Two-stage fuzzy stochastic programming with Value-at-Risk criteria

Shuming Wang*, Junzo Watada

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    33 Citations (Scopus)


    A new class of fuzzy stochastic optimization models - two-stage fuzzy stochastic programming with Value-at-Risk (FSP-VaR) criteria is built in this paper. Some properties of the two-stage FSP-VaR, such as value of perfect information (VPI), value of fuzzy random solution (VFRS), and bounds of the fuzzy random solution, are discussed. An Approximation Algorithm is proposed to compute the VaR by combining discretization method of fuzzy variable, random simulation technique and bisection method. The convergence of the approximation algorithm is proved. To solve the two-stage FSP-VaR, a hybrid mutation-neighborhood-based particle swarm optimization (MN-PSO) which comprises the Approximation Algorithm is proposed to search for the approximate optimal solution. Furthermore, a neural network-based acceleration method is discussed. A numerical experiment illustrates the effectiveness of the proposed hybrid MN-PSO algorithm. The comparison shows that the hybrid MN-PSO exhibits better performance than the one when using other approaches such as hybrid PSO and GA.

    Original languageEnglish
    Pages (from-to)1044-1056
    Number of pages13
    JournalApplied Soft Computing Journal
    Issue number1
    Publication statusPublished - 2011 Jan


    • Fuzzy random variable
    • Fuzzy stochastic programming
    • Particle swarm optimization
    • Value of fuzzy random solution
    • Value of perfect information
    • Value-at-Risk

    ASJC Scopus subject areas

    • Software


    Dive into the research topics of 'Two-stage fuzzy stochastic programming with Value-at-Risk criteria'. Together they form a unique fingerprint.

    Cite this