Affiliations: [a] College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050024, P.R. China. 44842802@qq.com, mijsh@263.net
Correspondence:
[†]
Address for correspondence: College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050024, P.R. China
Note: [*] Also works: School of Mathematics and Statistics, Minnan Normal University, Zhangzhou, Fujian 363000, P.R. China
Abstract: Multi-granulation rough set(MGRS), as a kind of fusion mechanism of different information or data, is an useful development of Pawlak rough set theory. Firstly, this paper gives an introduction for various types of MGRS, their properties and axiomatization characterizations are studied. We show that, except for the optimistic one, each of the existing MGRS means a single granulation rough set. Then, we made a comparative analysis on the different uncertainty measures among the various multi-granulation approximation spaces. At the basis of investigating for the existing uncertainty measures, we discuss their limitations via some examples, and propose a total ordered relation among approximation spaces, even in the more general covering ones. It will be better than the original partial relation in revealing uncertainty, which conceal in the approximation space or covering one. Finally, based on the total ordered relation, we present improved information entropy, rough entropy, knowledge granulation and axiomatic definition of the knowledge granulation measures. It is proved that they are more reasonable than the original ones. Then, some novel uncertainty measures and improved fusion uncertainty measures about various granulations are also proposed. By employing these measures, granulation measures of various MGRSs are defined and studied.
Keywords: Rough set, Multi-granulation, Total ordered relation, Uncertainty measure
