Fuzzy bilevel programming with multiple objectives and cooperative multiple followers

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.