CFP last date
20 June 2024
Reseach Article

An Improved Fuzzy Number Approximation using Shadowed Sets

by Mohamed A. H. El_hawy, Hesham A. Hassan, Hesham A. Hefny, Khaled T. Wassif
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 118 - Number 25
Year of Publication: 2015
Authors: Mohamed A. H. El_hawy, Hesham A. Hassan, Hesham A. Hefny, Khaled T. Wassif
10.5120/20961-3634

Mohamed A. H. El_hawy, Hesham A. Hassan, Hesham A. Hefny, Khaled T. Wassif . An Improved Fuzzy Number Approximation using Shadowed Sets. International Journal of Computer Applications. 118, 25 ( May 2015), 9-15. DOI=10.5120/20961-3634

@article{ 10.5120/20961-3634,
author = { Mohamed A. H. El_hawy, Hesham A. Hassan, Hesham A. Hefny, Khaled T. Wassif },
title = { An Improved Fuzzy Number Approximation using Shadowed Sets },
journal = { International Journal of Computer Applications },
issue_date = { May 2015 },
volume = { 118 },
number = { 25 },
month = { May },
year = { 2015 },
issn = { 0975-8887 },
pages = { 9-15 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume118/number25/20961-3634/ },
doi = { 10.5120/20961-3634 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T23:02:48.910174+05:30
%A Mohamed A. H. El_hawy
%A Hesham A. Hassan
%A Hesham A. Hefny
%A Khaled T. Wassif
%T An Improved Fuzzy Number Approximation using Shadowed Sets
%J International Journal of Computer Applications
%@ 0975-8887
%V 118
%N 25
%P 9-15
%D 2015
%I Foundation of Computer Science (FCS), NY, USA
Abstract

The shadowed sets are proposed by Pedrycz as a granule manner to approximate the fuzzy sets with preserving the uncertainty features. Many methods have been made in this context to maintain various characteristics of uncertainty for fuzzy sets. In this paper, a new method is proposed which it is preserve more than one kind of uncertainty in fuzzy sets. The new technique is based on the use of measures of uncertainty directly to induce ideal values of shadowed set. It's more simply and accurate for describing uncertainty. The features of new method are important for decision applications.

References
  1. George. J. Klir, Bo. Yuan, 1995,"Fuzzy Sets and Fuzzy Logic Theory and Applications", Prentice Hall press.
  2. Witold Pedrycz, 1998, "Shadowed Sets: Representing and Processing Fuzzy Sets", IEEE Transactions on systems, man, and cybernetics—part B: Cybernetics, Vol. 28, No. 1, FEBRUARY.
  3. Tahayori, H. ; Sadeghian, A. ; Pedrycz, W. , 2013,"Induction of Shadowed Sets Based on the Gradual Grade of Fuzziness", Fuzzy Systems, IEEE Transactions on , vol. 21, no. 5, pp. 937-949.
  4. P. Grzegorzewski , 2013," Fuzzy number approximation via shadowed sets ", Information Sciences Vol. 225, pp. 35–46.
  5. Witold Pedrycz, Fernando Gomide, 2007, "Fuzzy systems engineering toward human-centric computing", John Wiley & Sons press.
  6. Michael Hanss , 2005," Applied Fuzzy Arithmetic: An Introduction with Engineering Applications",Springer Science & Business Media.
  7. George J. Klir, Mark l. Wierman, 1999,"Uncertainty –Based Information Elements of Generalized Information Theory" Springer-Verlag Berlin Heidelberg GmbH.
  8. S. Chanas, 2001, "On the interval approximation of a fuzzy number", Fuzzy Sets and Systems, Vol. 122, pp. 353–356.
  9. A. De Luca, S. Termini, 1972,"A definition of a nonprobabilistic entropy in the setting of fuzzy sets , theory",Information and Control Volume 20, Issue 4, pp. 301–312.
  10. R. R. Yager, 1979, "On the measure of fuzziness and negation, Part I: membership in unit interval", International. J. General Systems, Vol. 5, pp. 221-229.
  11. W. Wang and C. Chiu, 1999,"Entropy and information energy for fuzzy sets", Fuzzy Sets and System, Vol. 108,pp. 333-339.
  12. M. Delgado, M. A. Vila, W. Voxman, 1998,"On a canonical representation of a fuzzy number", Fuzzy Sets and Systems, Vol. 93, pp. 125–135.
  13. P. Grzegorzewski, E. Mrowka, 2005,"Trapezoidal approximations of fuzzy numbers", Fuzzy Sets and Systems Vol. 153, pp. 115–135.
  14. A. Ban, 2008, "Approximation of fuzzy numbers by trapezoidal fuzzy numbers preserving the expected interval", Fuzzy Sets and Systems, Vol. 159, pp. 1327–1344.
  15. Olgierd Hryniewicz, , 2006, "An Evaluation of the Reliability of Complex Systems Using Shadowed Sets and Fuzzy Lifetime Data", International Journal of Automation and Computing, Vol. 2 ,pp. 145-150.
  16. P. Grzegorzewski, 2002, "Nearest interval approximation of a fuzzy number", Fuzzy Sets and Systems Vol. 130, pp. 321–330.
Index Terms

Computer Science
Information Sciences

Keywords

Fuzzy sets Shadowed sets Fuzziness measure Non-specificity measure.