Attribute reduction for imprecise decision tables

In this paper, we investigate approaches to attribute reduction for decision tables with imprecise decision attribute values. First, we introduce imprecise decision tables, and presumable and possible decision attribute value sets. We define several meaningful object sets based on the twofold decision attribute value sets. Using those object sets, we propose value-oriented and object-oriented approaches to attribute reduction of imprecise decision tables. We show some properties of several reducts defined by the approaches. These properties help the selection of reducts suitable for the problem and analyst preference. A numerical example is given.