Relational algebra for multi-ranked similarity-based databases

We present multi-ranked relational model of data which extends the classic Codd's model by considering similarity relations on domains and ranks assigned to values of tuples. The ranks represent degrees to which values in tuples match similarity-based queries. Unlike various single-ranked similarity-based database models where ranks are assigned to whole tuples, in the present model the ranks are assigned to tuple values. As a consequence, the multi-ranked model allows users to directly observe how values in tuples contribute to results of similarity-based queries. We present foundations of the model, relational operations and relational algebra as the primary query language, and its relationship to single-ranked models which have been used in the past. We argue that the multi-ranked model is more suitable for applications in which data analysts require a finer view on results of queries than in the single-ranked model.