Information granules and entropy theory in information systems

Information granulation and entropy theory are two main approaches to research uncertainty of an information system,which have been widely applied in many practical issues. In this paper,the characterizations and representations of infor-mation granules under various binary relations are investigated in information systems,an axiom definition of information granulation is presented,and some existing definitions of information granulation become its special forms. Entropy theory in information systems is further developed and the granulation monoton-icity of each of them is proved. Moreover,the complement relationship between information granulation and entropy is established. This investigation unifies the results of measures for uncertainties in complete information systems and incom-plete information systems.