2022/05/30 by Amir Saki, Saki, Amir, Usef Faghihi +1
Computer Science · Decision Sciences · #00A106 #00A30 #03E72 #60A10 #60A86 #Artificial Intelligence (cs.AI) #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #FOS: Mathematics #G.3 #I.2.3 #Logic in Computer Science (cs.LO) #Multi-Criteria Decision Making #Probability (math.PR) #Rough Sets and Fuzzy Logic
paper · pdf · doi:10.48550/arxiv.2205.15016
openalex publication_date 2022/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.