An algorithm for fuzzy multi-objective multi-follower partial cooperative bilevel programming

In a bilevel decision problem, both the leader and the follower may have multiple objectives to optimize under certain constraints. In the meantime, these objective functions and constraints may contain some uncertain parameters. In addition, there may have multiple followers involved in a bilevel decision problem. These followers may share their individual decision variables with each other but keep individual objectives in reacting any of the leader's decisions, which is a common situation in real bilevel decision activities. This study deals with all above three issues, fuzzy parameters, multi-objectives, and multi-followers in a partial cooperative situation, at the same time. After a set of models for describing different cases of the fuzzy multi-objective multi-follower bilevel programming with partial cooperation (FMMBP-PC) problem, this paper develops an approximation branch-and-bound algorithm to solve this problem.

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