Divergence Measures for Intuitionistic Fuzzy Sets

Characterization of dissimilarity/divergence between intuitionistic fuzzy sets (IFSs) is important as it has applications in different areas including image segmentation and decision making. This study deals with the problem of comparison of intuitionistic fuzzy sets. An axiomatic definition of divergence measures for IFSs is presented, which are particular cases of dissimilarities between IFSs. The relationships among IF-divergences, IF-dissimilarities, and IF-distances are studied. Finally, we propose a very general framework for comparison of IFSs, where depending on the conditions imposed on a particular function, we can realize measures of distance, dissimilarity, and divergence for IFSs. Some methods for building divergence measures for IFSs are also introduced, as well as some examples of IF-divergences. In particular, we have proved some results that can be used to generate measures of divergence for fuzzy sets as well as for intuitionistic fuzzy sets.

[1]  Inés Couso,et al.  Divergence measure between fuzzy sets , 2002, Int. J. Approx. Reason..

[2]  Janusz Kacprzyk,et al.  Distances between intuitionistic fuzzy sets , 2000, Fuzzy Sets Syst..

[3]  Janusz Kacprzyk,et al.  Analysis of Similarity Measures for Atanassov's Intuitionistic Fuzzy Sets , 2009, IFSA/EUSFLAT Conf..

[4]  Zeshui Xu,et al.  Some similarity measures of intuitionistic fuzzy sets and their applications to multiple attribute decision making , 2007, Fuzzy Optim. Decis. Mak..

[5]  Zeshui Xu,et al.  Preference Relations Based on Intuitionistic Multiplicative Information , 2013, IEEE Transactions on Fuzzy Systems.

[6]  H. B. Mitchell,et al.  On the Dengfeng-Chuntian similarity measure and its application to pattern recognition , 2003, Pattern Recognit. Lett..

[7]  Miin-Shen Yang,et al.  Similarity measures of intuitionistic fuzzy sets based on Hausdorff distance , 2004, Pattern Recognit. Lett..

[8]  Krassimir T. Atanassov,et al.  Intuitionistic fuzzy sets , 1986 .

[9]  Weixin Xie,et al.  Distance measure and induced fuzzy entropy , 1999, Fuzzy Sets Syst..

[10]  Vladimír Janis,et al.  An axiomatic definition of divergence for intuitionistic fuzzy sets , 2011, EUSFLAT Conf..

[12]  David L. Olson,et al.  Similarity measures between intuitionistic fuzzy (vague) sets: A comparative analysis , 2007, Pattern Recognit. Lett..

[13]  Bernadette Bouchon-Meunier,et al.  Towards general measures of comparison of objects , 1996, Fuzzy Sets Syst..

[14]  Przemyslaw Grzegorzewski,et al.  Distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric , 2004, Fuzzy Sets Syst..

[15]  P. K. Bhatia,et al.  A New Measure of Fuzzy Directed Divergence and Its Application in Image Segmentation , 2013 .

[16]  Krassimir T. Atanassov,et al.  Intuitionistic Fuzzy Sets - Theory and Applications , 1999, Studies in Fuzziness and Soft Computing.

[17]  Dimitrios K. Iakovidis,et al.  Intuitionistic Fuzzy Cognitive Maps , 2013, IEEE Transactions on Fuzzy Systems.

[18]  Etienne Kerre,et al.  A generalization of operators on intuitionistic fuzzy sets using triangular norms and conorms , 2002 .

[19]  Zhen Zhou,et al.  Similarity Measures on Intuitionistic Fuzzy Sets , 2007, FSKD.

[20]  A. K. Ray,et al.  Segmentation using fuzzy divergence , 2003, Pattern Recognit. Lett..

[21]  H.-Y. Zhang,et al.  Multicriteria Decision-Making Approach Based on Atanassov's Intuitionistic Fuzzy Sets With Incomplete Certain Information on Weights , 2013, IEEE Transactions on Fuzzy Systems.

[22]  Zhang Wen.  Measures of similarity between vague sets , 2004 .

[23]  Li Dengfeng,et al.  New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions , 2002, Pattern Recognit. Lett..

[24]  Dengfeng Li,et al.  New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions , 2002, Pattern Recognit. Lett..

[25]  Nikhil R. Pal,et al.  Fuzzy divergence, probability measure of fuzzy events and image thresholding , 1992, Pattern Recognit. Lett..

[26]  Sankar K. Pal,et al.  Entropy: a new definition and its applications , 1991, IEEE Trans. Syst. Man Cybern..

[27]  Shyi-Ming Chen,et al.  Similarity measures between vague sets and between elements , 1997, IEEE Trans. Syst. Man Cybern. Part B.

[28]  Dug Hun Hong,et al.  A Note on Similarity Measures between Vague Sets and between Elements , 1999, Inf. Sci..

[29]  A. K. Ray,et al.  A new measure using intuitionistic fuzzy set theory and its application to edge detection , 2008, Appl. Soft Comput..