Application of Intuitionistic Fuzzy Cross Entropy Measure in Decision Making for Medical Diagnosis

Authors: Shikha Maheshwari, Amit Srivastava

Abstract:

In medical investigations, uncertainty is a major challenging problem in making decision for doctors/experts to identify the diseases with a common set of symptoms and also has been extensively increasing in medical diagnosis problems. The theory of cross entropy for intuitionistic fuzzy sets (IFS) is an effective approach in coping uncertainty in decision making for medical diagnosis problem. The main focus of this paper is to propose a new intuitionistic fuzzy cross entropy measure (IFCEM), which aid in reducing the uncertainty and doctors/experts will take their decision easily in context of patient’s disease. It is shown that the proposed measure has some elegant properties, which demonstrates its potency. Further, it is also exemplified in detail the efficiency and utility of the proposed measure by using a real life case study of diagnosis the disease in medical science.

Keywords: Intuitionistic fuzzy cross entropy (IFCEM), intuitionistic fuzzy set (IFS), medical diagnosis, uncertainty.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1100573

References:

[1] K. T. Atanassov, “Intuitionistic fuzzy sets,” Fuzzy Sets and Systems, 20: 87–96, 1986.
[2] L. A. Zadeh, “Fuzzy sets,” Information and Control, 8(3): 338–353, 1965.
[3] S. K. De, R. Biswas, and A. R. Roy, An application of intuitionistic fuzzy sets in medical diagnosis, Fuzzy Sets and Systems, 117(2): 209- 213, 2001.
[4] K. C. Hung, “Medical Pattern Recognition: Applying an Improved Intuitionistics Fuzzy Cross-Entropy Approach,” Advances in fuzzy Systems, Article ID 863549, 2012.
[5] E. Szmidt and J. Kacprzyk, “Intuitionistic fuzzy sets in intelligent data analysis for medical diagnosis,” Proceedings of the Computational Science ICCS. Springer, Berlin, Germany, 2074, 263–271, 2001.
[6] E. Szmidt and J. Kacprzyk, “A Similarity Measure for Intuitionistic Fuzzy Sets and its Application in Supporting Medical Diagnostic Reasoning,” Artificial Intelligence and Soft Computing – ICAISC, 3070, 388-393, 2004.
[7] E. Szmidt and J. Kacprzyk, “A Similarity Measure for Intuitionistic Fuzzy Sets and its Application in Supporting Medical Diagnostic Reasoning,” Artificial Intelligence and Soft Computing – ICAISC, 3070, 388-393, 2004.
[8] C. M. Own, “Switching between type-2 fuzzy sets and intuitionistic fuzzy sets: an application in medical diagnosis,” Applied Intelligence, 31(3): 283-291, 2009.
[9] F. E. Boran and D. Akay, “A biparametric similarity measure on intuitionistic fuzzy sets with applications to pattern recognition,” Information Sciences, 255(10), 45-57, 2014.
[10] A. Srivastava, A. K. Singh and S. Maheshwari, "Dichotomous exponential entropy functional and its applications in medical diagnosis," International Conference on Signal Processing and Communication (ICSC), 21-26, 2013.
[11] K. Vlachos and G. D. Sergiadis, “Intuitionistic fuzzy information— applications to pattern recognition,” Pattern Recognition Letters, 28(2): 197–206, 2007.
[12] W. L. Hung and M.S. Yang, “On the J- Divergence of intuitionistic fuzzy sets with its applications to pattern recognition,” Information sciences, 178(6): 1641-1650, 2008.
[13] M. Junjun, Y. Dengbao, W. Cuicui, “A novel cross-entropy and entropy measures of IFSs and their applications,” Knowledge-Based Systems, 48: 37-45, 2013.
[14] P. Wei and J. Ye, “Improved intuitionistic fuzzy cross-entropy and its application to pattern recognition,” International Conference on Intelligent Systems and Knowledge Engineering, 114–116, 2010.
[15] M. Xia and Z. Xu, “Entropy/cross entropy-based group decision making under intuitionistic fuzzy environment”, Information Fusion, 13(1): 31- 47, 2012.
[16] Q. S. Zhang, S. Y. Jiang, “A note on information entropy measures for vague sets and its applications,” Information Sciences, 178(21): 4184- 4191, 2008.
[17] I. Montes, N. R. Pal, V. Janis and S. Montes, “Divergence Measures for Intuitionistic fuzzy sets,” IEEE Transactions on Fuzzy Systems, 2014. (in press).