Data Tables with Similarity Relations: Functional Dependencies, Complete Rules and Non-redundant Bases

We study rules \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$A \Longrightarrow B$\end{document} describing attribute dependencies in tables over domains with similarity relations. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$A \Longrightarrow B$\end{document} reads “for any two table rows: similar values of attributes from A imply similar values of attributes from B”. The rules generalize ordinary functional dependencies in that they allow for processing of similarity of attribute values. Similarity is modeled by reflexive and symmetric fuzzy relations. We show a system of Armstrong-like derivation rules and prove its completeness (two versions). Furthermore, we describe a non-redundant basis of all rules which are true in a data table and present an algorithm to compute bases.