Minimal information loss possibilistic approximations of random sets

The authors suggest an empirical measuring procedure which yields data governed by possibility theory. Such methods are needed in order to apply possibility theory successfully to the study of physical systems. Set-based statistics are used to generate empirically derived random sets. Normal possibility distributions are available for all consistent random sets, and a set of consistent transformations is available for all inconsistent random sets. The principle of uncertainty invariance is used in a modified form to select the consistent transformation with minimal information loss from the original random set