  Shannon entropy was defined for probability distributions and then its using
was expanded to measure the uncertainty of knowledge for systems with complete
information. In this article, it is proposed to extend the using of Shannon
entropy to under-defined or over-defined information systems. To be able to use
Shannon entropy, the information is normalized by an affine transformation. The
construction of affine transformation is done in two stages: one for homothety
and another for translation. Moreover, the case of information with a certain
degree of imprecision was included in this approach. Besides, the article shows
the using of Shannon entropy for some particular cases such as: neutrosophic
information both in the trivalent and bivalent case, bifuzzy information,
intuitionistic fuzzy information, imprecise fuzzy information, and fuzzy
partitions.
