Some Problems Related to Reducts of Consistent Incomplete Decision Tables

In multi-criteria decision making, attribute reduction has attracted the attention of researchers for more than two decades. So far, numerous scientists have proposed algorithms to construct reducts in decision tables. However, most of the suggested algorithms are heuristic which discovers a reduction based on criteria of the attribute set. In fact, studying the properties of reducts to build efficient attribute reduction models is an urgent problem. In this research, we present some properties of reducts in incomplete decision tables by the relational database theory approach. It was found that the properties of reducts in incomplete decision tables are equivalent to properties of the Sperner-systems in the theory of relational database. By studying the properties of the Sperner-systems, the efficient attribute reduction models can be built to improve the efficiency of multi-criteria decision making systems.