Relational Database Schema Design for Uncertain Incomplete Data

Abstract

Due to the development of big data and IoT, modern application are suffered from the incomplete and inaccuracy problem. But traditional relation schema design is not able to handle those problems properly, so it is necessary to establish a general framework to meet the completeness and accuracy requirement of application. Assume every tuple have a possibility degree with which they occur in relation, every functional dependency have a certainty degree which says to which tuples they apply. We develop a new notion of functional dependency called embedded possibilistic functional dependency (epFD) for our new framework, it contains certainty degree and do not need to define the semantic of NULLs. We also develop axiomatic, algorithm characterization and logical foundations for the implication problem of epFD. These allow us to detect the redundancy caused by our new functional dependency. So naturally, we establish variants of classical Boyce-Codd Normal Forms (BCNF) and Third Normal Forms (3NF) to deal with redundancy. BCNF eliminate all data redundancy but not dependency-preserving while 3NF is dependency-preserving with minimal redundancy. Then we show how to transform a given schema into a desired schema for application, which meet the requirement of completeness and accuracy, and the condition of generalized normal forms. Thus, the new schema can fit the purpose of design.