Generalized neighborhood systems-based pessimistic rough sets and their applications in incomplete information systems

In this paper, we point out that Lin’s general neighborhood systems-based rough set model is an extension of Qian’s optimistic rough set model, and thus called optimistic general neighborhood systmes-based rough set model. Then we present a new rough set model based on general neighborhood systems, and prove that it is an extension of Qian’s pessimistic rough set model. Later, we study the basic properties of the proposed pessimistic rough sets, and define the serial, reflexive, symmetric, transitive and Euclidean conditions for general neighborhood systems, and explore the further properties of related rough sets. Furthermore, we apply the pessimistic general neighborhood systems-based rough set model in the research of incomplete information system, and build a three-way decision model based on it. A simple practical example to show the effectiveness of our model is also presented.