Study On Fuzzy Random Events And Its Probabilities Theory Based On Axiomatic Fuzzy Sets

Probability theory is a mathematical tool to study the probability of random events,while fuzzy set is a mathematical theory to deal with fuzzy phenomena and simulate fuzzy logic thinking of human brain.In the objective world,randomness and fuzziness often coexist in the same thing,so it has important theoretical significance and practical value to study fuzzy random events and their probability.In this paper,a probabilistic model is established,which is combined with axiomatic fuzzy sets theory and probability theory,and it solves the fuzzy random events from the global perspectives,three main aspects are as follows:First,under the axiomatic fuzzy sets theory,fuzzy random events are defined by discretization of continuous random variables based on fuzzy partition(in this paper,fuzzy random events are axiomatic fuzzy sets which is defined in the sample space of a continuous random model),then the probability measure space of fuzzy random event is established.Second,under different T-norm operator,T-conorm operator and strong negation operator,we give the multiplication formula of fuzzy random event probability,prove the total probability formula of fuzzy random event and Bayes’ formula,and discuss the relationship between the probability of fuzzy random event and classical probability.Third,under the axiomatic fuzzy sets theory,fuzzy random variable and its expectation and variance are defined based on random variable theory,and some basic properties of expectation and variance of fuzzy random variable are discussed.The definition of K fuzzy random variable based on fuzzy partition is given,and some basic properties of K fuzzy random variable are studied,which further improves and enriches fuzzy random theory.