A Fundamental Probabilistic Fuzzy Logic Framework Suitable for Causal Reasoning

• URL: http://arxiv.org/abs/2205.15016v1
• Date: Mon, 30 May 2022 11:59:35 GMT
• Title: A Fundamental Probabilistic Fuzzy Logic Framework Suitable for Causal Reasoning
• Authors: Amir Saki and Usef Faghihi
• Abstract summary: We introduce a fundamental framework to create a bridge between Probability and Fuzzy Logic. Our theory formulates a random experiment of selecting crisp elements with the criterion of having a certain fuzzy attribute. Several formulas are presented, which make it easier to compute different conditional probabilities and expected values of random variables.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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