzzy sets based on Hausdorff distance, Pattern
Recognition Letters, 25 (2004), 1603-1611. https://doi.org/10.1016/j.patrec.2004.06.006
[14] W. L. Hung, M. S. Yang, Similarity measures of intuitionistic fuzzy sets based on Lp metric, International Journal
of Approximate Reasoning, 46 (2007), 120-136. https://doi.org/10.1016/j.ijar.2006.10.002
[15] W. L. Hung, M. S. Yang, On similarity measures between intuitionistic fuzzy sets, International Journal of Intelligent
systems, 23 (2008), 364-38. https://doi.org/10.1002/int.20271
[16] C. M. Hwang, M. S. Yang, W. L. Hung, New similarity measures of intuitionistic fuzzy sets based on the Jaccard
index with its application to clustering, International Journal of Intelligent Systems, 33 (2018), 1-17. https://doi.
org/10.1002/int.21990
[17] I. Iancu, Intuitionistic fuzzy similarity measures based on frank t-norms family, Pattern Recognition Letters, 42
(2014), 128-136. https://doi.org/10.1016/j.patrec.2014.02.010
[18] Q. Jiang, X. Jin, S. J. Lee, S. W. Yao, A new similarity/distance measure between intuitionistic fuzzy sets based on
the transformed isosceles triangles and its applications to pattern recognition, Expert Systems With Applications,
116 (2019), 439-453. https://doi.org/10.1016/j.eswa.2018.08.046
[19] D. F. Li, C. T. Cheng, New similarity measures of intuitionistic fuzzy sets and application to pattern recognition,
Pattern Recognition Letter, 23 (2002), 221-226. https://doi.org/10.1016/S0167-8655(01)00110-6
[20] Z. Liang, P. Shi, Similarity measures on intuitionistic fuzzy sets, Pattern Recognition Letter, 24 (2003), 2687-2693.
https://doi.org/10.1016/S0167-8655(03)00111-9
[21] H. W. Liu, New similarity measures between intuitionistic fuzzy sets and between elements, Mathematical and
Computer Modelling, 42 (2005), 61-70. https://doi.org/10.1016/j.mcm.2005.04.002
[22] H. B. Mitchell, On the Dengfeng Chuntian similarity measure and its application to pattern recognition, Pattern
Recognition Letter, 24 (2003), 3101-3104. https://doi.org/10.1016/S0167-8655(03)00169-7
[23] S. C. Ngan, An activation detection based similarity measure for intuitionistic fuzzy sets, Expert Systems with
Applications, 60 (2016), 62-80. https://doi.org/10.1016/j.eswa.2016.04.037
[24] R. T. Ngan, M. Ali, H. S. Le, δ-equality of intuitionistic fuzzy sets: A new proximity measure and applications in
medical diagnosis, Applied Intelligence, 48(2) (2018), 499-525. https://doi.org/10.1007/s10489-017-0986-0
[25] R. T. Ngan, H. S. Le, B. C. Cuong, M. Ali, H-max distance measure of intuitionistic fuzzy sets indecision making,
Applied Soft Computing, 69 (2018), 393-425. https://doi.org/10.1016/j.asoc.2018.04.036
[26] Y. Song, X. Wang, L. Lei, A. Xue, A new similarity measure between intuitionistic fuzzy sets and its application
to pattern recognition, Abstract and Applied Analysis, (2014), 384241. https://doi.org/10.1155/2014/384241
[27] E. Szmidt, J. Kacprzyk, A similarity measure for intuitionistic fuzzy sets and its application in supporting medical
diagnostic reasoning, Lecture Notes in Artificial Intelligence, 3070 (2004), 388-393. https://doi.org/10.1007/
978-3-540-24844-6_56
[28] K. I. Vlachos, G. D. Sergiadis, Intuitionistic fuzzy information applications to pattern recognition, Pattern Recognition
Letters, 28 (2007), 197-206. https://doi.org/10.1016/j.patrec.2006.07.004
[29] W. Wang, X. Xin, Distance measure between intuitionistic fuzzy sets, Pattern Recognition Letters, 26 (2005),
2063-2069. https://doi.org/10.1016/j.patrec.2005.03.018
[30] Z. S. Xu, J. Chen, J. J. Wu, Cluster algorithm for intuitionistic fuzzy sets, Information Sciences, 178 (2008),
3775-3790. https://doi.org/10.1016/j.ins.2008.06.008
[31] J. Ye, Cosine similarity measures for intuitionistic fuzzy sets and their applications, Mathematical and Computer
Modelling, 53 (2011), 91-97. https://doi.org/10.1016/j.mcm.2010.07.022
[32] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)
90241-X
[33] W. Y. Zeng, H. S. Cui, Y. Q. Liu, Q. Yin , Z. S. Xu, Novel distance measure between intuitionistic fuzzy sets and
its application in pattern recognition, Iranian Journal of Fuzzy Systems, 19(3) (2022), 127-137. https://doi.org/
10.22111/IJFS.2022.6947
[34] H. Zhang, L. Yu, New distance measures between intuitionistic fuzzy sets and interval-valued fuzzy sets, Information
Sciences, 245 (2013), 181-196. https://doi.org/10.1016/j.ins.2013.04.040
Iranian Journal of Fuzzy Systems
Volume 21, Issue 2
March and April 2024
Pages 87-104

Files

Share

How to cite

Statistics