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.