A comment on "On the Mitchell similarity measure and its application to pattern recognition"

  • Authors:

  • Cheng-Tan Tung;Sophia Liu;Bonnie Shuan Wang

  • Affiliations:

  • Department of Information Management, Central Police University, Taiwan;Department of Chemistry, National Tsing Hua University, Taiwan;Department of Land Economics, National Chengchi University, Taiwan

  • Venue:
  • Pattern Recognition Letters
  • Year:
  • 2013

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Abstract

We provide a careful analysis of the similarity measures of Mitchell [Mitchell, H.B., 2003. On the Dengfend-Chuntian similarity measure and its application to pattern recognition. Pattern Recognition Lett. 24, 3101-3104] and Julian et al. [Julian, P., Hung, K.C., Lin, S.J., 2012. On the Mitchell similarity measure and its application to pattern recognition. Pattern Recognition Lett. 33, 1219-1223] for Julian's application to pattern recognition problem. In this paper we will first point out that the similarity measure of Julian et al. (2012) does not satisfy the system of axioms for similarity measures and then provide a counter example to support our assertion. Second, we will show that foundation that the differentiability property proposed by Julian et al. (2012) is questionable, hindering the progress of the similarity measure. Our analysis should help researchers to realize new similarity measures under intuitionistic fuzzy sets environment.