Attribute Reduction Of Interval-valued Information System Based On Fuzzy Discernibility Matrix

In an information system, every attribute represent certain ability to distinguish or classify the objects of universe. The attribute set often include some redundant information, so it has become an important topic to find out a minimal attribute set that can keep the complete sorting information. Z. Pawlak proposed rough sets theory which can perfectly deal with the complete information system based on equivalence relation. Other information systems can't be solved directly with rough sets, so a lot of extent rough set theories are proposed to solve these incomplete information systems.In practical situations, we can hardly measure the value of object properties precisely. Instead, we can tell the precise values are most probably in an interval, so it is necessary to do some research on interval information systems. Existing methods include partial order relation rough set model, compatibility relation rough sets model and so on. The former can't be used widely because intervals seldom include each other. In the latter model, the similarity measurement is defined based on the overlapping of intervals.In this paper, we proposes a new method to measure the similarity of two interval values, this measurement is based on physical measuring and error processing theory, so it is more reasonable than original methods. Based on this, we introduce a new method of attributes reduction with fuzzy discernibility matrix. We also discuss a discretization argument of the similarity measurement function, which helps to improve the system robustness.