This paper considers a linear optimisation problem under uncertainty with at least one element modelled as a non-probabilistic uncertainty. The uncertainty is expressed in the coefficient matrices of constraints and/or coefficients of goal function. Previous work converts such problems to classical (linear) optimisation problems and eliminates uncertainty by converting the linear programming under uncertainty problem to a decision problem using imprecise probability and imprecise decision theory. Our aim here is to generalise this approach numerically and present three methods to calculate the solution. We investigate what numerical results can be obtained for interval and fuzzy types of uncertainty models and compare them to classical probabilistic cases — for two different optimality criteria: maximinity and maximality. We also provide an efficient method to calculate the maximal solutions in the fuzzy set model. A numerical example is considered for illustration of the results.

中文翻译：

---

非概率不确定性模型下的数值线性规划——区间和模糊集

本文考虑了不确定性下的线性优化问题，其中至少一个元素被建模为非概率不确定性。不确定性用约束的系数矩阵和/或目标函数的系数来表示。以前的工作将此类问题转换为经典（线性）优化问题，并通过使用不精确概率和不精确决策理论将不确定性问题下的线性规划转换为决策问题来消除不确定性。我们的目标是在数值上推广这种方法，并提出三种计算解决方案的方法。我们研究了对于区间和模糊类型的不确定性模型可以获得哪些数值结果，并将它们与经典概率案例进行比较——针对两种不同的最优性标准：最大值和最大值。我们还提供了一种有效的方法来计算模糊集模型中的最大解。考虑一个数值例子来说明结果。