Information Structures in an Ordered Information System Under Granular Computing View and Their Optimal Selection Based on Uncertainty Measures

Information structures ( i -structures) in an ordered information system (OIS) are mathematical structures of the information granules ( i -granules) granulated from the data set of this OIS. This article investigates i -structures in an OIS with granular computing (GrC) view, i.e., i -structures in an OIS are seen as granular structures. Dependence and independence between i- structures are first depicted in the same OIS. Then, information distance ( i -distance) between i -structures in the same OIS are proposed, and information entropy in an OIS can be expressed by i -distance between i -structures in this OIS is proved. Next, properties of i -structures in an OIS are shown. Moreover, group, lattice and map characters of i -structures in an OIS are received, and some invariant characters of i -structures in an OIS under homomorphisms are obtained. Finally, the optimal selection of i -structures in an OIS based on the proposed measures are studied. These results will contribute to build a framework of GrC in an OIS.