Set-valued And Interval-valued Information Systems Based On Ordered Concentration

In order to study the incomplete information system, Zhang Wenxiu et al establish the set-valued information system model and the interval-valued information system model, also translate the incomplete information system into the set-valued information system and interval-valued information system to handle. The set-valued information system and interval-valued information system are both extended models of single-valued information system. An important characteristic of information systems is that information is always preference ordering. According to the preference of the decision maker a dominance relation attribute always exists. Therefore, research on set-valued information system and interval-valued information system’s dominance relation in information system is of great significance to expand the application of rough sets theory.For the treatment of preference information, we describe dominance relation mainly from two aspects:attribute increasing preference order and attribute decreasing preference order. However, these two kinds of definition methods can not deal with some practical problems. For example, health diagnosis for patients of the indicator-temperature, which is not the higher the better, and not the lower the better, but is more closer to the normal temperature of the human body as possible. Therefore, this paper focuses on a new attribute preference relation and establishes a new dominance relation. This new dominance relation can represent a kind of attribute preference which is not the increasing preference order and not the decreasing preference order, but the condition attribute values tend to the standard values of attribute, such dominance relation is called as attribute ordered concentration. And then the attribute set ordered relation respectively is applied in set-valued information system and interval-valued information system, because the set-valued information system’s attribute values have the conjunction and disjunction, so in the set-valued information system two cases are considered. We construct different attribute ordered concentration models in different information systems, their definitions are given, at the same time, we give the corresponding dominance relation and dominance class, followed up with their respective properties theorem are given and proved. At last we give a detailed analysis for the examples.