Fuzzy/probability similar to fractal/smooth

Many applications of probability theory are based on the assumption that, a s the number of cases increase, the relative frequency of cases with a cert ain property tends to a number - probability that this property is true. L. Zadeh has shown that in many real-life situations, the frequency oscillate s and does not converge at all. It is very difficult to describe such situa tions by using methods from traditional probability theory. Fuzzy logic is not based on any convergence assumptions and therefore, provides a natural description of such situations. However, a natural next question arises: ho w can we describe this oscillating behavior? Since we cannot describe it by using a single parameter (such as probability), we need to use a multi-D f ormalism. In this paper, we describe an optimal formalism for describing su ch oscillations, and show that it complements traditional probability techn iques in the same way as fractals complement smooth curves and surfaces.