Information structures and uncertainty measures in a fully fuzzy information system

An information system is an important model in the field of artificial intelligence and its information structures mean a mathematical structure of the family of information granules granulated from a data set. Uncertainty measurement is a critical evaluating tool. This paper investigates information structures and uncertainty measures in a fully fuzzy information system. A class-consistent relation on the set of objects in a fully fuzzy information system is first proposed, information granules are structured based on this relation and information structures are described through vectors that consists of information granules. Then, dependence between information structures in the same fully fuzzy information system is depicted from two aspects and information distance for calculating the difference between information structures is defined. Next, properties of information structures in fully fuzzy information systems are given by using inclusion degree, condition information amount, information distance and lower approximation operator. Moreover, group, mapping and lattice characterizations of information structures in fully fuzzy information systems are obtained. Finally, as an application for information structures in a fully fuzzy information system, measuring its uncertainty is investigated. These results will be very helpful for establishing a framework of granular computing in information systems.