On probabilistic methods in fuzzy theory

By Fuzzy theory we mean Zadeh’s mathematical theory of generalized sets and their associated logics. At this state of the art, fuzzy theory has provided significant contributions to artificial intelligence via a broader umbrella of soft computing. Like other theories of mathematics, such as number theory and potential theory, fuzzy theory has its own agenda, concepts, and techniques. However, just like number theory and potential theory, probabilistic methods can be proved to be useful for fuzzy analysis. In fact, this is somewhat plausible because fuzzy theory also aims at solving decision-making problems under complex uncertainties. In the following, because of the limited space, we will simply display the essentials of probabilistic ingredients that are useful in making fuzzy theory a quality science, i.e., providing guidelines of system designs and theoretical justifications of fuzzy inference procedures.