Solution Strategy for Bilevel Linear Programming in Fuzzy Random Circumstances

In this study, we focus on bilevel programming when the coefficients in the upper and lower level objective functions are assumed to be fuzzy random variables. To treat the considered problem, we first use the maximum performance of fuzzy random variable to tackle fuzzy random coefficients in both objective functions, and correspondingly build the lower and upper bound bilevel models for the original problem. In essential, the constructed two models are fuzzy bilevel programming problems. Then we apply the signed distance method to reduce these two models into crisp bilevel linear programming models. By the Kth best algorithm, two deterministic bilevel programming problems can be coped with, and then the lower and upper bound optimal solutions are obtained for the decision makers. Finally, a numerical example is provided in support of the proposed method.

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