Fuzzy Goal Programming Procedure to Bilevel Multiobjective Linear Fractional Programming Problems

作者: Mahmoud A. Abo-Sinna , Ibrahim A. Baky

DOI: 10.1155/2010/148975

关键词: Fuzzy classificationMathematicsMembership functionDefuzzificationMathematical optimizationFuzzy logicLinear-fractional programmingVariable (computer science)Fuzzy numberGoal programming

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

参考文章(28)
G. Anandalingam, A Mathematical Programming Model of Decentralized Multi-Level Systems Journal of the Operational Research Society. ,vol. 39, pp. 1021- 1033 ,(1988) , 10.1057/JORS.1988.172
Lu�s N. Vicente, Paul H. Calamai, Bilevel and multilevel programming: A bibliography review Journal of Global Optimization. ,vol. 5, pp. 291- 306 ,(1994) , 10.1007/BF01096458
Omar Ben-Ayed, Bilevel linear programming Computers & Operations Research. ,vol. 20, pp. 485- 501 ,(1993) , 10.1016/0305-0548(93)90013-9
Ue-Pyng Wen, Sen-Fon Lin, Finding an efficient solution to linear bilevel programming problem: An effective approach Journal of Global Optimization. ,vol. 8, pp. 295- 306 ,(1996) , 10.1007/BF00121271
X Shi, H Xia, Interactive bilevel multi-objective decision making Journal of the Operational Research Society. ,vol. 48, pp. 943- 949 ,(1997) , 10.1057/PALGRAVE.JORS.2600435
Hsu-Shih Shih, Young-Jou Lai, E. Stanley Lee, Fuzzy approach for multi-level programming problems Computers & Operations Research. ,vol. 23, pp. 73- 91 ,(1996) , 10.1016/0305-0548(95)00007-9
Young-Jou Lai, Hierarchical optimization: a satisfactory solution Fuzzy Sets and Systems. ,vol. 77, pp. 321- 335 ,(1996) , 10.1016/0165-0114(95)00086-0
Xinping Shi, Hong Sheng Xia, Model and interactive algorithm of bi-level multi-objective decision-making with multiple interconnected decision makers Journal of Multi-criteria Decision Analysis. ,vol. 10, pp. 27- 34 ,(2001) , 10.1002/MCDA.285