A complete set of fuzzy relational algebraic operators in fuzzy relational databases

Relational algebra is the theoretical basis of database design and queries. This paper extends our efforts on fuzzy relational algebraic operations under the so-called extended possibility-based data representation framework. With a more general setting of the division operator (÷´), a complete set of fuzzy algebraic operators {∪, ×, -, σ, Π} is obtained, which can be proven and used to formulate other operators such as ∩, ÷´, and others. Like in the classical database model, this is important and desirable for designing fuzzy query languages.