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AN OVERVIEW OF DISTANCE AND SIMILARITY MEASURES OF INTUITIONISTIC FUZZY SETS

School of Economics and Management, Southeast University, Nanjing, Jiangsu 210096, China

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Department of Management Science and Engineering, School of Economics and Management, Tsinghua University, Beijing 100084, China

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https://doi.org/10.1142/S0218488508005406Cited by:309 (Source: Crossref)

Abstract

The Intuitionistic Fuzzy Sets (IFSs), originated by Atanassov [1], is a useful tool to deal with vagueness and ambiguity. In the short time since their first appearance, many different distance and similarity measures of IFSs have been proposed, but they are scattered through the literature. In this paper, we give a comprehensive overview of distance and similarity measures of IFSs. Based on the weighted Hamming distance, the weighted Euclidean distance, and the weighted Hausdorff distance, respectively, we define some continuous distance and similarity measures for IFSs. We also utilize geometric distance model to define some continuous distance and similarity measures for IFSs, which are the various combinations and generalizations of the weighted Hamming distance, the weighted Euclidean distance and the weighted Hausdorff distance. Then we extend these distance and similarity measures for Interval-Valued Intuitionistic Fuzzy Sets (IVIFSs).

Keywords:

References

K. Atanassov, Fuzzy Sets and Systems 20, 87 (1986), DOI: 10.1016/S0165-0114(86)80034-3. Crossref, Web of Science, Google Scholar
L. A. Zadeh, Information and Control 8, 338 (1965), DOI: 10.1016/S0019-9958(65)90241-X. Crossref, Google Scholar
G. Deschrijver and E. E. Kerre, Fuzzy Sets and Systems 133, 227 (2003), DOI: 10.1016/S0165-0114(02)00127-6. Crossref, Web of Science, Google Scholar
K. Atanassov and G. Gargov, Fuzzy Sets and Systems 31, 343 (1989), DOI: 10.1016/0165-0114(89)90205-4. Crossref, Web of Science, Google Scholar
J. Goguen, Journal of Mathematical Analysis and Applications 18, 145 (1967), DOI: 10.1016/0022-247X(67)90189-8. Crossref, Web of Science, Google Scholar
L. A. Zadeh, IEEE Transactions on Systems, Man, and Cybernetics 3, 28 (1973). Google Scholar
D. Dubois, W. Ostasiewicz and H. Prade, Fundamentals of Fuzzy Sets, The Handbooks of Fuzzy Sets Series, eds. D. Dubois and H. Prade (Kluwer, Dordrecht, 2000) pp. 21–124. Crossref, Google Scholar
D. Duboiset al., Fuzzy Sets and Systems 156, 485 (2005), DOI: 10.1016/j.fss.2005.06.001. Crossref, Web of Science, Google Scholar
C. Cornelis, K. Atanassov and E. Kerre, Intuitionistic fuzzy sets and interval-valued fuzzy sets: a critical comparison, Proceedings of Third European Conference on Fuzzy Logic and Technologies (Eusflat'03) pp. 159–163. Google Scholar
K. Atanassov, Answer to D. Dubois, S. Gottwald, P. Hajek, J. Kacprzyk and H. Prade's paper Terminological difficulties in fuzzy set theory — the case of "intuitionistic fuzzy sets", Fuzzy Sets and Systems 156 (2005) 496-499 . Google Scholar
G. Takeuti and S. Titani, Journal of Symbolic Logic 49, 851 (1984). Crossref, Web of Science, Google Scholar
D. Van Dalen (ed.) , Brouwer's Cambridge Lectures on Intuitionism ( Cambridge University Press , Cambridge , 1981 ) . Google Scholar
H. B. Mitchell, Pattern Recognition Letters 24, 3101 (2003), DOI: 10.1016/S0167-8655(03)00169-7. Crossref, Web of Science, Google Scholar
