Similarity Measures for Relational Databases

We enrich sets with an integrated notion of similarity, measured in a (complete) lattice, special cases of which are reflexive sets and bounded metric spaces. Relations and basic relational operations of traditional relational algebra are interpreted in such richer structured environments. An canonical similarity measure between relations is introduced. In the special case of reflexive sets it is just the well known Egli-Milner ordering while in the case of bounded metric spaces it is the Hausdorff metric. Some examples of how to perform approximate searches (e.g., similarity search and relaxed answers) are given.