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A method based on crisp possibilistic mean value for solving fuzzy random bilevel programming problem. (Chinese. English summary) Zbl 1424.90247

Summary: A kind of bilevel programming problem involving fuzzy random variable coefficients in both objective functions and constraint functions is considered. Based on the notion of the expectation of a fuzzy random variable, the fuzzy random bilevel programming problem is converted into a fuzzy bilevel programming problem. Subsequently, the crisp possibilistic mean value of a fuzzy number is used to defuzzy the upper and lower level objective functions and fuzzy chance constrained method based on possibility is applied to handle fuzzy constraint functions, and then a fuzzy random bilevel crisp possibilistic mean value-chance constrained programming model is developed. Then the crisp equivalent model is given and the \(K\)-th best algorithm is employed to deal with it. Finally, numerical examples testify the feasibility of the proposed method.

MSC:

90C29 Multi-objective and goal programming
90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
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