The principle of possibility maximum specificity as a basis for measurement uncertainty expression

This paper deals with the foundations of a possibility/fuzzy expression of measurement uncertainty. Indeed the notion of possibility distribution is clearly identified to a family of probability distributions whose coverage intervals are included in the level cuts of the possibility distribution Thus the fuzzy inclusion ordering, dubbed specificity ordering, constitutes the basis of a maximal specificity principle. The latter is sounder than the maximal entropy principle to deal with cases of partial or incomplete information in a measurement context. The two approaches can be compared on some common practical measurement cases thanks to the respective coverage intervals they provide.

I. Introduction

In very many cases, the obj ective of uncertainty evaluation is to determine a coverage interval (or coverage region) for the measurement result. Commonly, this coverage interval will be for a 95 % coverage probability, an interval that is expected to contain 95 % of the values that could be attributed to the output quantity. There is no compelling scientific reason for this choice. It almost certainly stems from the traditional use of 95 % in statistical hypothesis testing, although the reasons for the choice in that area are very different. The overriding reason for the use of 95 % in uncertainty evaluation is a practical one [1]. It has become so well established that for purpose of comparison with other results its use is almost mandated.