JournalsKart submission@journalskart.com 8882640642, 011-43101010
Register Login
Peer-Reviewed Open Access Journal

DIAS Technology Review

The Institute has a unique distinction of publishing a bi-annual International journal DIAS Technology Review – The International Journal for Business and IT. The Editorial Board comprises of...

P-ISSN: 0972-9658 English Since 2004
Submit Manuscript Browse Archives
Current Issue

Vol. 21 No. 1 (2024)

Articles 41th Edition of DTR Apr 2024 – Sept 2024
DOI 10.65301/dias.2024.21.1.5

Hybrid Information Theoretic Measures and Their Applications in Data Mining

Authors
DR
Dr. Sonia

Assistant Professor cum Statistician, NC Medical College, Israna, Panipat, India
49 Views
59 Downloads
Published 2024-09-30
Pages 96-110
Abstract

Information theory, introduced by Shannon (1948), revolutionized the understanding of communication and uncertainty by providing a mathematical measure of information through entropy. Shannon entropy quantifies the average uncertainty associated with a random variable and has been widely applied in communication systems, statistics, pattern recognition, machine learning, and signal processing. Despite its success, Shannon’s framework relies on precise probability distributions, which are often unavailable or unreliable in practical situations.

References
  1. i. Alkhazaleh, S., & Salleh, A. R. (2012). Generalised interval-valued fuzzy soft set. Journal of Applied Mathematics, Article ID 870504.
  2. ii. Alkhazaleh, S., Salleh, A. R., & Hassan, N. (2011). Fuzzy parameterized interval-valued fuzzy soft set. Applied Mathematical Sciences, 5(67), 3335–3346.
  3. iii. Bhandari, D., & Pal, N. R. (1993). Some new information measures for fuzzy sets. Information Sciences, 67, 209–228.
  4. iv. Cheng, C., Xiao, F., & Cao, Z. (2019). A new distance for intuitionistic fuzzy sets based on similarity matrix. IEEE Access, 7, 70436–70446.
  5. v. De Luca, A., & Termini, S. (1972). A definition of a non-probabilistic entropy in the setting of fuzzy sets. Information and Control, 20, 301–312.
  6. vi. Du, W. S., & Hu, B. Q. (2015). Aggregation distance measure and its induced similarity measure between intuitionistic fuzzy sets. Pattern Recognition Letters, 60, 65–71.
  7. vii. Feng, Q., & Guo, X. (2017). Uncertainty measures of interval-valued intuitionistic fuzzy soft sets and their applications in decision making. Intelligent Data Analysis, 21(1), 77–95.
  8. viii. Hartley, R. V. L. (1928). Transmission of information. Bell System Technical Journal, 7, 535–563.
  9. ix. Havrda, J. H., & Charvát, F. (1967). Quantification method of classification processes: Concept of structural α-entropy. Kybernetika, 3, 30–35.
  10. x. Hung, W. L., & Yang, M. S. (2006). Fuzzy entropy on intuitionistic fuzzy sets. International Journal of Intelligent Systems, 21(4), 443–451.
  11. xi. Jiang, Y. C., Tang, Y., Liu, H., & Chen, Z. Z. (2013). Entropy on intuitionistic fuzzy soft sets and on interval-valued fuzzy soft sets. Information Sciences, 240, 95–114.
  12. xii. Kaufmann, A. (1975). Introduction to the theory of fuzzy subsets: Fundamental theoretical elements. Academic Press.
  13. xiii. Kullback, S. (1959). Information theory and statistics. John Wiley & Sons.
  14. xiv.Li, Y., Qin, K., & He, X. (2014). Some new approaches to constructing similarity measures. Fuzzy Sets and Systems, 234, 46–60.
  15. xv. Luo, M., & Zhao, R. (2018). A distance measure between intuitionistic fuzzy sets and its application in medical diagnosis. Artificial Intelligence in Medicine, 89, 34–39.
  16. xvi. Luo, X., Li, W., & Zhao, W. (2018). Intuitive distance for intuitionistic fuzzy sets with applications in pattern recognition. Applied Intelligence, 48, 2792–2808.
  17. xvii. Mahanta, J., & Panda, S. (2020). A novel distance measure for intuitionistic fuzzy sets with diverse applications. International Journal of Intelligent Systems. https://doi.org/10.1002/int.22312
  18. xviii. Maji, P. K., Biswas, R., & Roy, A. R. (2001). Fuzzy soft sets. Journal of Fuzzy Mathematics, 9(3), 589–602.
  19. xix. Molodtsov, D. (1999). Soft set theory—First results. Computers & Mathematics with Applications, 37(4–5), 19–31.
