To analyze the uncertain data frequently encountered in practice, this paper proposes novel fixed-effects models that incorporate an uncertain measure to investigate variables of interest and nuisance variables in factor designs. First, an uncertain fixed-effects (UFE) model of a single-factor design is established, and uncertain estimation and hypothesis testing are conducted. We then extend the UFE model to two-factor designs with and without interactions and classify them as balanced or unbalanced based on the equality of replicates within each combination. In the above UFE models, the effectiveness and practicality of estimation and hypothesis methods are demonstrated through three real-world cases, including both balanced and unbalanced designs. These examples highlight the models' ability to handle uncertain experimental data.

翻译：为分析实践中常见的不确定性数据，本文提出了一种融合不确定性测度的新型固定效应模型，用于研究因子设计中关注变量与干扰变量。首先，建立了单因子设计的不确定性固定效应（UFE）模型，并进行了不确定性估计与假设检验。随后将UFE模型扩展至含交互项与不含交互项的双因子设计，并根据各组合内重复试验的等值性将其划分为平衡与非平衡设计。通过三个包含平衡与非平衡设计的实际案例，验证了上述UFE模型中估计与假设检验方法的有效性与实用性。这些实例突显了该模型处理不确定性实验数据的能力。