Abstract
Due to some unreasonable results obtained from most current similarity measures for intuitionistic fuzzy sets (IFSs), we introduce a necessary condition to obtain a stronger definition of similarity measures for IFSs, and present a new similarity measure derived from a general idea of similarity measures for concepts on a lattice. In experiments, we focus our attention on two basic directions of performance evaluation: one is how much the proposed measure is reasonable and the other is how much accuracy the measure produces when it is applied to classification problems. The experimental results show that the proposed measure is reasonable and achieves a satisfactory performance on classification problems.
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A partial order on a nonempty set \(P\) is a binary relation on \(P\) satisfying reflexivity, antisymmetry, and transitivity.
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References
Atanassov K (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96
Atanassov K (1989) More on intuitionistic fuzzy sets. Fuzzy Sets Syst 33(1):37–45d
Boran FE, Akay D (2014) A biparametric similarity measure on intuitionistic fuzzy sets with applications to pattern recognition. Inform Sci 255:45–57
Bustince H, Goswami DP, Mukherjee UK, Pal NR (2011) On averaging operators for Atanassov’s intuitionistic fuzzy sets. Inform Sci 181(6):1116–1124
Dengfeng L, Chuntian C (2002) New similarity measures of intuitionistic fuzzy sets and application to pattern recognition. Pattern Recogn Lett 23:221–225
Deschrijver G, Cornelis C, Kerre EE (2004) On the representation of intuitionistic fuzzy t-norms and t-conorms. IEEE T Fuzzy Syst 12:45–61
Farhadinia B (2014) An efficient similarity measure for intuitionistic fuzzy sets. Soft Comput 18:85–94
Guo K, Song Q (2014) On the entropy for Atanassov’s intuitionistic fuzzy sets: an interpretation from the perspective of amount of knowledge. Appl Soft Comput 24:328–340
Hu K, Li J (2013) The entropy and similarity measure of interval valued intuitionistic fuzzy sets and their relationship. Int J Fuzzy Syst 15(3):279–288
Hung WL, Yang MS (2004) Similarity measures of intuitionistic fuzzy sets based on hausdorff distance. Pattern Recogn Lett 25(14):1603–1611
Hung WL, Yang MS (2008) On similarity measures between intuitionistic fuzzy sets. Int J Intell Syst 23(3):364–383
Hwang CM, Yang MS (2012) Modified cosine similarity measure between intuitionistic fuzzy sets. 4th international conference (AICI 2012). Chengdu, China, pp 285–293
Hwang CM, Yang MS, Hung WL, Lee MG (2012) A similarity measure of intuitionistic fuzzy sets based on the sugeno integral with its application to pattern recognition. Inform Sci 189:93–109
Julian P, Hung KC, Lin SJ (2012) On the mitchell similarity measure and its application to pattern recognition. Pattern Recogn Lett 33(9):1219–1223
Khatibi V, Montazer GA (2009) Intuitionistic fuzzy set vs fuzzy set application in medical pattern recognition. Artif Intell Med 47(1):43–52
Li Y, Olson D, Qin Z (2007) Similarity measures between intuitionistic fuzzy (vague) sets: a comparative analysis. Pattern Recogn Lett 28(2):278–285
Li J, Deng G, Li H, Zeng W (2012) The relationship between similarity measure and entropy of intuitionistic fuzzy sets. Inform Sci 188:314–321
Liang Z, Shi P (2003) Similarity measures on intuitionistic fuzzy sets. Pattern Recogn Lett 24(15):2687–2693
Liu G (2009) Closures of intuitionistic fuzzy relations. In: Wen P, Li Y, Polkowski L, Yao Y, Tsumoto S, Wang G (eds), Rough sets and knowledge technology, Springer, Heidelberg pp 281–288
Liu HW (2005) New similarity measures between intuitionistic fuzzy sets and between elements. Math Comput Model 42:61–70
Mitchell HB (2003) On the dengfeng–chuntian similarity measure and its application to pattern recognition. Pattern Recogn Lett 24(16):3101–3104
Papakostas GA, Hatzimichailidis AG, Kaburlasos VG (2013) Distance and similarity measures between intuitionistic fuzzy sets: a comparative analysis from a pattern recognition point of view. Pattern Recogn Lett 34(14):1609–1622
Rezaei H, Mukaidono M (2007) New similarity measures of intuitionistic fuzzy sets. J Adv Comput Intell Intell Inf 11(2):202–209
Song Y, Wang X, Lei L, Xue A (2014) A new similarity measure between intuitionistic fuzzy sets and its application to pattern recognition. Abs Appl Anal 2014:1–11
Szmidt E, Kacprzyk J (2000) Distances between intuitionistic fuzzy sets. Fuzzy Sets Syst 114(3):505–518
Szmidt E, Kacprzyk J (2001) Entropy for intuitionistic fuzzy sets. Fuzzy Sets Syst 118:467–477
Szmidt E, Kacprzyk J (2005) A new measure of entropy and its connection with a similarity measure for intuitionistic fuzzy sets. In: EUSFLAT-LFA’05, Barcelona, Spain pp 461–466
Tripathy BC, Das PC (2012) On convergence of series of fuzzy real numbers. Kuwait J Sci Eng 39(1A):57–70
Tripathy BC, Ray GC (2012) On mixed fuzzy topological spaces and countability. Soft Comput 10(16):1691–1695
Tripathy BC, Sarma B (2012) On i-convergent double sequences of fuzzy real numbers. Kyungpook Math J 52(2):189–200
Tripathy BC, Baruah A, Et M, Gungor M (2012) On almost statistical convergence of new type of generalized difference sequence of fuzzy numbers. Iran J Sci Technol A 36(2):147–155
Xu Z (2007) Some similarity measures of intuitionistic fuzzy sets and their applications to multiple attribute decision making. Fuzzy Optim Decis Making 6:109–121
Yang J, Chiclana F (2012) Consistency of 2d and 3d distances of intuitionistic fuzzy sets. Expert Syst Appl 39:8665–8670
Ye J (2011) Cosine similarity measures for intuitionistic fuzzy sets and their applications. Math Comput Model 53(1–2):91–97
Yu D (2014) Intuitionistic fuzzy information aggregation under confidence levels. Appl Soft Comput 19:147–160
Zadeh L (1965) A fuzzy sets. Inf Control 8:338–353
Acknowledgments
The author thanks the anonymous referees for very useful suggestion to improve this paper and gratefully acknowledges the financial support provided by Thammasat University Research Fund under the TU Research Scholar, Contract No. 1/8/2557.
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Communicated by V. Loia.
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Intarapaiboon, P. A hierarchy-based similarity measure for intuitionistic fuzzy sets. Soft Comput 20, 1909–1919 (2016). https://doi.org/10.1007/s00500-015-1612-x
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DOI: https://doi.org/10.1007/s00500-015-1612-x