  20. xx. Mukherjee, A., & Sarkar, S. (2014). Similarity measures for interval-valued intuitionistic fuzzy soft sets and its application in medical diagnosis problem. New Trends in Mathematical Sciences, 2(3), 159–165.
  21. xxi. Mukherjee, A., & Sarkar, S. (2015). Distance-based similarity measures for interval-valued intuitionistic fuzzy soft sets and its application. New Trends in Mathematical Sciences, 3(4), 34–42.
  22. xxii. Pal, N. R., & Pal, S. K. (1989). Object background segmentation using new definitions of entropy. IEEE Proceedings, 366, 284–295.
  23. xxiii. Papakostas, G. A., Hatzimichailidis, A. G., & Kaburlasos, V. G. (2013). Distance and similarity measures between intuitionistic fuzzy sets: A comparative analysis from a pattern recognition point of view. Pattern Recognition Letters, 34(14), 1609–1622.
  24. xxiv. Pawlak, Z. (1982). Rough sets. International Journal of Information and Computer Sciences, 11, 341–356.
  25. xxv. Rajarajeswari, P., & Uma, N. (2013). Intuitionistic fuzzy multi similarity measure based on cotangent function. International Journal of Engineering Research & Technology, 2(11), 1323–1329.
  26. xxvi. Rényi, A. (1961). On measures of entropy and information. In Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability (Vol. 1, pp. 547–562). University of California Press.
  27. xxvii. Shannon, C. E. (1948). A mathematical theory of communication. Bell System Technical Journal,
  28. 27, 379–423.
  29. xxviii. Sharma, B. D., & Taneja, I. J. (1977). Three generalized additive measures of entropy. Ekonomicko-Matematicky Obzor, 13, 419–433.
  30. xxix. Shi, L. L., & Ye, J. (2013). Study on fault diagnosis of turbine using an improved cosine similarity measure for vague sets. Journal of Applied Sciences, 13(10), 1781–1786.
  31. xxx. Szmidt, E., & Kacprzyk, J. (2000). Distances between intuitionistic fuzzy sets. Fuzzy Sets and Systems, 114(3), 505–518.
  32. xxxi. Szmidt, E., & Kacprzyk, J. (2001). Entropy for intuitionistic fuzzy sets. Fuzzy Sets and Systems,
  33. 118(3), 467–477.xxxii. Szmidt, E., & Kacprzyk, J. (2004). A similarity measure for intuitionistic fuzzy sets and its
  34. application in supporting medical diagnostic reasoning. In Lecture Notes in Computer Science (Vol.3070). Springer.
  35. xxxiii. Tian, M. Y. (2013). A new fuzzy similarity based on cotangent function for medical diagnosis. Advanced Modeling and Optimization, 15(2), 151–156.
  36. xxxiv. Tsallis, C. (1988). Possible generalization of Boltzmann–Gibbs statistics. Journal of Statistical Physics, 52, 479–487.
  37. xxxv. Wang, W., & Xin, X. (2005). Distance measure between intuitionistic fuzzy sets. Pattern Recognition Letters, 26, 2063–2069.
  38. xxxvi. Weaver, W. (1949). The mathematics of communication. Scientific American, 181, 11–15.
  39. xxxvii. Xu, Z. (2007). Some similarity measures of intuitionistic fuzzy sets and their applications to multiple attribute decision making. Fuzzy Optimization and Decision Making, 6(2), 109–121.
  40. xxxviii. Yager, R. R. (1979). On the measure of fuzziness and negation. Part I: Membership in the unit interval. International Journal of General Systems, 5(4), 221–229.
  41. xxxix. Yang, X. B., Lin, T. Y., Yang, J. Y., Li, Y., & Yu, D. (2009). Combination of interval-valued fuzzy set and soft set. Computers & Mathematics with Applications, 58(3), 521–527.
  42. xl. Ye, J. (2011). Cosine similarity measures for intuitionistic fuzzy sets and their applications. Mathematical and Computer Modelling, 53, 91–97.
  43. xli. Yiarayong, P. (2020). On interval-valued fuzzy soft set theory applied to semigroups. Soft Computing, 24(8), 3113–3168.
  44. xlii. Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338–353.
  45. xliii. Zadeh, L. A. (1968). Probability measures of fuzzy events. Journal of Mathematical Analysis and Applications, 23, 421–427.
Download
download PDF
How to Cite
Dr. Sonia . (2024). Hybrid Information Theoretic Measures and Their Applications in Data Mining. DIAS Technology Review, 21(1), 96-110.
About This Journal
DIA
DIAS Technology Review
Published by Journalskart
P-ISSN 0972-9658
✓ Citation copied to clipboard