In the paper, probability distribution and fuzzy system based on the triple I algorithm and modified Reichenbach operator are discussed.Firstly, the joint probability density functions of two-dimensional random variables, the marginal probability density functions and numerical characteristics are obtained by using the center of gravity defuzzifier method.Secondly, the generalized center of gravity fuzzy systems and the center of gravity fuzzy systems based on singleton fuzzier method and non-singleton fuzzier method are obtained respectively.Meanwhile, it is pointed out that the center of gravity fuzzy systems are regression functions in the sense of probability theory.Finally, we prove the fuzzy systems not only have the universal approximation but also possess the first-order approximation accuracy.