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ABOUT FUZZY DATABASE QUERY LANGUAGES AND THEIR RELATIONAL COMPLETENESS THEOREM

Two fuzzy database query languages are proposed. They are used to query fuzzy databases that are enhanced from relational databases in such a way that fuzzy sets are allowed in both attribute values and truth values. A fuzzy calculus query language is constructed based on the relational calculus, and a fuzzy algebra query language is also constructed based on the relational algebra. In addition, a fuzzy relational completeness theorem such that the languages have equivalent expressive power is proved. 1. INTRODUCTION Database technology has been advanced up to the relational database stage with the purpose that user interfaces with databases may approach a level of human interfaces. It is recognized that the fuzzy theory is suitably applied to some human-oriented engineering fields, one of which is information processing , in particular database retrievals. In fact, fuzzy database models that allow fuzzy attribute values and fuzzy truth values in enhanced relational databases have been studied in [3] and [4]. However, these studies are restricted to just some particular applications and not grounded on theories of fuzzy database query languages. The fuzzy database systems would not be systematically developed on the basis of these studies; it is due to Codd's relational database theory that relational database systems have been systematically developed. It is desirable that theoretical foundations of fuzzy databases be established in order to systematically develop fuzzy database systems. There was an excelent work done in the field of the fuzzy database theory; it develops a theoretical foundation for the fuzzy functional dependencies of 219