Integrating Fuzzy Logic with Causal Inference: Enhancing the Pearl and Neyman-Rubin Methodologies
This work addresses the challenge of handling subjective and imprecise data in causal inference for researchers and practitioners, representing an incremental advancement by extending existing methods with fuzzy logic.
The paper tackles the problem of vagueness and imprecision in causal inference by integrating fuzzy logic into Pearl and Neyman-Rubin methodologies, introducing fuzzy causal effect formulas like FATE and GFATE, and showing their equivalence to classical ATE in linear SEMs with robustness to data perturbations.
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.