New uncertainty measurement for hybrid data and its application in attribute reduction

Due to limitations in data acquisition, data in real life often contains a wealth of uncertain information. Uncertainty measurement (UM) constructed within the framework of rough set theory (RST) is an important tool for processing uncertain information. Some basic UMs in RST such as classification precision, rough membership degree, dependence degree, and attribute importance cannot accurately measure the uncertainty of a hybrid information system (HIS). For example, dependence degree only considers the information provided by the lower approximation of the decision and ignores the upper approximation, which may lead to some information loss. In addition to these basic UMs, some extended entropy-based UMs such as rough entropy, information entropy and conditional entropy are also frequently used to measure the uncertainty of a HIS. However, these three UMs also have their own drawbacks. For instance, rough entropy is sensitive to the distribution of hybrid data. When the distribution of hybrid data is uneven, the calculation results of rough entropy may be greatly affected, leading to a decrease in measurement accuracy. This paper proposes four new UMs in a HIS and provides an application in attribute reduction. First of all, a distance function is defined to deal with each type of attribute in a HIS and construct a tolerance relation. On this basis, four UMs are listed to measure the uncertainty of a HIS. Next, the strength and weakness of the proposed UMs are verified by statistical analysis. Subsequently, the UM with the best performance is selected to design an attribute reduction algorithm. Finally, the designed algorithm is compared with other five attribute reduction algorithms to show its superior performance.