A Comparison of Possibility and Probability Approaches for Modelling Poor Knowledge on Measurement Distribution

This paper deals with a fuzzy/possibility representation of measurement uncertainty that often arises in physical domains. The construction of the possibility distribution is based on the stacking up of probability coverage intervals. The paper shows that the specificity of the possibility distribution depends on the nature of the a priori information available about the entity under measurement. In particular the following commonly occurring situations reflecting different amounts of a priori information are considered: only the mode and /or the support of the underlying continuous probability distribution is known; in addition, a shape information such as symmetry and unimodality is known. The associated possibility distributions are compared to the coverage intervals obtained by using the maximum entropy principle.