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International Journal of Mathematics and Mathematical Sciences
Volume 2010, Article ID 148975, 15 pages
Research Article

Fuzzy Goal Programming Procedure to Bilevel Multiobjective Linear Fractional Programming Problems

1Department of Statistics, Faculty of Science, King Abdul Aziz University, Jeddah, Saudi Arabia
2Department of Basic Sciences, Benha Higher Institute of Technology, Benha University, El-Kalyoubia, Egypt

Received 11 July 2009; Accepted 1 February 2010

Academic Editor: Alexander Rosa

Copyright © 2010 Mahmoud A. Abo-Sinna and Ibrahim A. Baky. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper presents a fuzzy goal programming (FGP) procedure for solving bilevel multiobjective linear fractional programming (BL-MOLFP) problems. It makes an extension work of Moitra and Pal (2002) and Pal et al. (2003). In the proposed procedure, the membership functions for the defined fuzzy goals of the decision makers (DMs) objective functions at both levels as well as the membership functions for vector of fuzzy goals of the decision variables controlled by first-level decision maker are developed first in the model formulation of the problem. Then a fuzzy goal programming model to minimize the group regret of degree of satisfactions of both the decision makers is developed to achieve the highest degree (unity) of each of the defined membership function goals to the extent possible by minimizing their deviational variables and thereby obtaining the most satisfactory solution for both decision makers. The method of variable change on the under- and over-deviational variables of the membership goals associated with the fuzzy goals of the model is introduced to solve the problem efficiently by using linear goal programming (LGP) methodology. Illustrative numerical example is given to demonstrate the procedure.