Skip to main navigation menu Skip to main content Skip to site footer

Some applications of fuzzy measures with coding theory

Abstract

Abstract: A Fuzzy measures have been seen to take part in developing various methods for the creation of fuzzy mean codeword lengths. This approach is taken by the current communication, which providing the application of fuzzy entropy measurements for the creation of novel fuzzy codeword lengths. Additionally, we want to provide more light on the problems of correspondence between weighted mean and possible weighted fuzzy entropy using fuzzy measures.

JEL Codes: C890

Received: 22/07/2024.  Accepted: 02/10/2024.  Published: 03/03/2025.

Keywords

Fuzzy entropy, Fuzzy mean codeword length, Monotonic function, Weighted mean

PDF

References

  1. Belis, M. & Guiasu, S. (1968). A quantitative qualitative measure of information in cybernetic systems. IEEE Transactions on Information Theory, 14, 593-594. DOI: https://doi.org/10.1109/TIT.1968.1054185
  2. Campbell, L.L. (1965). A coding theorem and Renyi's entropy. Information and control, 8: 423-429. DOI: https://doi.org/10.1016/S0019-9958(65)90332-3
  3. Frumin, L. L., Gelash, A. A. & Turitsyn, S. K. (2017). New approaches to coding information using inverse scattering transform. Phys. Rev. Lett., 118(22), 5 pp. DOI: https://doi.org/10.1103/PhysRevLett.118.223901
  4. Germe M.M., Demamu J. and Alaba B.A. (2023). Updates on Properties of Hamming Distance of Binary Fuzzy Codes Over Fuzzy Vector Spaces and Their Application in Decoding Process. Fuzzy Information and Engineering, 15 (4), 335-346 DOI: https://doi.org/10.26599/FIE.2023.9270024
  5. Germe M.M., Demamu J. and Alaba B.A. (2023). Binary Fuzzy Codes and Some Properties of Hamming Distance of Fuzzy Codes. 15, 26-35 DOI: https://doi.org/10.26599/FIE.2023.9270003
  6. Guiasu, S. & Picard, C.F. (1971). Borne in ferictur dela longuerur utile de certains codes. Comptes Rendus Mathematique Academic des Sciences Paris, 273, 248-251.
  7. Gupta R. and Kumar S. (2022). A new generalization of Renyi’s entropy of order β with coding theory in fuzzy environment. AIP Conference Proceedings 2555(1):040003 DOI: https://doi.org/10.1063/5.0108754
  8. Gurdial & Pessoa, F. (1977). On useful information of order a. Journal of Combinatorics Information and System Sciences, 2, 158-162.
  9. Hayashi, M. (2019). Universal channel coding for general output alphabet. IEEE Trans. Inform. Theory, 65 (1), 302–321. DOI: https://doi.org/10.1109/TIT.2018.2877456
  10. Joshi, R. & Kumar, S. (2018). A new weighted (α, β)-norm information measure with application in coding theory. Physica A: Statistical Mechanics and its Applications, 510(C), 538-551. DOI: https://doi.org/10.1016/j.physa.2018.07.015
  11. Kapur, J.N. (1967). Generalized entropy of order a and type b. Mathematics Seminar, 4, 79-84.
  12. Kapur, J.N. (1986). Four families of measures of entropy. Indian Journal of Pure and Applied Mathematics, 17, 429-449.
  13. Kapur, J.N. (1994). Measures of Information and their Applications. Wiley Eastern, New York.
  14. Kapur, J.N. (1998). Entropy and Coding. Mathematical Sciences Trust Society, New Delhi.
  15. Kawan, C. & Yüksel, S. (2018). On optimal coding of non-linear dynamical systems. IEEE Trans. Inform. Theory, 64(10), 6816–6829. DOI: https://doi.org/10.1109/TIT.2018.2844211
  16. Kraft, L.G. (1949). A Device for Quantizing Grouping and Coding Amplitude Modulated Pulses. M.S. Thesis, Electrical Engineering Department, MIT.
  17. Lee, Si-Hyeon & Chung, Sae-Young (2018). A unified random coding bound. IEEE Trans. Inform. Theory,64 (10), 6779–6802. DOI: https://doi.org/10.1109/TIT.2018.2864731
  18. Ouahada, K., & Ferreira, H.C. (2019). New Distance Concept and Graph Theory Approach for Certain Coding Techniques Design and Analysis. Communications in Applied and Industrial Mathematics, 10(1), 53-70. DOI: https://doi.org/10.1515/caim-2019-0012
  19. Renyi, A. (1961). On measures of entropy and information. Proceedings 4th Berkeley Symposium on Mathematical Statistics and Probability, 1, 547-561.
  20. Saraswat R. N. & Umar A. (2021). “Some New coding Information Inequalities” in the book title “Intelligent System Algorithms and Applications in Science and Technology”. Apple Academic Press, Taylor-Francis Group Chapter 22, ISBN 9781774630211 DOI: https://doi.org/10.1201/9781003187059-27
  21. Singh S. and Sharma S. (2019). On Generalized Fuzzy Entropy and Fuzzy Divergence Measure with Applications. International Journal of Fuzzy System Applications, 8(3) DOI: https://doi.org/10.4018/IJFSA.2019070102
  22. Umar A. & Saraswat R.N. (2022). Decision-Making in Machine Learning Using Novel Picture Fuzzy Divergence Measure. Neural Computing and Applications, 34(1), pp. 457–475. DOI: 10.2174/2666255813666200224093221. DOI: https://doi.org/10.1007/s00521-021-06353-4
  23. Umar A. & Saraswat R.N. (2024). Decision making using novel Fermatean fuzzy divergence measure and weighted aggregation operators. Journal of Ambient Intelligence and Humanized Computing, 15(6), pp. 2827–2838. DOI: https://doi.org/10.1007/s12652-024-04774-2

Downloads

Download data is not yet available.