Information structures in a lattice-valued information system

Abstract

An information system as a database that represents relationships between objects and attributes is an important mathematical model in the field of artificial intelligence. A lattice-valued information system is the generalization of an information system. Its information structures are mathematical structures of the families of information granules granulated from its data sets. This paper explores information structures in a lattice-valued information system. The concept of information structures in a lattice-valued information system is first introduced by set vectors. Then, dependence, partial dependence, and independence between two information structures are proposed. Next, information distance between two information structures is studied. Moreover, properties of information structures are given. Finally, group, lattice, and mapping characterizations of information structures are obtained. These results will be helpful for building a framework of granular computing in lattice-valued information systems.