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Bi-level Multi-objective Programming Problems with Fuzzy Parameters: Modified TOPSIS Approach

Received: 5 October 2016     Accepted: 30 November 2016     Published: 27 December 2016
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Abstract

In this paper, a modified TOPSIS (techniques for order preference by similarity to ideal solution) approach for solving bi-level multi-objective programming (BL-MOP) problems with fuzzy parameters is presented. These fuzzy parameters are assumed to be characterized by fuzzy numerical data, reflecting the experts' imprecise or fuzzy understanding of the nature of the parameters in the problem formulation process. Firstly, the corresponding non-fuzzy bi-level programming model is introduced based on the α-level set. Secondly, a modified TOPSIS approach is developed, in which the fuzzy goal programming (FGP) approach is used to solve the conflicting bi-objective distance functions instead of max-min operator. As the FGP approach utilized to achieve the highest degree of each membership goal by minimizing the sum of the unwanted deviational variables. Finally, an algorithm to clarify the modified TOPSIS approach, as well as Illustrative numerical example and comparison with the existing methods, are presented.

Published in International Journal of Management and Fuzzy Systems (Volume 2, Issue 5)
DOI 10.11648/j.ijmfs.20160205.11
Page(s) 38-50
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Bi-level Programming, Fuzzy Sets, Fuzzy Parameters, TOPSIS, Fuzzy Goal Programming, Multi-objective Programming

References
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[3] Mahmoud. A. Abo-Sinna, A. H. Amer and A. S. Ibrahim, Extensions of TOPSIS for large-scale multi-objective nonlinear programming problems with block angular structure, Appl. Math. Model. 32 (2008) 292-302.
[4] Ibrahim A. Baky and M. A. Abo-Sinna, TOPSIS for bi-level MODM problems, Appl. Math. Model. 37 (3) (2012) 1004-1015.
[5] Ibrahim A. Baky, Fuzzy goal programming algorithm for solving decentralized bi-level multi-objective programming problems, Fuzzy Sets Systems, vol. 160, no. 18, pp. (2009) 2701-2713.
[6] Ibrahim A. Baky, Solving multi-level multi-objective linear programming problems through fuzzy goal programming approach, Applied Mathematical Modelling, 34 (9) (2010) 2377-2387.
[7] Ibrahim A. Baky, M. H. Eid, M. A. Elsayed, Bi-level multi-objective programming problem with fuzzy demands: a fuzzy goal programming algorithm, Journal of Operational Research Society of India (OPSEARCH), 51 (2) (2014) 280-296.
[8] Ibrahim A. Baky, M. H. Eid, M. A. Elsayed, Bi-level multi-objective programming problem with fuzzy parameters: TOPSIS approach, the 38th International Conference for statistics, computer science and its applications, Cairo, Egypt, 8-18 April, 13-33, 2013.
[9] C. T. Chen, Extensions of the TOPSIS for group decision-making under fuzzy environment, Fuzzy Set Syst. 114 (2000) 1-9.
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[16] S. Pramanik and P. P. Dey, Bi-level multi-objective programming problem with fuzzy parameters. International Journal of Computer Applications, 30(11)(2011) 13-20.
[17] B. B. Pal, B. N. Moitra, and U. Maulik, A goal programming procedure for fuzzy multi-objective linear fractional programming problem, Fuzzy Sets and Systems, 139(2) (2003) 395-405.
[18] S. Sinha, Fuzzy programming approach to multi-level programming problems, Fuzzy Sets and Systems, 136 (2003)189-202.
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Cite This Article
  • APA Style

    Ibrahim A. Baky, M. A. El Sayed. (2016). Bi-level Multi-objective Programming Problems with Fuzzy Parameters: Modified TOPSIS Approach. International Journal of Management and Fuzzy Systems, 2(5), 38-50. https://doi.org/10.11648/j.ijmfs.20160205.11

