Theoretical aspects of design of and retrieval from similarity-based relational database systems

The similarity-based relational data model originated by Buckles/Petry permits the representation of inexact information in the form of a relational database. In this dissertation, a theoretically sound definition of fuzzy functional dependency was developed. Inference rules for fuzzy functional dependencies were presented and proved to be sound and complete. The concept of a fuzzy key for similarity-based data model was developed and normal forms were defined for this data model. These developments provide the capability to incorporate the fuzzy information about the real world in the design process. To provide a higher-level query language for this data model, a complete fuzzy domain relational calculus was designed which is an extension of domain calculus for ordinary relational databases. It was proven also that for any fuzzy relational algebra expression, there is an equivalent safe formula in fuzzy domain calculus. As a first step towards more advanced query methods for the similarity-based data model, the concept of dual measure of possibility/necessity as applied to simple non-fuzzy queries for this data model was developed.