Informativity in the Category of Multivalued Information Transformers

Consideration is given to the information transformers described by multivalued mappings. The paper focuses on the study of informativity. The classes of equivalent informativity are shown to form a partially ordered Abelian monoid which is isomorphic to the special family of coverings of some set. Another approach to comparing information transformers is based on the concept of the abstract problem of decision making. The concept of semantical informativity stems from this approach. It is shown that one information transformer is more informative than another one if and only if it provides a higher quality in any decision-making problem.