A new approach based on possibilistic programming technique and fractile optimization for bilevel programming in a hybrid uncertain circumstance

摘要

Fuzzy random bilevel programming is very important for modeling hierarchical decision processes consisting of two decision makers with a hybrid uncertainty of fuzziness and randomness. This type of problem is usually much more difficult to handle than either purely fuzzy bilevel programming or purely stochastic bilevel programming due to complexity of hybrid uncertainty and NP-hardness of bilevel programming. In this paper, a novel approach based on Me-based possibilistic programming technique and fractile optimization is proposed to transform and cope with the fuzzy random bilevel programming problem. On the basis of the Me-based possibilistic programming method, the original problem is first converted into a Me-based bilevel chance constrained programming model. Then fractile criterion optimization and probabilistic chance constrained conditions are employed to transform the Me-based bilevel chance constrained model into an equivalent deterministic bilevel nonlinear programming problem. Furthermore, different satisfactory solutions associated with varying optimistic-pessimistic attitudes of the decision makers can be searched by the fuzzy interactive solution approach, which are helpful for the decision makers to gain more desirable information under uncertainty. Finally, several numerical examples are provided to illustrate the feasibility of the proposed model and solution methodology.