A dynamic approach for updating the lower approximation in adjustable multi-granulation rough sets
- PDF / 1,388,043 Bytes
- 16 Pages / 595.276 x 790.866 pts Page_size
- 28 Downloads / 160 Views
FOUNDATIONS
A dynamic approach for updating the lower approximation in adjustable multi-granulation rough sets Meishe Liang1,2 · Jusheng Mi1
· Tao Feng3 · Bin Xie4
Published online: 19 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Granular computing (GrC) is one of the key issues in the field of information sciences. Research on the theory and algorithms of granular computing has very important practical significance in huge amounts of information. In multi-granulation rough set theory, two subsets are calculated to approximate the target concept, which are extremely time-consuming for large-scale data. In this paper, to address the issue above, we propose efficient algorithms for updating the lower approximation when a single object is added into or deleted from the target concept in an incomplete information system. Firstly, adjustable multi-granulation rough sets (AMGRSs) are introduced in an incomplete information system, and the related properties and theorems are explored. Secondly, it is proved that local-AMGRSs and AMGRSs are equivalent in an incomplete information system. Finally, dynamic algorithms for updating the lower approximation are proposed, and the efficiency of these algorithms is verified by an experiment. Keywords Granular computing · Multi-granulation · Rough set · Lower approximation
1 Introduction Due to the influence of collection and transmission, there are various pieces of uncertain and inaccurate information in many fields, such as natural sciences, social sciences and Communicated by A. Di Nola.
B
Jusheng Mi [email protected] Meishe Liang [email protected] Tao Feng [email protected] Bin Xie [email protected]
1
College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050024, People’s Republic of China
2
Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043, People’s Republic of China
3
College of Science, Hebei University of Science and Technology, Shijiazhuang 050018, People’s Republic of China
4
Information and Technology College, Hebei Normal University, Shijiazhuang 050024, People’s Republic of China
engineering technology. This kind of uncertainty is mainly manifested in the absent and inaccurate data. With the development of computer sciences and Internet technology, we have entered the era of big data information (Zhang and Zhang 2012; Zhang et al. 2015). The demand for information analysis tools is getting higher and higher (Zhang et al. 2015, 2016, 2018). For a long time, many researchers have been looking for effective ways to deal with uncertain and incomplete problems scientifically (Villuendas-Rey 2019), which has been one of the current and future research frontiers. As an approach of knowledge representation and data mining, GrC can reduce the complexity of problem-solving by granularity concept, which may be an important mathematical tool to explore big data. At present, the mature models of granular calculation theory are: fuzzy words computing propo
Data Loading...
