Matrix-based incremental updating approximations in multigranulation rough set under two-dimensional variation
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ORIGINAL ARTICLE
Matrix‑based incremental updating approximations in multigranulation rough set under two‑dimensional variation Yi Xu1,2 · Quan Wang3 · Weikang Sun3 Received: 25 January 2020 / Accepted: 1 October 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Multigranulation rough set model (MGRS) uses multiple equivalence relations on the universe to calculate the approximations, which can solve problem in mutigranulation spaces. In practical applications, information systems often dynamically update due to the variation of objects, attributes or attribute values. Incremental approach is an effective method to calculate approximations for dynamically updated information system. However, existing incremental updating approximations in MGRS mainly focus on single-dimensional variation of objects, attributes or attribute values respectively, without considering multi-dimensional variation of objects, attributes and attribute values. In this paper, we propose matrix-based incremental updating approximations in multigranulation rough set under two-dimensional variation of objects, attributes and attribute values. One is the simultaneous variation of objects and attributes (VOA). The other is the simultaneous variation of objects and attribute values (VOV). First, we give the incremental approaches to update the relevant matrices for the dynamically updated information system due to VOA and VOV. Second, based on the updated matrices, we propose two matrix-based incremental algorithms to update approximations. Finally, examples and experimental results demonstrate the effectiveness of the proposed algorithms for incremental updating approximations in multigranulation rough set under two-dimensional variation. Keywords Multigranulation rough set · Approximation · Matrix · Incremental · Two-dimensional variation
1 Introduction Multigranulation rough set model (MGRS) proposed by Qian et al. [1] is an extension of the Pawlak rough set [2], which defines the approximations by multiple equivalence relations on the universe instead of a single equivalence relation. As MGRS can solve problem in multigranulation spaces, it has become an important research direction in the field of rough set. The generalized multigranulation rough set models and applications have been widely investigated [3–6]. For example, Feng et al. [7] proposed variable * Yi Xu [email protected] 1
Key Laboratory of Intelligent Computing and Signal Processing, Ministry of Education, Anhui University, Hefei 230039, China
2
School of Computer Science and Technology, