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Reseach Article

Hybrid Fuzzy-Linear Programming with Shadowed Fuzzy Numbers

by Mohamed A. H. El_Hawy, Khaled T. Wassif, Hesham A. Hefny, Hesham A. Hassan
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 155 - Number 14
Year of Publication: 2016
Authors: Mohamed A. H. El_Hawy, Khaled T. Wassif, Hesham A. Hefny, Hesham A. Hassan
10.5120/ijca2016912577

Mohamed A. H. El_Hawy, Khaled T. Wassif, Hesham A. Hefny, Hesham A. Hassan . Hybrid Fuzzy-Linear Programming with Shadowed Fuzzy Numbers. International Journal of Computer Applications. 155, 14 ( Dec 2016), 42-50. DOI=10.5120/ijca2016912577

@article{ 10.5120/ijca2016912577,
author = { Mohamed A. H. El_Hawy, Khaled T. Wassif, Hesham A. Hefny, Hesham A. Hassan },
title = { Hybrid Fuzzy-Linear Programming with Shadowed Fuzzy Numbers },
journal = { International Journal of Computer Applications },
issue_date = { Dec 2016 },
volume = { 155 },
number = { 14 },
month = { Dec },
year = { 2016 },
issn = { 0975-8887 },
pages = { 42-50 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume155/number14/26779-2016912577/ },
doi = { 10.5120/ijca2016912577 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-07T00:01:22.300305+05:30
%A Mohamed A. H. El_Hawy
%A Khaled T. Wassif
%A Hesham A. Hefny
%A Hesham A. Hassan
%T Hybrid Fuzzy-Linear Programming with Shadowed Fuzzy Numbers
%J International Journal of Computer Applications
%@ 0975-8887
%V 155
%N 14
%P 42-50
%D 2016
%I Foundation of Computer Science (FCS), NY, USA
Abstract

Linear programming problem in an environment that includes different types of uncertainties represents real-world situations. In such situations, different forms of uncertain data parameters are commonly found in that problem. Fuzzy sets and their extensions are important tools of representing vague information. For decades, a lot of approaches are developed to solve fuzzy-linear programming problems. The existence of hybrid types of uncertainties in the fuzzy-linear programming problem imposes a real challenge to solve it. There is a need for introducing an efficient methodology to transform different types of uncertainties into a unified form. This paper introduces a new approach to solve hybrid fuzzy-linear programming using an improved version of shadowed fuzzy numbers (SFNs). SFNs are useful transformation tool for different types of uncertainties. They have the advantage of preserving the characteristics of uncertainty for different types of fuzzy sets used in the problem.

References
  1. George. J. Klir, Bo. Yuan, (1995) Fuzzy Sets and Fuzzy Logic Theory and Applications. Prentice Hall press.
  2. George J. Klir, Wierman Mark l, (1999 ) Uncertainty –Based Information Elements of Generalized Information Theory. Springer-Verlag Berlin Heidelberg GmbH .
  3. Atanassov .K, (1999) Intuitionistic Fuzzy Sets. Theory and Applications. Physica-Verlag, Heidelberg New York.
  4. Atanassov .K, (1986) Intuitionistic fuzzy sets. Fuzzy Sets and Systems Vol. 20, Issue (1), pp.87 -96.
  5. Witold Pedrycz, (1998) Shadowed Sets: Representing and Processing Fuzzy Sets. IEEE Transactions on systems, man, and cybernetics—part B: Cybernetics, Vol. 28, No. 1.
  6. Pedrycz Witold. (2005). Granular Computing with Shadowed Sets. Ślęzak et al. (Eds.): RSFDGrC 2005, LNAI 3641, Springer-Verlag Berlin Heidelberg, pp. 23 – 32.
  7. Mohamed A. H. El_Hawy, Hesham A. Hassan, Hesham A. Hefny, Khaled T. Wassif , (May 2015) An Improved Fuzzy Number Approximation using Shadowed Sets. International Journal of Computer Applications (0975 – 8887), Vol. 118 , No.25, pp. 9-15.
  8. Mohamed A. H. El_Hawy, Hesham A. Hassan, Hesham A. Hefny, Khaled T. Wassif (2015) A Proposed Shadowed Intuitionistic Fuzzy Numbers. Computer Engineering & Systems (ICCES), 2015 10th, IEEE.
  9. R.E. Bellmann, L.A. Zadeh, (1970 ) Decision making in fuzzy environment. Management Sci. Vol.17, pp. 141–164.
  10. Jagdeep Kaur , Amit Kumar, (2016) An Introduction to Fuzzy Linear Programming Problems Theory, Methods and Applications. Springer International Publishing Switzerland .
  11. P.P. Angelov, (1997) Optimization in an intuitionistic fuzzy environment. Fuzzy sets and systems. Vol.86, pp. 299–306.
  12. Jaroslav Ramík, Milan Vlach, (2016 ) Intuitionistic fuzzy linear programming and duality: a level sets approach. Fuzzy Optimization and Decision Making, pp. 1–33, Springer Science Business Media New York.
  13. Dipti Dubey, Aparna Mehra, “Linear programming with Triangular Intuitionistic Fuzzy Number”, EUSFLAT-LFA, Aix-les-Bains, France, 2011.
  14. D. Dubeyetal, (2012) Fuzzy linear programming under interval uncertainty based on IFS representation. Fuzzy Sets and Systems, Vol.188, pp. 68 –87.
  15. A. Kaufmann, M.M. Gupta, (1985) Introduction to Fuzzy Arithmetic Theory and Applications. Van Nostrand Reinhold, New York.
  16. C. R. Bector, Suresh Chandra, ( 2005) Fuzzy Mathematical Programming and Fuzzy Matrix Games. Springer-Verlag Berlin Heidelberg.
  17. Grzegorzewski, P, (2003) Distances and orderings in a family of intuitionistic fuzzy numbers. In: EUSFLAT Conf., pp. 223–227.
  18. M. Kumar and S.P. Yadav, (2012 ) Analyzing Fuzzy System Reliability Using Arithmetic Operations on Different Types of Intuitionistic Fuzzy Numbers. K. Deep et al. (Eds.): Proceedings of the International Conference on SocProS 2011, AISC 130, pp. 725–736. Springer India.
  19. Witold Pedrycz, (2009) From Fuzzy Sets to Shadowed Sets: Interpretation and Computing. INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, VOL. 24, pp. 48–61.
  20. 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.
  21. 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, 5, pp.937-949.
  22. Xia Liang , Cuiping Wei, Meimei Xia, (September, 2013) New Entropy, Similarity Measure of Intuitionistic Fuzzy Sets and their Applications in Group Decision Making. International Journal of Computational Intelligence Systems, Vol. 6, No. 5, pp. 987-1001.
  23. Mohamed. A. H. El-Hawy, K. T. Wassif, H. A. Hefny and H. A. Hassan, (Dec. 2015) Hybrid multi-attribute decision making based on shadowed fuzzy numbers. IEEE Seventh International Conference on Intelligent Computing and Information Systems (ICICIS), Cairo, 2015, pp. 514-521.
  24. Jin-Shieh Su, (2007) Fuzzy Programming Based on Interval-Valued Fuzzy Numbers and Ranking. Int. J. Contemp. Math. Sciences, Vol. 2, No. 8, pp. 393 – 410.
Index Terms

Computer Science
Information Sciences

Keywords

Shadowed sets Fuzzy numbers Intuitionistic fuzzy numbers Non-specificity measure Entropy measure Fuzzy linear programming