A New Solution Method for a Class of Fuzzy Random Bilevel Programming Problems

  • Aihong RenEmail author
  • Xingsi Xue
Conference paper
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 81)


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.


Bilevel 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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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsBaoji University of Arts and SciencesBaojiChina
  2. 2.College of Information Science and EngineeringFujian University of TechnologyFuzhouChina
  3. 3.Fujian Provincial Key Laboratory of Big Data Mining and ApplicationsFujian University of TechnologyFuzhouChina

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