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    ACS Style

    Ibrahim A. Baky; M. A. El Sayed. Bi-level Multi-objective Programming Problems with Fuzzy Parameters: Modified TOPSIS Approach. Int. J. Manag. Fuzzy Syst. 2016, 2(5), 38-50. doi: 10.11648/j.ijmfs.20160205.11

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    AMA Style

    Ibrahim A. Baky, M. A. El Sayed. Bi-level Multi-objective Programming Problems with Fuzzy Parameters: Modified TOPSIS Approach. Int J Manag Fuzzy Syst. 2016;2(5):38-50. doi: 10.11648/j.ijmfs.20160205.11

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  • @article{10.11648/j.ijmfs.20160205.11,
      author = {Ibrahim A. Baky and M. A. El Sayed},
      title = {Bi-level Multi-objective Programming Problems with Fuzzy Parameters: Modified TOPSIS Approach},
      journal = {International Journal of Management and Fuzzy Systems},
      volume = {2},
      number = {5},
      pages = {38-50},
      doi = {10.11648/j.ijmfs.20160205.11},
      url = {https://doi.org/10.11648/j.ijmfs.20160205.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijmfs.20160205.11},
      abstract = {In this paper, a modified TOPSIS (techniques for order preference by similarity to ideal solution) approach for solving bi-level multi-objective programming (BL-MOP) problems with fuzzy parameters is presented. These fuzzy parameters are assumed to be characterized by fuzzy numerical data, reflecting the experts' imprecise or fuzzy understanding of the nature of the parameters in the problem formulation process. Firstly, the corresponding non-fuzzy bi-level programming model is introduced based on the α-level set. Secondly, a modified TOPSIS approach is developed, in which the fuzzy goal programming (FGP) approach is used to solve the conflicting bi-objective distance functions instead of max-min operator. As the FGP approach utilized to achieve the highest degree of each membership goal by minimizing the sum of the unwanted deviational variables. Finally, an algorithm to clarify the modified TOPSIS approach, as well as Illustrative numerical example and comparison with the existing methods, are presented.},
     year = {2016}
    }
    

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    T1  - Bi-level Multi-objective Programming Problems with Fuzzy Parameters: Modified TOPSIS Approach
    AU  - Ibrahim A. Baky
    AU  - M. A. El Sayed
    Y1  - 2016/12/27
    PY  - 2016
    N1  - https://doi.org/10.11648/j.ijmfs.20160205.11
    DO  - 10.11648/j.ijmfs.20160205.11
    T2  - International Journal of Management and Fuzzy Systems
    JF  - International Journal of Management and Fuzzy Systems
    JO  - International Journal of Management and Fuzzy Systems
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    PB  - Science Publishing Group
    SN  - 2575-4947
    UR  - https://doi.org/10.11648/j.ijmfs.20160205.11
    AB  - In this paper, a modified TOPSIS (techniques for order preference by similarity to ideal solution) approach for solving bi-level multi-objective programming (BL-MOP) problems with fuzzy parameters is presented. These fuzzy parameters are assumed to be characterized by fuzzy numerical data, reflecting the experts' imprecise or fuzzy understanding of the nature of the parameters in the problem formulation process. Firstly, the corresponding non-fuzzy bi-level programming model is introduced based on the α-level set. Secondly, a modified TOPSIS approach is developed, in which the fuzzy goal programming (FGP) approach is used to solve the conflicting bi-objective distance functions instead of max-min operator. As the FGP approach utilized to achieve the highest degree of each membership goal by minimizing the sum of the unwanted deviational variables. Finally, an algorithm to clarify the modified TOPSIS approach, as well as Illustrative numerical example and comparison with the existing methods, are presented.
    VL  - 2
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    ER  - 

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Author Information
  • Department of Mathematics, Faculty of Science, Tabuk University, Tabuk, Saudi Arabia

  • Department of Basic Engineering Sciences, Faculty of Engineering, Benha University, El Qalyoubia, Egypt

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