L-fuzzifying approximation operators derived from general L-fuzzifying neighborhood systems

A further study on generalized neighborhood systems-based pessimistic rough sets

The generalized neighborhood system-based rough set is an important extension of Pawlak’s rough set. The rough sets based on generalized neighborhood systems include two basic models: optimistic and pessimistic rough sets. In this paper, we give a further study on pessimistic rough sets. At first, to regain some properties of Pawlak’s rough sets that are lost in pessimistic rough sets, we introduce the mediate, transitive, positive (negative) alliance conditions for generalized neighborhood systems. At second, some approximation operators generated by special generalized neighborhood systems are characterized, which include serial, reflexive, symmetric, mediate, transitive, and negative alliance generalized neighborhood systems and their combinations (e.g. reflexive and transitive). At third, we discuss the topologies generated by the upper and lower approximation operators of the pessimistic rough sets. Finally, combining practical examples, we apply pessimistic rough sets to rule extraction of incomplete information systems. Particularly, we prove that different decision rules can be obtained when different neighborhood systems are chosen. This enables decision makers to choose decisions based on personal preferences.

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.