Distributional Representations of Random Interval Measurements

The measurement of set-valued and interval data is considered. Their random interval mathematical representations are introduced. The conditions for distributional (probabilistic and possibilistic) representations and conversions to and among them are established. Some properties of empirical random sets and possibilistic histograms related to strong probabilistic compatibility are described. Finally, the nature of probability distributions which are strongly stochastically compatible with a given possibility distribution, and the derivation of frequency distributions from empirical random sets, are discussed.