Solving the Fuzzy BiLevel Linear Programming with Multiple Followers through Structured Element Method

The optimal solution of fuzzy bilevel linear programming with multiple followers (MFFBLP) model is shown to be equivalent to the optimal solution of the bilevel linear programming with multiple followers by using fuzzy structured element theory. The optimal solution to this model is found out by adopting the Kuhn-Tucker approach. Finally, an illustrative numerical example for this model is also provided to demonstrate the feasibility and efficiency of the proposed method.

[1]  Guangquan Zhang,et al.  A ${\bm \lambda}$-Cut and Goal-Programming-Based Algorithm for Fuzzy-Linear Multiple-Objective Bilevel Optimization , 2010, IEEE Transactions on Fuzzy Systems.

[2]  Guangquan Zhang,et al.  Model and approach of fuzzy bilevel decision making for logistics planning problem , 2007, J. Enterp. Inf. Manag..

[3]  Konstantin Kogan,et al.  Optimal co-investment in supply chain infrastructure , 2009, Eur. J. Oper. Res..

[4]  Jie Lu,et al.  On bilevel multi-follower decision making: General framework and solutions , 2006, Inf. Sci..

[5]  Tharam S. Dillon,et al.  Decentralized multi-objective bilevel decision making with fuzzy demands , 2007, Knowl. Based Syst..

[6]  Wayne F. Bialas,et al.  Two-Level Linear Programming , 1984 .

[7]  Si-zong Guo,et al.  Comparison and Ordering of Fuzzy Numbers Based on Method of Structured Element , 2009 .

[8]  Jie Lu,et al.  The Definition of Optimal Solution and an Extended Kuhn-Tucker Approach for Fuzzy Linear Bilevel Programming , 2005, IEEE Intell. Informatics Bull..

[9]  Masatoshi Sakawa,et al.  Stackelberg solutions for fuzzy random two-level linear programming through probability maximization with possibility , 2012, Fuzzy Sets Syst..

[10]  Jie Lu,et al.  Fuzzy bilevel Programming: Multi-Objective and Multi-Follower with Shared Variables , 2008, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[11]  Ichiro Nishizaki,et al.  Interactive fuzzy programming for two-level linear fractional programming problems , 2001, Fuzzy Sets Syst..

[12]  Surabhi Sinha,et al.  Fuzzy programming approach to multi-level programming problems , 2003, Fuzzy Sets Syst..

[13]  Jie Lu,et al.  An algorithm for fuzzy multi-objective multi-follower partial cooperative bilevel programming , 2008, J. Intell. Fuzzy Syst..

[14]  Ichiro Nishizaki,et al.  Interactive fuzzy programming for multi-level linear programming problems with fuzzy parameters , 2000, Fuzzy Sets Syst..

[15]  E. Stanley Lee,et al.  Compensatory fuzzy multiple level decision making , 2000, Fuzzy Sets Syst..

[16]  Masatoshi Sakawa,et al.  Interactive decision making for multiobjective nonconvex programming problems with fuzzy numbers through coevolutionary genetic algorithms , 2000, Fuzzy Sets Syst..

[17]  F. Galiana,et al.  Nodal price control: a mechanism for transmission network cost allocation , 2006, IEEE Transactions on Power Systems.

[18]  Stephan Dempe,et al.  Foundations of Bilevel Programming , 2002 .

[19]  Ichiro Nishizaki,et al.  Interactive fuzzy programming for two-level nonconvex programming problems with fuzzy parameters through genetic algorithms , 2002, Fuzzy Sets Syst..

[20]  Kin Keung Lai,et al.  Manufacturer's revenue-sharing contract and retail competition , 2008, Eur. J. Oper. Res..

[21]  Xiaoning Zhang,et al.  Stackelberg games and multiple equilibrium behaviors on networks , 2007 .

[22]  Ichiro Nishizaki,et al.  Interactive fuzzy programming for decentralized two-level linear programming problems , 2002, Fuzzy Sets Syst..

[23]  Heinrich von Stackelberg,et al.  Stackelberg (Heinrich von) - The Theory of the Market Economy, translated from the German and with an introduction by Alan T. PEACOCK. , 1953 .

[24]  Guo Si-zong Comparison and sequencing of fuzzy numbers based on the method of structured element , 2009 .