Novel distance measure between intuitionistic fuzzy sets and its application in pattern recognition

Document Type : Research Paper

Authors

1 School of Artificial Intelligence, Beijing Normal University, Beijing 100875, PR China

2 Business School, Sichuan University, Chengdu 610064, PR China

Abstract

In this article, we propose a new distance measure between intuitionistic fuzzy sets(IFSs), which takes into account the membership degree, non-membership degree, and their difference between membership and non-membership degree of intuitionistic fuzzy sets, as well as the exponential distance measure to avoid information loss. Meanwhile we prove that it satisfies the axiomatic definition of distance measure, and do comparison analysis with some widely used distance measures. Finally, we apply our distance measure in pattern recognition, these results show that our distance measure can significantly overcome the drawback of information loss and have more widely application scope.

Keywords

References

[1] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1) (1986), 87-96.
[2] K. Atanassov, More on intuitionstic fuzzy sets, Fuzzy Sets and Systems, 33(1) (1989), 37-46.
[3] K. Atanassov, G. Pasi, P. Yager, Intuitionistic fuzzy interpretations of multi-criteria multi-person and multimeasurement tool decision making, International Journal of Systems Science, 36 (2005), 859-868.
[4] T. Chaira, A novel intuitionistic fuzzy C-means clustering algorithm and its application to medical images, Applied Soft Computing, 11 (2011), 1711-1717.
[5] T. Chaira, A. K. Ray, A new measure using intuitionistic fuzzy set theory and its application to edge detection, Applied Soft Computing, 8 (2008), 919-927.
[6] T. Y. Chen, A comparative analysis of score functions for multiple criteria decision making in intuitionistic fuzzy settings, Information Sciences, 181 (2011), 3652-3676.
[7] C. Chen, X. Deng, Several new results based on the study of distance measure of intuitionistic fuzzy sets, Iranian Journal of Fuzzy Systems, 17 (2020), 147-163.
[8] T. Y. Chen, C. H. Li, Determining objective weights with intuitionistic fuzzy entropy measures: A comparative analysis, Information Sciences, 180 (2010), 4207-4222.
[9] T. Y. Chen, C. H. Li, Objective weights with intuitionistic fuzzy entropy measures and computational experiment analysis, Applied Soft Computing, 11 (2011), 5411-5423.
[10] X. J. Gou, Z. S. Xu, Exponential operations for intuitionistic fuzzy numbers and interval numbers in multi-attribute decision making, Fuzzy Optimization and Decision Making, 16 (2017), 183-204.
[11] X. J. Gou, Z. S. Xu, H. C. Liao, Expotential operations over interval-valued intuitionistic fuzzy numbers, International Journal of Machine Learning and Cybernetics, 7 (2016), 501-518.
[12] C. Huang, M. W. Lin, Z. S. Xu, Pythagorean fuzzy MULTIMOORA method based on distance measure and score function: Its application in multicriteria decision making process, Knowledge and Information Systems, 62 (2020), 4373-4406.
[13] W. L. Hung, M. S. Yang, Similarity measures of intuitionistic fuzzy sets based on Lp metric, International Journal of Approximate Reasoning, 46 (2007), 120-136.
[14] W. L. Hung, M. S. Yang, On the J-divergence of intuitionistic fuzzy sets with its application to pattern recognition, Information Sciences, 178 (2008), 1641-1650.
[15] J. Q. Li, G. N. Deng, H. X. Li, W. Y. Zeng, The relationship between similarity measure and entropy of intuitionistic fuzzy sets, Information Sciences, 188 (2012), 314-321.
[16] M. W. Lin, C. Huang, R. Q. Chen, H. Fujita, X. Wang, Directional correlation coefficient measures for Pythagorean fuzzy sets: Their applications to medical diagnosis and cluster analysis, Complex and Intelligent Systems, 7 (2021), 1025-1043.
[17] H. W. Liu, G. J. Wang, Multi-criteria decision-making methods based on intuitionistic fuzzy sets, European Journal of Operational Research, 179 (2007), 220-233.
[18] G. A. Papakostas, A. G. Hatzimichailidis, V. G. Kaburlasos, Distance and similarity measures between intuitionistic fuzzy sets: A comparative analysis from a pattern recognition point of view, Pattern Recognition Letters, 34 (2013), 1609-1622.
[19] M. P. Pedro, C. Pedro, H. Bustince, E. Barrenechea, M. Pagola, J. Fernandez, Image segmentation using Atanassov intuitionistic fuzzy sets, Expert Systems with Applications, 40 (2013), 15-26.
[20] K. Rezaei, New distance and similarity measures for hesitant fuzzy soft sets, Iranian Journal of Fuzzy Systems, 16 (2019), 159-176.
[21] E. Szmidt, J. Kacprzyk, Distances between intuitionistic fuzzy sets, Fuzzy Sets and Systems, 114 (2000), 505-518.
[22] I. K. Vlachos, G. D. Sergiadis, Intuitionistic fuzzy information: Applications to pattern recognition, Pattern Recognition Letters, 28 (2007), 197-206.
[23] W. Q. Wang, X. L. Xin, Distance measure between intuitionstic fuzzy sets, Pattern Recognition Letters, 26 (2005), 2063-2069.
[24] J. Q. Wang, Z. H. Zhang, Multi-criteria decision-making method with incomplete certain information based on intuitionistic fuzzy number, Control and Decision, 24 (2009), 226-230.
[25] G. W. Wei, Gray relational analysis method for intuitionistic fuzzy multiple attribute decision making, Expert Systems with Applications, 38 (2011), 11671-11677.
[26] M. M. Xia, Z. S. Xu, Entropy/cross entropy-based group decision making under intuitionistic fuzzy environment, Information Fusion, 13 (2012), 31-47.
[27] Z. S. Xu, Intuitionistic preference relations and their application in group decision making, Information Sciences, 177 (2007), 2363-2379.
[28] Z. S. Xu, J. Chen, An overview of distance and similarity measures of intuitionistic fuzzy sets, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 16 (2008), 529-555.
[29] Z. S. Xu, J. Chen, J. J. Wu, Clustering algorithm for intuitionistic fuzzy sets, Information Sciences, 178 (2008), 3775-3790.
[30] L. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-356.
[31] H. M. Zhang, L. Y. Yu, New distance measures between intuitionistic fuzzy sets and interval-valued fuzzy sets, Information Sciences, 245 (2013), 181-196.
Iranian Journal of Fuzzy Systems
Volume 19, Issue 3
May and June 2022
Pages 127-137

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