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.

Let $X$ and $Z$ be random vectors, and $Y=g(X,Z)$. In this paper, on the one hand, for the case that $X$ and $Z$ are continuous, by using the ideas from the total variation and the flux of $g$, we develop a point of view in causal inference capable of dealing with a broad domain of causal problems. Indeed, we focus on a function, called Probabilistic Easy Variational Causal Effect (PEACE), which can measure the direct causal effect of $X$ on $Y$ with respect to continuously and interventionally changing the values of $X$ while keeping the value of $Z$ constant. PEACE is a function of $d\ge 0$, which is a degree managing the strengths of probability density values $f(x|z)$. On the other hand, we generalize the above idea for the discrete case and show its compatibility with the continuous case. Further, we investigate some properties of PEACE using measure theoretical concepts. Furthermore, we provide some identifiability criteria and several examples showing the generic capability of PEACE. We note that PEACE can deal with the causal problems for which micro-level or just macro-level changes in the value of the input variables are important. Finally, PEACE is stable under small changes in $\partial g_{in}/\partial x$ and the joint distribution of $X$ and $Z$, where $g_{in}$ is obtained from $g$ by removing all functional relationships defining $X$ and $Z$.

In this paper, we introduce a new causal framework capable of dealing with probabilistic and non-probabilistic problems. Indeed, we provide a direct causal effect formula called Probabilistic vAriational Causal Effect (PACE) and its variations satisfying some ideas and postulates. Our formula of causal effect uses the idea of the total variation of a function integrated with probability theory. The probabilistic part is the natural availability of changing an exposure values given some variables. These variables interfere with the effect of the exposure on a given outcome. PACE has a parameter $d$ determining the degree of considering the natural availability of changing the exposure values. The lower values of $d$ refer to the scenarios for which rare cases are important. In contrast, with the higher values of $d$, our framework deals with the problems that are in nature probabilistic. Hence, instead of a single value for causal effect, we provide a causal effect vector by discretizing $d$. Further, we introduce the positive and negative PACE to measure the positive and the negative causal changes in the outcome while changing the exposure values. Furthermore, we provide an identifiability criterion for PACE to deal with observational studies. We also address the problem of computing counterfactuals in causal reasoning. We compare our framework to the Pearl, the mutual information, the conditional mutual information, and the Janzing et al. frameworks by investigating several examples.

Computer scientists use causal inference for reasoning. In causal inference, researchers are interested in finding the relationship between two observable events. In this paper, we will explore the first step towards finding causality using probabilistic fuzzy logic (PFL). We will also show that PFL is more precise than Pearl’s causality model.

In this paper we propose the CTS (Concious Tutoring System) technology, a biologically plausible cognitive agent based on human brain functions.This agent is capable of learning and remembering events and any related information such as corresponding procedures, stimuli and their emotional valences. Our proposed episodic memory and episodic learning mechanism are closer to the current multiple-trace theory in neuroscience, because they are inspired by it [5] contrary to other mechanisms that are incorporated in cognitive agents. This is because in our model emotions play a role in the encoding and remembering of events. This allows the agent to improve its behavior by remembering previously selected behaviors which are influenced by its emotional mechanism. Moreover, the architecture incorporates a realistic memory consolidation process based on a data mining algorithm.