No Access

A λ-CUT APPROXIMATE ALGORITHM FOR GOAL-BASED BILEVEL RISK MANAGEMENT SYSTEMS

YA GAO

Faculty of Information Technology, University of Technology, Sydney, PO Box 123, Broadway, NSW 2007, Australia

Search for more papers by this author

GUANGQUAN ZHANG

Faculty of Information Technology, University of Technology, Sydney, PO Box 123, Broadway, NSW 2007, Australia

Search for more papers by this author

JIE LU

Faculty of Information Technology, University of Technology, Sydney, PO Box 123, Broadway, NSW 2007, Australia

Corresponding author.

Search for more papers by this author

THARAM DILLON

Digital Ecosystems and Business Intelligence Institute, Curtin University of Technology, Perth, WA 6845, Australia

Search for more papers by this author

, and

XIANYI ZENG

Ecole Nationale Supérieure des Arts et Industries Textiles, 9 rue de l'Ermitage 59100 Roubaix, France

Search for more papers by this author

https://doi.org/10.1142/S0219622008003113Cited by:10 (Source: Crossref)

Abstract

Bilevel programming techniques are developed for decentralized decision problems with decision makers located in two levels. Both upper and lower decision makers, termed as leader and follower, try to optimize their own objectives in solution procedure but are affected by those of the other levels. When a bilevel decision model is built with fuzzy coefficients and the leader and/or follower have goals for their objectives, we call it fuzzy goal bilevel (FGBL) decision problem. This paper first proposes a λ-cut set based FGBL model. A programmable λ-cut approximate algorithm is then presented in detail. Based on this algorithm, a FGBL software system is developed to reach solutions for FGBL decision problems. Finally, two examples are given to illustrate the application of the proposed algorithm.

Keywords:

References

J. Amat and B. McCarl, J. Oper. Res. Soc. 32, 783 (1981). Crossref, Web of Science, Google Scholar
J. F. Bard , Practical Bilevel Optimization: Algorithms and Applications ( Kluwer Academic Publishers , Boston , 1998 ) . Crossref, Google Scholar
W. Candler and R. Townsley, Compu. Oper. Res. 9, 59 (1982), DOI: 10.1016/0305-0548(82)90006-5. Crossref, Web of Science, Google Scholar
A. Charnes and W. W. Cooper , Management Models and Industrial Applications of Linear Programming I ( Wiley , 1961 ) . Google Scholar
A. Charnes and W. W. Cooper, Eur. J. Oper. Res. 1, 39 (1977). Crossref, Google Scholar
C. Feng and C. Wen, J. Eastern Asia Soc. Transport. Studies 6, 4253 (2005). Google Scholar
Y. Gaoet al., A bilevel model for railway train set organizing optimization, 2007 Int. Conf. Intelligent Systems and Knowledge Engineering (ISKE2007) (Atlantis Press, 2007) pp. 777–782. Google Scholar
Y. Gaoet al., A λ-cut approximate approach to supporting fuzzy goal based bilevel decision making in risk management, The First Int. Conf. Risk Analysis and Crisis Response (Atlantis Press, 2007) pp. 132–137. Google Scholar
B. F. Hobbs, B. Metzler and J. S. Pang, IEEE Trans. Power System 15, 637 (2000). Crossref, Web of Science, Google Scholar
C. Hu, C. Teng and S. Li, Eur. J. Oper. Res. 176(3), 1319 (2007), DOI: 10.1016/j.ejor.2005.10.049. Crossref, Web of Science, Google Scholar
J. P. Ignizio , Goal Programming and Extensions ( Lexington Books , Massachusetts , 1976 ) . Google Scholar
J. P. Ignizio, Comp. Oper. Res. 10, 277 (1983), DOI: 10.1016/0305-0548(83)90003-5. Crossref, Web of Science, Google Scholar
Y. Lai, Fuzzy Sets Syst. 77, 321 (1996), DOI: 10.1016/0165-0114(95)00086-0. Crossref, Web of Science, Google Scholar
S. M. Lee , Goal Programming for Decision Analysis ( Auerbach Publishers , 1972 ) . Google Scholar
S. Li, H. Wu and Y. Yang, Int. J. Inform. Technol. Decision Making 3(1), 109 (2004), DOI: 10.1142/S0219622004000064. Link, Web of Science, Google Scholar
J. Luet al., Int. J. Global Optimization 38(4), 597 (2007), DOI: 10.1007/s10898-006-9098-9. Crossref, Web of Science, Google Scholar
J. Lu, C. Shi and G. Zhang, Inform. Sci. 176(11), 1607 (2006), DOI: 10.1016/j.ins.2005.04.010. Crossref, Web of Science, Google Scholar
J. Lu, F. Wu and G. Zhang, J. Intell. Fuzzy Syst. 18(1), 83 (2007). Web of Science, Google Scholar
S. Pramanik and T. K. Roy, Eur. J. Oper. Res. 176(2), 1151 (2007), DOI: 10.1016/j.ejor.2005.08.024. Crossref, Web of Science, Google Scholar
O. M. Saad, Appl. Math. Comput. 170(1), 216 (2005), DOI: 10.1016/j.amc.2004.11.026. Crossref, Web of Science, Google Scholar
M. Sakawa , Fuzzy Sets and Interactive Multi-Objective Optimization ( Plenum Press , New York , 1993 ) . Crossref, Google Scholar
M. Sakawa, I. Nishizaki and Y. Uemura, Fuzzy Sets Syst. 109, 3 (2000), DOI: 10.1016/S0165-0114(98)00130-4. Crossref, Web of Science, Google Scholar
C. Shi, J. Lu and G. Zhang, Appl. Math. Comp. 162, 51 (2005), DOI: 10.1016/j.amc.2003.12.089. Crossref, Web of Science, Google Scholar
H. S. Shih, Y. J. Lai and E. S. Lee, Comp. Oper. Res. 23, 73 (1996), DOI: 10.1016/0305-0548(95)00007-9. Crossref, Web of Science, Google Scholar
H. V. Stackelberg , Theory of the Market Economy ( Oxford University Press , New York , 1952 ) . Google Scholar
R. Stulz, Risk management and derivatives, Tech. Rep. (Thomson South-Western, Mason, Ohio, 2003) . Google Scholar
M. Wang, H. Wang and C. Lin, Int. J. Inform. Technol. Decision Making 4(4), 663 (2005), DOI: 10.1142/S0219622005001696. Link, Web of Science, Google Scholar
H. Yu, C. Dang and S. Wang, Int. J. Inform. Technol. Decision Making 5(3), 557 (2006), DOI: 10.1142/S0219622006002131. Link, Web of Science, Google Scholar
G. Zhang and J. Lu, J. Enterprise Inform. Mngment 20(2), 178 (2007), DOI: 10.1108/17410390710725760. Crossref, Web of Science, Google Scholar
G. Zhang , J. Lu and T. Dillon , Intel. Decis. Making , eds. L. Jain and G. Wren ( Springer , 2007 ) . Google Scholar