Solving the General Fuzzy Random Bilevel Programming Problem Through $Me$ Measure-Based Approach

This paper addresses the general fuzzy random bilevel programming problem in which not only both objective functions, but also the constraints contain fuzzy random variable coefficients. From point of view of different decision attitudes of the decision-makers at both levels under the noncooperative case, the expected value based on $Me$ measure is adopted to handle fuzzy stochastic objective functions at the upper and lower levels so as to capture any attitudes between extremely optimistic and pessimistic, and the rough approximation strategy is applied to convert fuzzy stochastic constraints into two approximation stochastic constraints for purpose of avoiding losing much information. Accordingly, the upper and lower approximation stochastic bilevel programming models are built. Then, these two stochastic bilevel programming models are transformed into their equivalent deterministic forms by virtue of expectation optimization and chance constrained conditions. With the help of differential evolution algorithm, the lower and upper bounds of the upper level objective function can be obtained by solving the resulting deterministic problems. By this means, it is helpful to provide more information for decision-makers to select the most desirable alternatives. Finally, a numerical example and a real-case study are provided to demonstrate the effectiveness of the proposed approach.