Probability density function and fuzzy system based on a set of input - output data

Abstract

Based on a set of input - output data, we first build a joint probability density function of certain two-dimensional random variables utilizing fuzzy inference rules, then propose its marginal probability density function and numerical characteristics. Finally, it is pointed out that the fuzzy system constructed with center of gravity defuzzifier is a regression function in the sense of probability theory and has the first-order approximation accuracy.