Solution concepts and an approximation Kuhn–Tucker approach for fuzzy multiobjective linear bilevel programming

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Springer Optimization and Its Applications, 2008, 17 pp. 457 - 480
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© 2008 Springer Science+Business Media, LLC. 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.
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