In this paper, we generalize the Pearl and Neyman-Rubin methodologies in causal inference by introducing a generalized approach that incorporates fuzzy logic. Indeed, we introduce a fuzzy causal inference approach that consider both the vagueness and imprecision inherent in data, as well as the subjective human perspective characterized by fuzzy terms such as 'high', 'medium', and 'low'. To do so, we introduce two fuzzy causal effect formulas: the Fuzzy Average Treatment Effect (FATE) and the Generalized Fuzzy Average Treatment Effect (GFATE), together with their normalized versions: NFATE and NGFATE. When dealing with a binary treatment variable, our fuzzy causal effect formulas coincide with classical Average Treatment Effect (ATE) formula, that is a well-established and popular metric in causal inference. In FATE, all values of the treatment variable are considered equally important. In contrast, GFATE takes into account the rarity and frequency of these values. We show that for linear Structural Equation Models (SEMs), the normalized versions of our formulas, NFATE and NGFATE, are equivalent to ATE. Further, we provide identifiability criteria for these formulas and show their stability with respect to minor variations in the fuzzy subsets and the probability distributions involved. This ensures the robustness of our approach in handling small perturbations in the data. Finally, we provide several experimental examples to empirically validate and demonstrate the practical application of our proposed fuzzy causal inference methods.

翻译：本文通过引入一种融合模糊逻辑的广义方法，对因果推断中的Pearl与Neyman-Rubin方法论进行了推广。具体而言，我们提出了一种模糊因果推断方法，该方法同时考虑了数据固有的模糊性与不精确性，以及以“高”、“中”、“低”等模糊术语为特征的主观人类视角。为此，我们引入了两个模糊因果效应公式：模糊平均处理效应（FATE）与广义模糊平均处理效应（GFATE），及其标准化版本：NFATE与NGFATE。在处理二元处理变量时，我们的模糊因果效应公式与经典的因果推断常用指标——平均处理效应（ATE）公式一致。在FATE中，处理变量的所有取值被视为同等重要；而GFATE则考虑了这些取值的稀有性与频率。我们证明，对于线性结构方程模型（SEMs），我们公式的标准化版本（NFATE与NGFATE）与ATE等价。此外，我们为这些公式提供了可识别性准则，并证明了它们对于模糊子集及相关概率分布的微小变化具有稳定性，这确保了我们的方法在处理数据微小扰动时的稳健性。最后，我们通过多个实验案例对所提出的模糊因果推断方法进行了实证验证与实用性展示。