A New Solution Method for a Class of Fuzzy Random Bilevel Programming Problems
This paper investigates a kind of bilevel programming with fuzzy random variable coefficients in both objective functions and the right hand side of constraints. On the basis of the notion of Er-expected value of fuzzy random variable, the upper and lower level objective functions can be replaced with their corresponding Er-expected values. In terms of probability over defuzzified operator, fuzzy stochastic constraints can be converted into the equivalent forms. Based on these, the fuzzy random bilevel programming problem can be transformed into its deterministic one. Then we suggest differential evolution algorithm to solve the final crisp problem. Finally, a numerical example is given to illustrate the proposed method.
KeywordsBilevel programming Fuzzy random variable Er-expected value of fuzzy random variable Differential evolution algorithm
This work was supported by the National Natural Science Foundation of China (Grant No.61602010), Natural Science Basic Research Plan in Shaanxi Province of China (Grant No.2017JQ6046) and Science Foundation of Baoji University of Arts and Sciences (Grant No.ZK16049).
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