Stochastic Dominance-based Interval-valued Information Systems

Nowadays, rough set theory including theoretical research and applied research has a quick devel-opment. While with the further study of applied research, classical rough set theory and the extended research of information systems have being paid attention by many scholars. Interval-valued infor-mation systems, the basic tool to express and deal with knowledge in rough set theory, abound in practical problems. Therefore, a-stochastic dominance-based interval-valued information systems will be discussed in this paper.Firstly, the concept of stochastic dominance relation is recommended, and the stochastic dominance-based complete and incomplete information systems are proposed; so the a-stochastic dominance-based information systems are constructed by introducing Levy distance. Secondly, the incremental updating of object set and attribute set is discussed, meanwhile the database dynamic maintenance in rough set theory is partly studied. Thirdly, the stochastic dominance-based informa-tion decision-making systems are introduced and the difference between these information systems and the usual decision-making information systems is explained as well. Then a way calculating each object’s superiority or inferiority under a decision is presented. Lastly, stochastic dominance-based interval-valued information systems are partitioned according to the span of the interval. And the computing procedure of dominance classes in sorted interval-valued information systems is illustrated by an example.