Affiliations: [a] School of Mathematics and Statistics, Hunan University of Commerce, Changsha, P.R.China
| [b] School of Mathematics and Statistics, Yulin Normal University, Yulin, P.R.China
Correspondence:
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Corresponding author. Jiali He, School of Mathematics and Statistics, Yulin Normal University, Yulin 537000, P.R.China. E-mail: jialihe100@126.com.
Note: [1] This work is supported by Natural Science Foundation of Guangxi (2018GXNSFDA294003, 2018GXNSFAA294134) and Excellent Youth Foundation of Hunan Provincial Department of Education (16B141).
Abstract: A set-valued information system is the generalization of a single-valued information system and its information structures reflect the internal features of this kind of information system. This paper investigates information structures in a set-valued information system from granular computing viewpoint, i.e., information structures are viewed as granular structures. The distance between two objects in a set-valued information system is first introduced. Then, the fuzzy Tcos-equivalence relation, induced by this kind of information system by using Gaussian kernel method, is obtained, where Gaussian kernel is based on this distance. Next, information structures of this kind of information system are described by set vectors. Moreover, relationships between information structures are studied from two sides of dependence and separation. Finally, as a simple application for the proposed information structures, granularity measure of uncertainty for a set-valued information system is investigated. These results will be helpful for establishing a framework of granular computing in an information system.
Keywords: Set-valued information system, granular computing, distance, information
granule, information structure, dependence, information distance, inclusion degree, entropy
