ABSTRACT
In real world application of fuzzy sets, an important task is to determine membership functions of the fuzzy sets in question. In this chapter, the authors discuss how to determine a membership function of a fuzzy set. The main distinction between random phenomena and fuzzy phenomena is that random events themselves have clear and well-defined meaning, whereas a fuzzy concept does not have a precise extension because it is hard to judge if an object belongs to the concept. Probability theory applies the random concept to generalized laws of causality-laws of probability. Fuzzy set theory applies the fuzzy property to the generalized law of the excluded middle-the law of membership from fuzziness. In many cases, the degree of membership can be determined by fuzzy statistical methods. Very often in a multiphase fuzzy statistical experiment, participants have difficulty declaring the highest degree of membership of objects being evaluated.
