Information structures in an incomplete real-valued information system

An information system as a database that shows relationships between objects and attributes is a crucial mathematical model in the field of artificial intelligence. A real-valued information system is an information system where information function values of each attribute are real numbers. This paper explores information structures in an incomplete real-valued information system. Distances between two objects in a given subsystem of an incomplete real-valued information system is first constructed. Then, the fuzzy T-cos-equivalence relation, induced by this subsystem by using Gaussian kernel method, is obtained, where Gaussian kernel is based on this distance. Next, information structure of this subsystem is proposed. Moreover, relationships between two information structures are studied from the two aspects of dependence and separation. Finally, the dependence between two information structures is studied by using inclusion degree. These results will be helpful for establishing a framework of granular computing.