Fuzzy representation of incomplete knowledge about infinite support probability distributions in a measurement context

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 mean, or the mode of the underlying infinite support continuous probability distribution is known; in addition, a dispersion parameter and/or shape information such as symmetry and unimodality are known. The associated possibility distributions are determined from probability inequalities and represent the maximal unpresumptive distribution consistent with available knowledge. They allow to determine the impact of each piece of information on the reduction of coverage interval lengths.