Bi-level Multi-objective Programming Problems with Fuzzy Parameters: Modified TOPSIS Approach
International Journal of Management and Fuzzy Systems
Volume 2, Issue 5, October 2016, Pages: 38-50
Received: Oct. 5, 2016;
Accepted: Nov. 30, 2016;
Published: Dec. 27, 2016
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Ibrahim A. Baky, Department of Mathematics, Faculty of Science, Tabuk University, Tabuk, Saudi Arabia; Department of Basic Engineering Sciences, Faculty of Engineering, Benha University, El Qalyoubia, Egypt
M. A. El Sayed, Department of Basic Engineering Sciences, Faculty of Engineering, Benha University, El Qalyoubia, Egypt
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.
Ibrahim A. Baky,
M. A. El Sayed,
Bi-level Multi-objective Programming Problems with Fuzzy Parameters: Modified TOPSIS Approach, International Journal of Management and Fuzzy Systems.
Vol. 2, No. 5,
2016, pp. 38-50.
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