Name
Abstract | ||
|---|---|---|
A special class of neighborhood systems, called 1-neighborhood systems, are important in rough set theory. By using a concept “core” originated in general topology, we define two types of rough sets based on 1-neighborhood systems in this paper. We discuss properties of these rough sets from the perspective of both common 1-neighborhood systems and several special classes of 1-neighborhood systems, such as reflexive, symmetric, transitive, or Euclidean 1-neighborhood systems. By using these properties, we discuss the relationship among several classes of 1-neighborhood systems with various special properties. We give a necessary and sufficient condition for a reflexive and symmetric 1-neighborhood system being a unary. We also prove that a reflexive and transitive 1-neighborhood system is representative. The proofs of these results show that the rough sets we defined in this paper not only have application background, but also have theoretic importance. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1016/j.ins.2013.06.031 | Information Sciences |
Keywords | Field | DocType |
1-Neighborhood system,Core,Minimal description,Unary,Representative | Reflexivity,Discrete mathematics,General topology,Unary operation,Rough set,Mathematical proof,Euclidean geometry,Mathematics,Dominance-based rough set approach,Transitive relation | Journal |
Volume | Issue | ISSN |
248 | null | 0020-0255 |
Citations | PageRank | References |
3 | 0.39 | 17 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Zuoming Yu | 1 | 46 | 4.22 |
| Xiaole Bai | 2 | 1094 | 57.04 |
| Ziqiu Yun | 3 | 557 | 23.69 |