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

Ibrahim A. Baky; M. A. El Sayed

doi:doi:10.11648/j.ijmfs.20160205.11

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

Ibrahim A. Baky, M. A. El Sayed

Published in International Journal of Management and Fuzzy Systems (Volume 2, Issue 5)

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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[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.
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[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.
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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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TY - JOUR
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
SP - 38
EP - 50
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
IS - 5
ER -

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Author Information

Ibrahim A. Baky

Department of Mathematics, Faculty of Science, Tabuk University, Tabuk, Saudi Arabia
M. A. El Sayed

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

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Plain Text BibTeX RIS

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}
}

Copy | Download