Fuzzy to Random Uncertainty Alignment

The objective of this paper is to present new and simple mathematical approach to deal with uncertainty alignment between fuzzy and random data. In particular we present a method to describe fuzzy (possibilistic) distribution in terms of a pair (or more) of related random (probabilistic) events, both fixed and variable. Our approach uses basic properties of both fuzzy and random distributions. We show that the data fuzziness can be viewed as a non uniqueness of related random events. We also show how fuzzy-random consistancy principle can be given precise mathemtaical meaning. Various types of fuzzy distributions are examined, special cases considered, and several numerical examples presented