Abstract
Similarity of intuitionistic fuzzy sets (IFSs) is an important measure to indicate the similarity degree between IFSs. Recently, Ye (2011) proposed a similarity measure between IFSs based on the cosine concept. Although this cosine similarity measure has good concept and merit, the measure is not satisfied the definition of a similarity between IFSs and not presented well for analyzing IFS data. In this paper, we modify the cosine similarity measure between IFSs. This modified similarity measure between IFSs is not only to satisfy the definition of a similarity between IFSs, but also to improve the efficiency of the Ye’s measure. An example is used to demonstrate this phenomenon.
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References
Zadeh, L.A.: Fuzzy Sets. Information and Control 8, 338–356 (1965)
Atanassov, K.: Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems 20, 87–96 (1986)
Atanassov, K.: Intuitionistic Fuzzy Sets: Theory and Applications. Physica-Verlag, Heidelberg (1999)
Atanassov, K., Georgeiv, G.: Intuitionistic Fuzzy Prolog. Fuzzy Sets and Systems 53, 121–128 (1993)
Pankowska, A., Wygralak, M.: General IF-Sets with Triangular Norms and Their Applications to Group Decision Making. Information Sciences 176, 2713–2754 (2006)
De, S.K., Biswas, R., Roy, A.R.: An Application of Intuitionistic Fuzzy Sets in Medical Diagnosis. Fuzzy Sets and Systems 117, 209–213 (2001)
Hung, W.L., Yang, M.S.: On the J-Divergence of Intuitionistic Fuzzy Sets with Its Application to Pattern Recognition. Information Sciences 178, 1641–1650 (2008)
Dengfeng, L., Chuntian, C.: New Similarity Measures of Intuitionistic Fuzzy Sets and Application to Pattern Recognition. Pattern Recognition Letters 23, 221–225 (2002)
Liang, Z., Shi, P.: Similarity Measures on Intuitionistic Fuzzy Sets. Pattern Recognition Letters 24, 2687–2693 (2003)
Mitchell, H.B.: On the Dengfeng-Chuntian Similarity Measure and Its Application to Pattern Recognition. Pattern Recognition Letters 24, 3101–3104 (2003)
Hung, W.L., Yang, M.S.: Similarity Measures of Intuitionistic Fuzzy Sets Based on Hausdorff Distance. Pattern Recognition Letters 25, 1603–1611 (2004)
Xu, Z.S., Chen, J.: An Overview of Distance and Similarity Measures of Intuitionistic Fuzzy Sets. International Journal of Uncertainty, Fuzziness and Knowlege-Based Systems 16, 529–555 (2008)
Ye, J.: Cosine Similarity Measures for Intuitionistic Fuzzy Sets and Their Applications. Mathematical and Computer Modelling 53, 91–97 (2011)
Li, Y., Olson, D.L., Qin, Z.: Similarity Measures between Intuitionistic Fuzzy (Vague) Sets: A Comparative Analysis. Pattern Recognition Letters 28, 2687–2693 (2007)
Chen, S.M.: Measures of Similarity between Vague Sets. Fuzzy Sets and Systems 74, 217–223 (1995)
Hong, D.H., Kim, C.: A Note on Similarity Measures between Vague Sets and between Elements. Information Science 115, 83–96 (1999)
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Hwang, CM., Yang, MS. (2012). Modified Cosine Similarity Measure between Intuitionistic Fuzzy Sets. In: Lei, J., Wang, F.L., Deng, H., Miao, D. (eds) Artificial Intelligence and Computational Intelligence. AICI 2012. Lecture Notes in Computer Science(), vol 7530. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33478-8_36
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DOI: https://doi.org/10.1007/978-3-642-33478-8_36
Publisher Name: Springer, Berlin, Heidelberg
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