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Fuzzy bilevel programming with multiple objectives and cooperative multiple followers

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Abstract

Classic bilevel programming deals with two level hierarchical optimization problems in which the leader attempts to optimize his/her objective, subject to a set of constraints and his/her follower’s solution. In modelling a real-world bilevel decision problem, some uncertain coefficients often appear in the objective functions and/or constraints of the leader and/or the follower. Also, the leader and the follower may have multiple conflicting objectives that should be optimized simultaneously. Furthermore, multiple followers may be involved in a decision problem and work cooperatively according to each of the possible decisions made by the leader, but with different objectives and/or constraints. Following our previous work, this study proposes a set of models to describe such fuzzy multi-objective, multi-follower (cooperative) bilevel programming problems. We then develop an approximation Kth-best algorithm to solve the problems.

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Authors and Affiliations

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

    Guangquan Zhang & Jie Lu

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  1. Guangquan Zhang
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  2. Jie Lu
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Correspondence to Guangquan Zhang.

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Zhang, G., Lu, J. Fuzzy bilevel programming with multiple objectives and cooperative multiple followers. J Glob Optim 47, 403–419 (2010). https://doi.org/10.1007/s10898-008-9365-z

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  • DOI: https://doi.org/10.1007/s10898-008-9365-z

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