Affiliations: [a] Department of Information Management, National Formosa University, Huwei 63201, Yunlin, Taiwan | [b] Department of Mathematics, Central Michigan University, Mt. Pleasant, Michigan 48859, USA | [c] Institute of Information Science, Academia Sinica, Nankang 115, Taipei, Taiwan. liaucj@iis.sinica.edu.tw
Correspondence:
[†]
Address for correspondence: Institute of Information Science, Academia Sinica, Nankang 115, Taipei, Taiwan.
Note: [*] This work was carried out while the first author was visiting the Institute of Information Science, Academia Sinica, Taiwan.
Abstract: The notions of approximation and definability in classical rough set theory and their generalizations have received much attention. In this paper, we study such generalizations from the perspective of neighborhood systems. We introduce four different types of definability, called interior definability, closure definability, interior-closure (IC) definability, and weak IC definability respectively. We also point out the relationship between IC definability and other types of definability for some special kinds of neighborhood systems. Several examples are presented to illustrate the concepts introduced in this paper.
