In this paper, a Stieltjes integral approximation method for uncertain variational inequality problem (UVIP) is studied. Firstly, uncertain variables are introduced on the basis of variational inequality. Since the uncertain variables are based on nonadditive measures, there is usually no density function. Secondly, the expected value model of UVIP is established after the expected value is discretized by the Stieltjes integral. Furthermore, a gap function is constructed to transform UVIP into an uncertain constraint optimization problem, and the optimal value of the constraint problem is proved to be the solution of UVIP. Finally, the convergence of solutions of the Stieltjes integral discretization approximation problem is proved.

中文翻译：

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不确定变量变分不等式的一种逼近方法

本文研究了不确定变分不等式问题(UVIP)的Stieltjes积分逼近方法。首先，在变分不等式的基础上引入不确定变量。由于不确定变量基于非加性测量，因此通常没有密度函数。其次，对期望值进行Stieltjes积分离散化后，建立了UVIP的期望值模型。进而构造间隙函数将UVIP转化为不确定约束优化问题，证明约束问题的最优值就是UVIP的解。最后证明了Stieltjes积分离散化近似问题解的收敛性。