Summary: The modeling of problems in scientific observation has motivated the development of mathematical tools to deal with the several ways of classifying or granulating the universes of discourse: the world as it is perceived. The aim of this paper is to review and clarify various mathematical aspects related to observability problems within a classical Boolean structure or a fuzzy context. In doing so, it is shown how ideas arising in fuzzy sets theory can become fine tools to handle most of the granulating problems. In the last section we study the observability of the label “probable” viewed as a fuzzy set.
For the entire collection see [Zbl 0983.00027].