A Fundamental Probabilistic Fuzzy Logic Framework Suitable for Causal Reasoning
This foundational work addresses the integration of probability and fuzzy logic for causal reasoning, but appears incremental as it builds on existing concepts.
The paper introduces a probabilistic fuzzy logic framework that bridges probability theory and fuzzy logic by formulating random experiments based on fuzzy attributes, with applications in causal inference.
In this paper, we introduce a fundamental framework to create a bridge between Probability Theory and Fuzzy Logic. Indeed, our theory formulates a random experiment of selecting crisp elements with the criterion of having a certain fuzzy attribute. To do so, we associate some specific crisp random variables to the random experiment. Then, several formulas are presented, which make it easier to compute different conditional probabilities and expected values of these random variables. Also, we provide measure theoretical basis for our probabilistic fuzzy logic framework. Note that in our theory, the probability density functions of continuous distributions which come from the aforementioned random variables include the Dirac delta function as a term. Further, we introduce an application of our theory in Causal Inference.