An interval programming approach for bilevel linear programming problem with fuzzy random coefficients

In the real world, many decision making problems often need to be modeled as a class of bilevel programming problems where fuzzy random coefficients are contained in both objective functions and constraint functions. To deal with these problems, an interval programming approach based on the α-level set is proposed to determine the optimal value range containing the best and worst optimal values so as to provide more information for decision makers. Furthermore, by incorporating expectation optimization model into probabilistic chance constraints, the best and worst optimal problems are transformed into deterministic ones. In addition, an estimation of distribution algorithm is designed to derive the best and worst Stackelberg solutions. Finally, a numerical example is given to show the application of the proposed models and algorithm.