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Dr. Mohamed Aly Elsayed Fahim :: Publications:

Title:
Bi-level multi-objective programming problem with fuzzy demands: a fuzzy goal programming algorithm
Authors: Ibrahim A. Baky , Mohamed H. Eid, Mohamed Aly Elsayed
Year: 2013
Keywords: Bi-level programming . Fuzzy sets . Fuzzy demands . Goal programming . Fuzzy goal programming . Multi-objective programming
Journal: journal of Operational Research Society of India (OPSEARCH)
Volume: 145
Issue: ISSN 0030-3887
Pages: DOI 10.1007/s12597-013-0145-2
Publisher: springer
Local/International: International
Paper Link:
Full paper Mohamed Aly Elsayed Fahim_10.1007_s12597-013-0145-2.pdf
Supplementary materials Not Available
Abstract:

In this paper, a fuzzy goal programming (FGP) algorithm for solving bi-level multi-objective programming problems with fuzzy demands is presented. These fuzzy demands reflect the experts' imprecise or fuzzy understandings of the nature of parameters in the problem formulation process are assumed to be characterized as fuzzy numbers. Using the level sets of fuzzy parameters, the corresponding non fuzzy bi-level programming problem is introduced. In the proposed algorithm, the membership functions for the defined fuzzy goals of all objective functions at the two levels, as well as the membership functions for the vector of decision variables controlled by FLDM are developed in the model formulation of the problem. Then FGP algorithm is used to achieve the highest degree of each of the membership goals by minimizing their deviational variables and thereby obtaining the most satisfactory solution for all decision makers. Illustrative numerical example is given to demonstrate the proposed algorithm.

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