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Solution Concepts and an Approximation Kuhn–Tucker Approach for Fuzzy Multiobjective Linear Bilevel Programming

In: Pareto Optimality, Game Theory And Equilibria

Author

Listed:
  • Guangquan Zhang

    (University of Technology)

  • Jie Lu

    (University of Technology)

  • Tharam Dillon

    (University of Technology)

Abstract

When modeling an organizational bilevel decision problem, uncertainty often appears in the parameters of either objective functions or constraints of the leader and the follower. Furthermore, the leader and the follower may have multiple objectives to consider simultaneously in their decision making. To deal with the two issues, this study builds a fuzzy multiobjective linear bilevel programming (FMOLBLP) model. It then proposes the definitions of optimal solutions and related theorems for solving a FMOLBLP problem. Based on these theorems, it develops an approximation Kuhn–Tucker approach to solve the FMOLBLP problem where fuzzy parameters can be described by any form of membership functions of fuzzy numbers. An example illustrates the applications of the proposed approach.

Suggested Citation

  • Guangquan Zhang & Jie Lu & Tharam Dillon, 2008. "Solution Concepts and an Approximation Kuhn–Tucker Approach for Fuzzy Multiobjective Linear Bilevel Programming," Springer Optimization and Its Applications, in: Altannar Chinchuluun & Panos M. Pardalos & Athanasios Migdalas & Leonidas Pitsoulis (ed.), Pareto Optimality, Game Theory And Equilibria, pages 457-480, Springer.
    • Handle: RePEc:spr:spochp:978-0-387-77247-9_17
    DOI: 10.1007/978-0-387-77247-9_17
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    Citations

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    Cited by:

    1. Sauli Ruuska & Kaisa Miettinen & Margaret M. Wiecek, 2012. "Connections Between Single-Level and Bilevel Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 153(1), pages 60-74, April.
    2. Guangquan Zhang & Jie Lu, 2010. "Fuzzy bilevel programming with multiple objectives and cooperative multiple followers," Journal of Global Optimization, Springer, vol. 47(3), pages 403-419, July.

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