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...

ISSN: 2231-2498 Quarterly English Since 2011
Current Issue

Vol. 21 No. 1 (2024)

Articles 41th Edition of DTR Apr 2024 – Mar 2024

Hybrid Information Theoretic Measures and Their Applications inData Mining

Authors

Assistant Professor cum Statistician, NC Medical College, Israna, Panipat, India

20 Views
11 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
  2. Mathematics, Article ID 870504.
  3. ii. Alkhazaleh, S., Salleh, A. R., & Hassan, N. (2011). Fuzzy parameterized interval-valued fuzzy soft
  4. set. Applied Mathematical Sciences, 5(67), 3335–3346.
  5. iii. Bhandari, D., & Pal, N. R. (1993). Some new information measures for fuzzy sets. Information
  6. Sciences, 67, 209–228.
  7. iv. Cheng, C., Xiao, F., & Cao, Z. (2019). A new distance for intuitionistic fuzzy sets based on similarity
  8. matrix. IEEE Access, 7, 70436–70446.
  9. v. De Luca, A., & Termini, S. (1972). A definition of a non-probabilistic entropy in the setting of fuzzy
  10. sets. Information and Control, 20, 301–312.
  11. vi. Du, W. S., & Hu, B. Q. (2015). Aggregation distance measure and its induced similarity measure
  12. between intuitionistic fuzzy sets. Pattern Recognition Letters, 60, 65–71.
  13. vii. Feng, Q., & Guo, X. (2017). Uncertainty measures of interval-valued intuitionistic fuzzy soft sets
  14. and their applications in decision making. Intelligent Data Analysis, 21(1), 77–95.
  15. viii. Hartley, R. V. L. (1928). Transmission of information. Bell System Technical Journal, 7, 535–563.
  16. ix. Havrda, J. H., & Charvát, F. (1967). Quantification method of classification processes: Concept of
  17. structural α-entropy. Kybernetika, 3, 30–35.
  18. x. Hung, W. L., & Yang, M. S. (2006). Fuzzy entropy on intuitionistic fuzzy sets. International Journal
  19. of Intelligent Systems, 21(4), 443–451.
  20. xi. Jiang, Y. C., Tang, Y., Liu, H., & Chen, Z. Z. (2013). Entropy on intuitionistic fuzzy soft sets and on
  21. interval-valued fuzzy soft sets. Information Sciences, 240, 95–114.
  22. xii. Kaufmann, A. (1975). Introduction to the theory of fuzzy subsets: Fundamental theoretical elements.
  23. Academic Press.
  24. xiii. Kullback, S. (1959). Information theory and statistics. John Wiley & Sons.
  25. xiv.Li, Y., Qin, K., & He, X. (2014). Some new approaches to constructing similarity measures. Fuzzy
  26. Sets and Systems, 234, 46–60.
  27. xv. Luo, M., & Zhao, R. (2018). A distance measure between intuitionistic fuzzy sets and its application
  28. in medical diagnosis. Artificial Intelligence in Medicine, 89, 34–39.
  29. xvi. Luo, X., Li, W., & Zhao, W. (2018). Intuitive distance for intuitionistic fuzzy sets with applications
  30. in pattern recognition. Applied Intelligence, 48, 2792–2808.
  31. xvii. Mahanta, J., & Panda, S. (2020). A novel distance measure for intuitionistic fuzzy sets with
  32. diverse applications. International Journal of Intelligent Systems. https://doi.org/10.1002/int.22312
  33. xviii. Maji, P. K., Biswas, R., & Roy, A. R. (2001). Fuzzy soft sets. Journal of Fuzzy Mathematics,
  34. 9(3), 589–602.
  35. xix. Molodtsov, D. (1999). Soft set theory—First results. Computers & Mathematics with Applications, 37(4–5), 19–31.
  36. xx. Mukherjee, A., & Sarkar, S. (2014). Similarity measures for interval-valued intuitionistic fuzzy
  37. soft sets and its application in medical diagnosis problem. New Trends in Mathematical Sciences,
  38. 2(3), 159–165.
  39. xxi. Mukherjee, A., & Sarkar, S. (2015). Distance-based similarity measures for interval-valued
