Causal discovery for fuzzy rule learning

Lucie Kunitomo-Jacquin, Aurore Lomet, Jean-Philippe Poli

Abstract: In this paper, we focus on allying fuzzy logic, which is a suitable model for human-like information, and causality, which is a key concept for humans to generate knowledge from observations and to build explanations. If a fuzzy premise causes a fuzzy consequence, then acting on the fuzzy premise will have an impact on the fuzzy consequence. This is not necessarily the case for common fuzzy rules whose induction is based on correlation. Indeed, correlations may be due to some latent common cause of fuzzy premise and consequence. In this case, a change in the value of the fuzzy premise may not affect the fuzzy consequence as it should. We propose an approach to construct a set of causality-based fuzzy rules from crisp observational data. The idea is to identify causal relationships on the set of fuzzified inputs and outputs by well-known constraints-based causal discovery algorithms such as Peter-Clark and Fast Causal Inference. The causal discovery algorithms are combined with entropy-based conditional independent testing that avoids making hypotheses on the data distribution. Experiments are conducted to evaluate our approach in terms of ability to recover causal relationships between fuzzy sets in the presence of a latent common cause. The results illustrate the interest of our approach compared to a correlation-based approach and state-of-the-art approaches.