Functional dependencies revisited under graduality and imprecision

In the database area, the notion of data property has been recognized for two main purposes: data control when the property is a constraint; and knowledge discovery when the property is the result of a mining process. Among the properties, functional dependencies (FD) have received special attention for many years, since they are connected with database design. Different extensions of functional dependencies have been proposed but the semantics sometimes remains obscure. This paper discusses the semantics of basic extensions of a functional dependency when fuzzy sets (and/or possibility) theory is used. The case of a relational database where tuples may contain imperfectly known values is specifically investigated.