A Novel Similarity Measure for Interval-Valued Intuitionistic Fuzzy Sets and Its Applications

In this paper, a novel similarity measure for interval-valued intuitionistic fuzzy sets is introduced, which is based on the transformed interval-valued intuitionistic triangle fuzzy numbers. Its superiority is shown by comparing the proposed similarity measure with some existing similarity measures by some numerical examples. Furthermore, the proposed similarity measure is applied to deal with pattern recognition and medical diagnosis problems.

[1]  Xiaohong Zhang,et al.  New Operations of Totally Dependent-Neutrosophic Sets and Totally Dependent-Neutrosophic Soft Sets , 2018, Symmetry.

[2]  F. Smarandache.  A Unifying Field in Logics: Neutrosophic Logic. , 1999 .

[3]  B. Sridevi,et al.  • SIMILARITY MEASURE BETWEEN INTERVAL-VALUED INTUITIONISTIC FUZZY SETS AND THEIR APPLICATIONS TO MEDICAL DIAGNOSIS AND PATTERN RECOGNITION , 2018 .

[4]  Fanyong Meng,et al.  Entropy and similarity measure for Atannasov’s interval-valued intuitionistic fuzzy sets and their application , 2016, Fuzzy Optim. Decis. Mak..

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

[6]  Pei Wang,et al.  Entropy, similarity measure of interval-valued intuitionistic fuzzy sets and their applications , 2011, Inf. Sci..

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

[8]  Ting-Yu Chen,et al.  A note on distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric , 2007, Fuzzy Sets Syst..

[9]  Humberto Bustince,et al.  Vague sets are intuitionistic fuzzy sets , 1996, Fuzzy Sets Syst..

[10]  Huimin Zhang,et al.  New distance measures between intuitionistic fuzzy sets and interval-valued fuzzy sets , 2013, Inf. Sci..

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

[12]  José Carlos Rodriguez Alcantud,et al.  A multimodal adaptive approach on soft set based diagnostic risk prediction system , 2018, J. Intell. Fuzzy Syst..

[13]  Yıldıray Çelik,et al.  Fuzzy soft set theory applied to medical diagnosis using fuzzy arithmetic operations , 2013 .

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

[15]  Z. S. Xu,et al.  An Overview of Distance and Similarity Measures of Intuitionistic Fuzzy Sets , 2008, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

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

[17]  Minxia Luo,et al.  A distance measure between intuitionistic fuzzy sets and its application in medical diagnosis , 2018, Artif. Intell. Medicine.

[18]  Pushpinder Singh,et al.  A New Method on Measure of Similarity between Interval-Valued Intuitionistic Fuzzy Sets for Pattern Recognition , 2012 .

[19]  Z. Xu.  On Similarity Measures of interval-valued Intuitionistic Fuzzy Sets and Their Application to Pattern Recognitions , 2007 .

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

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

[22]  Weiqiong Wang,et al.  Distance measure between intuitionistic fuzzy sets , 2005, Pattern Recognit. Lett..

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

[24]  Xiaohong Zhang,et al.  Neutrosophic Duplet Semi-Group and Cancellable Neutrosophic Triplet Groups , 2017, Symmetry.

[25]  Krassimir T. Atanassov,et al.  Interval-Valued Intuitionistic Fuzzy Sets , 2019, Studies in Fuzziness and Soft Computing.

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

[27]  Jun Ye,et al.  Cosine similarity measures for intuitionistic fuzzy sets and their applications , 2011, Math. Comput. Model..

[28]  Diyar Akay,et al.  A biparametric similarity measure on intuitionistic fuzzy sets with applications to pattern recognition , 2014, Inf. Sci..

[29]  Xiaodong Liu,et al.  Entropy and Subsethood for General Interval-Valued Intuitionistic Fuzzy Sets , 2005, FSKD.

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

[31]  W.-L. Gau,et al.  Vague sets , 1993, IEEE Trans. Syst. Man Cybern..

[32]  Ranjit Biswas,et al.  An application of intuitionistic fuzzy sets in medical diagnosis , 2001, Fuzzy Sets Syst..