During the flotation process, a fuzzy distributional chance-constrained programming approach is proposed to design the circuit structure, equipment size and operating conditions considering stochastic and epistemic uncertainties. Stochastic uncertainties are irreducible, such as fluctuations in copper price and circuit feed mass flowrate, and epistemic uncertainties are due to the complicated flotation mechanism. To achieve the probability measure in the chance constraints, a finite number of scenarios are defined for the stochastic uncertainties by using discrete probability distribution sets. Moreover, the epistemic uncertainties are handled by fuzzy sets. In this context, a fuzzy probability-box of profits combining probability theory with fuzzy theory can be obtained to assess the distribution profile. The integral whole optimization of the flotation process is solved by using a rule-oriented genetic algorithm, adapted from the non-dominated sorting genetic algorithm (NSGA-II), and the design rules are embedded in initialization, crossover and mutation. Finally, the sensitivity analysis of epistemic uncertainties on the optimal designs is carried out to get the critical uncertain variable. The method proposed here can fully reflect the flexibility of the process design under mixed uncertainties, and the optimal designs are compromise solutions that take into account the economic indicator and uncertainty quantification.

在浮选过程中，提出了一种基于随机和认知不确定性的模糊分布机会受限编程方法来设计电路结构，设备尺寸和工作条件。随机不确定性是无法避免的，例如铜价和线路进料质量流量的波动，而认知不确定性则是由复杂的浮选机制引起的。为了在机会约束中实现概率测度，通过使用离散概率分布集为随机不确定性定义了有限数量的场景。此外，认知不确定性由模糊集处理。在这种情况下，可以获得将概率理论与模糊理论相结合的利润的模糊概率盒，以评估分配曲线。浮选过程的整体优化是通过使用面向规则的遗传算法（从非支配排序遗传算法（NSGA-II）改编而来的）解决的，并且将设计规则嵌入到初始化，交叉和变异中。最后，对最优设计的认知不确定性进行敏感性分析，得出关键不确定性变量。本文提出的方法可以充分反映混合不确定性条件下工艺设计的灵活性，而最佳设计是兼顾经济指标和不确定性量化的折衷解决方案。对优化设计的认知不确定性进行敏感性分析，得到关键不确定性变量。本文提出的方法可以充分反映混合不确定性条件下工艺设计的灵活性，而最佳设计是兼顾经济指标和不确定性量化的折衷解决方案。对优化设计的认知不确定性进行敏感性分析，得到关键不确定性变量。本文提出的方法可以充分反映混合不确定性条件下工艺设计的灵活性，而最佳设计是兼顾经济指标和不确定性量化的折衷解决方案。