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

[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