Two kinds of fuzziness in attribute values of the fuzzy relational databases can be distinguished: One is that attribute values are possibility distributions, and the other is that there are resemblance relations in attribute domains. The fuzzy relational databases containing these two kinds of fuzziness simultaneously are called extended possibility-based fuzzy relational databases. In this paper, we focus on such fuzzy relational databases. We classify two kinds of fuzzy data redundancies and define their removal. On this basis, we define fuzzy relational operations in relational algebra, which, being similar to the conventional relational databases, are complete and sound. In particular, we investigate fuzzy querying strategies and give the form of fuzzy querying with SQL.

Based on the semantic equivalence degree the formal definitions of fuzzy functional dependencies (FFDs) and fuzzy multivalued dependencies (FMVDs) are first introduced to the fuzzy relational databases, where fuzziness of data appears in attribute values in the form of possibility attributions, as well as resemblance relations in attribute domain elements, called extended possibility-based fuzzy relational databases. A set of inference rules for FFDs and FMVDs is then proposed. It is shown that FFDs and FMVDs are consistent and the inference rules are sound and complete, just as Armstrong's axioms for classic cases.

No abstract