In this thesis we study a particular rank-aware relational model over domains with similarities. The model results by generalization of the classical relational model of data by considering residuated lattice (instead of the two-element Boolean algebra) as the basic structure of truth values. We first focus on similarity-based functional dependencies within the model and compare them with other approaches. We also present a~graph-based method of inference and show its application in closures computing. We further study the sensitivity issues and answer questions related to similarity-preservation. We show that the similarity of query results can be estimated from similarity of input data for arbitrary complex queries.