Abstract
Although there exist many similarity measures for intuitionistic fuzzy sets (IFSs), most of them can not satisfy the axioms of similarity measure or provide reasonable results. In this paper, a review of existing similarity measures for IFSs and their drawbacks is carried out. Then a new similarity measure between IFSs on the base of their knowledge measures is proposed. A comprehensive analysis of the performance features of the proposed measure is conducted in a comparative example. Finally, the proposed similarity measure is employed in application to the turbine fault diagnosis. We point out that the new proposed similarity measure overcomes the drawbacks of the existing similarity measures and gives reliable results in real world application.
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References
Atanassov, K.T.: Intuitionistic Fuzzy Sets. Fuzzy Sets Systems 20(1), 87–96 (1986)
Atanassov, K.T.: Intuitionistic Fuzzy Sets. Springer, New York (1999)
Boran, F.R., Akay, D.: A biparametric similarity measure on intuitionistic fuzzy sets with applications to pattern recognition. Inf. Sci. 255, 45–57 (2014)
Bustince, H., Mohedano, V., Barrenechea, E., Pagola, M.: An algorithm for calculating the threshold of an image representing uncertainty through A-IFSs. In: IPMU 2006, pp. 2383–2390 (2006)
Chen, S.M.: Measures of similarity between vague sets. Fuzzy Sets Syst. 74(2), 217–223 (1995)
Dengfeng, L., Chuntian, C.: New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions. Pattern Recognit. Lett. 23(1–3), 221–225 (2002)
Hong, D.H., Kim, C.: A note on similarity measures between vague sets and between elements. Inf. Sci. 115(1–4), 83–96 (1999)
Hung, W.L., Yang, M.S.: Similarity measures of intuitionistic fuzzy sets based on the Hausdorff distance. Pattern Recognit. Lett. 25(14), 1603–1611 (2004)
Li, D.F., Cheng, C.: New similarity measures of intuitionistic fuzzy sets and application to pattern recognition. Pattern Recognit. Lett. 23, 221–225 (2002)
Li, F., Xu, Z.: Similarity measures between vague sets. J. Softw. 12(6), 922–927 (2001)
Li, Y.H., Olson, D.L., Qin, Z.: Similarity measures between intuitionistic fuzzy (vague) sets: A comparative analysis. Pattern Recognit. Lett. 28, 278–285 (2007)
Liang, Z., Shi, P.: Similarity measures on intuitionistic fuzzy sets. Pattern Recognit. Lett. 24(15), 2687–2693 (2003)
Liu, H.W.: New similarity measures between intuitionistic fuzzy sets and between elements. Math. Comput. Model. 42, 61–70 (2005)
Lu, Z.K., Ye, J.: Cosine similarity measure between vague sets and its application of fault diagnosis. Res. J. Appl. Sci. Eng. Technol. 6(14), 2625–2629 (2013)
Mitchell, H.B.: On the Dengfeng-Chuntian similarity measure and its application to pattern recognitions. Pattern Recognit. Lett. 24(16), 3101–3104 (2003)
Miaoying, T.: A new fuzzy similarity measure based on cotangent function for medical diagnosis. Adv. Model. Optim. 15(2), 151–156 (2013)
Nguyen, H.: A new knowledge-based measure for intuitionistic fuzzy sets and its application in multiple attribute group decision making. Expert Syst. Appl. 42, 8766–8774 (2015)
Shi, L.L., Ye, J.: Study on fault diagnosis of turbine using an improved cosine similarity measure of vague sets. J. Appl. Sci. 13(10), 1781–1786 (2013)
Song, Y., Wang, X., Lei, L., Xue, A.: A new similarity measure between intuitionistic fuzzy sets and its application to pattern recognition. Appl. Intell. 42, 252–261 (2015)
Szmidt, E., Kacprzyk, J.: Geometric similarity measures for the intuitionistic fuzzy sets. In: 8th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT 2013), pp. 840–847 (2013)
Tan, C., Chen, X.: Dynamic similarity measures between intuitionistic fuzzy sets and its application. Int. J. Fuzzy Syst. 16(4), 511–519 (2014)
Ye, J.: Fault diagnosis of turbine based on fuzzy cross entropy of vague sets. Expert Syst. Appl. 36, 8103–8106 (2009)
Ye, J.: Cosine similarity measures for intuitionistic fuzzy sets and their applications. Math. Comput. Model. 53(1–2), 91–97 (2011)
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Nguyen, H. (2016). A New Similarity Measure for Intuitionistic Fuzzy Sets. In: Nguyen, N.T., Trawiński, B., Fujita, H., Hong, TP. (eds) Intelligent Information and Database Systems. ACIIDS 2016. Lecture Notes in Computer Science(), vol 9621. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-49381-6_55
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DOI: https://doi.org/10.1007/978-3-662-49381-6_55
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