T. Gerstenkorn and J. Mafiko, Fuzzy Sets and Systems 44, 39 (1991), DOI: 10.1016/0165-0114(91)90031-K. Crossref, Web of Science, Google Scholar
H. Bustince and P. Burillo, Fuzzy Sets and Systems 74, 237 (1995), DOI: 10.1016/0165-0114(94)00343-6. Crossref, Web of Science, Google Scholar
D. H. Hong and S. Y. Hwang, Fuzzy Sets and Systems 75, 77 (1995), DOI: 10.1016/0165-0114(94)00330-A. Crossref, Web of Science, Google Scholar
D. H. Hong, Fuzzy Sets and Systems 95, 113 (1998), DOI: 10.1016/S0165-0114(96)00311-9. Crossref, Web of Science, Google Scholar
W. L. Hung and J. W. Wu, Information Sciences 144, 219 (2002), DOI: 10.1016/S0020-0255(02)00181-0. Crossref, Web of Science, Google Scholar
Z. S. Xu, Lecture Notes in Computer Science 4224, 16 (2006), DOI: 10.1007/11875581_2. Crossref, Google Scholar
D. F. Li and C. T. Cheng, Pattern Recognition Letters 23, 221 (2002). Web of Science, Google Scholar
P. Burillo and H. Bustince, Fuzzy Sets and Systems 78, 305 (1996), DOI: 10.1016/0165-0114(96)84611-2. Crossref, Web of Science, Google Scholar
E. Szmidt and J. Kacprzyk, Fuzzy Sets and Systems 114, 505 (2000), DOI: 10.1016/S0165-0114(98)00244-9. Crossref, Web of Science, Google Scholar
E. Szmidt and J. Kacprzyk, Lecture Notes in Artificial Intelligence 3070, 388 (2004). Google Scholar
E. Szmidt and J. Kacprzyk, Fuzzy Sets and Systems 118, 467 (2001), DOI: 10.1016/S0165-0114(98)00402-3. Crossref, Web of Science, Google Scholar
C. L. Hwang and K. Yoon , Multiple Attribute Decision Making: Methods and Applications ( Springer , Berlin , 1981 ) . Crossref, Google Scholar
Y. Narukawa and V. Torra, Lecture Notes in Artificial Intelligence 3885, 150 (2006). Google Scholar
G. Choquet, Theory of capacities, Ann. Inst. Fourier 5 (1953) 131-295 . Google Scholar
Z. S. Xu, Fuzzy Optimization and Decision Making 6, 109 (2007), DOI: 10.1007/s10700-007-9004-z. Crossref, Web of Science, Google Scholar
Z. Z. Liang and P. F. Shi, Pattern Recognition Letters 24, 2687 (2003), DOI: 10.1016/S0167-8655(03)00111-9. Crossref, Web of Science, Google Scholar
S. B. Nadler Jr , Hyperspaces of Sets ( Marcel Deckker , New York , 1978 ) . Google Scholar
W. L. Hung and M. S. Yang, Pattern Recognition Letters 25, 1603 (2004), DOI: 10.1016/j.patrec.2004.06.006. Crossref, Web of Science, Google Scholar
P. Grzegorzewski, Fuzzy Sets and Systems 148, 319 (2004), DOI: 10.1016/j.fss.2003.08.005. Crossref, Web of Science, Google Scholar
W. Q. Wang and X. L. Xin, Pattern Recognition Letters 26, 2063 (2005), DOI: 10.1016/j.patrec.2005.03.018. Crossref, Web of Science, Google Scholar
D. Dubois and H. Prade , Fuzzy Sets and Systems ( Academic Press , New York , 1980 ) . Google Scholar
R. R. Yager, IEEE Transactions on Systems Man, and Cybernetices-Part B 18, 183 (1988), DOI: 10.1109/21.87068. Crossref, Web of Science, Google Scholar
V. Torra, International Journal of Intelligent Systems 12, 153 (1997). Crossref, Web of Science, Google Scholar
V. Torra and Y. Narukawa , Modeling Decisions: Information Fusion and Aggregation Operators ( Springer , Berlin , 2007 ) . Crossref, Google Scholar
Z. S. Xu and Q. L. Da, International Journal of Intelligent Systems 17, 569 (2002), DOI: 10.1002/int.10038. Crossref, Web of Science, Google Scholar
Z. S. Xu and Q. L. Da, International Journal of Intelligent Systems 18, 953 (2003), DOI: 10.1002/int.10127. Crossref, Web of Science, Google Scholar
M. Sugeno, Theory of Fuzzy Integrals and its Applications (Ph.D. Dissertation, Tokyo Institute of Technology, Tokyo, Japan, 1974) . Google Scholar