  This paper develops a category-theoretic approach to uncertainty,
informativeness and decision-making problems. It is based on appropriate first
order fuzzy logic in which not only logical connectives but also quantifiers
have fuzzy interpretation. It is shown that all fundamental concepts of
probability and statistics such as joint distribution, conditional
distribution, etc., have meaningful analogs in new context. This approach makes
it possible to utilize rich conceptual experience of statistics. Connection
with underlying fuzzy logic reveals the logical semantics for fuzzy decision
making. Decision-making problems within the framework of IT-categories and
generalizes Bayesian approach to decision-making with a prior information are
considered. It leads to fuzzy Bayesian approach in decision making and provides
methods for construction of optimal strategies.
