A Principle of Uncertainty and Information Invariance*

The paper introduces a new principle, referred to as the principle of uncertainty and information invariance, for making transformations between different mathematical theories by which situations under uncertainty can be characterized. This principle requires that the amount of uncertainty (and related information) be preserved under these transformations. The principle is developed in sufficient details for transformations between probability theory and possibility theory under interval, log-interval and ordinal scales. Its broader use is discussed only in general terms and illustrated by an example.