  40. intuitionistic fuzzy soft sets and its application. New Trends in Mathematical Sciences, 3(4), 34–42.
  41. xxii. Pal, N. R., & Pal, S. K. (1989). Object background segmentation using new definitions of
  42. entropy. IEEE Proceedings, 366, 284–295.
  43. xxiii. Papakostas, G. A., Hatzimichailidis, A. G., & Kaburlasos, V. G. (2013). Distance and similarity
  44. measures between intuitionistic fuzzy sets: A comparative analysis from a pattern recognition point
  45. of view. Pattern Recognition Letters, 34(14), 1609–1622.
  46. xxiv. Pawlak, Z. (1982). Rough sets. International Journal of Information and Computer Sciences, 11,
  47. 341–356.
  48. xxv. Rajarajeswari, P., & Uma, N. (2013). Intuitionistic fuzzy multi similarity measure based on
  49. cotangent function. International Journal of Engineering Research & Technology, 2(11), 1323–1329.
  50. xxvi. Rényi, A. (1961). On measures of entropy and information. In Proceedings of the Fourth
  51. Berkeley Symposium on Mathematical Statistics and Probability (Vol. 1, pp. 547–562). University of
  52. California Press.
  53. xxvii. Shannon, C. E. (1948). A mathematical theory of communication. Bell System Technical Journal,
  54. 27, 379–423.
  55. xxviii. Sharma, B. D., & Taneja, I. J. (1977). Three generalized additive measures of entropy. Ekonomicko-Matematicky Obzor, 13, 419–433.
  56. 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.
  57. xxx. Szmidt, E., & Kacprzyk, J. (2000). Distances between intuitionistic fuzzy sets. Fuzzy Sets and
  58. Systems, 114(3), 505–518.
  59. xxxi. Szmidt, E., & Kacprzyk, J. (2001). Entropy for intuitionistic fuzzy sets. Fuzzy Sets and Systems,
  60. 118(3), 467–477.xxxii. Szmidt, E., & Kacprzyk, J. (2004). A similarity measure for intuitionistic fuzzy sets and its
  61. application in supporting medical diagnostic reasoning. In Lecture Notes in Computer Science (Vol.
  62. 3070). Springer.
  63. xxxiii. Tian, M. Y. (2013). A new fuzzy similarity based on cotangent function for medical diagnosis.
  64. Advanced Modeling and Optimization, 15(2), 151–156.
  65. xxxiv. Tsallis, C. (1988). Possible generalization of Boltzmann–Gibbs statistics. Journal of Statistical
  66. Physics, 52, 479–487.
  67. xxxv. Wang, W., & Xin, X. (2005). Distance measure between intuitionistic fuzzy sets. Pattern Recognition Letters, 26, 2063–2069.
  68. xxxvi. Weaver, W. (1949). The mathematics of communication. Scientific American, 181, 11–15.
  69. xxxvii. Xu, Z. (2007). Some similarity measures of intuitionistic fuzzy sets and their applications to
  70. multiple attribute decision making. Fuzzy Optimization and Decision Making, 6(2), 109–121.
  71. xxxviii. Yager, R. R. (1979). On the measure of fuzziness and negation. Part I: Membership in the unit
  72. interval. International Journal of General Systems, 5(4), 221–229.
  73. xxxix. Yang, X. B., Lin, T. Y., Yang, J. Y., Li, Y., & Yu, D. (2009). Combination of interval-valued fuzzy
  74. set and soft set. Computers & Mathematics with Applications, 58(3), 521–527.
  75. xl. Ye, J. (2011). Cosine similarity measures for intuitionistic fuzzy sets and their applications.
  76. Mathematical and Computer Modelling, 53, 91–97.
  77. xli. Yiarayong, P. (2020). On interval-valued fuzzy soft set theory applied to semigroups. Soft
  78. Computing, 24(8), 3113–3168.
  79. xlii. Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338–353.
  80. xliii. Zadeh, L. A. (1968). Probability measures of fuzzy events. Journal of Mathematical Analysis and
  81. Applications, 23, 421–427.
✓ Citation copied to clipboard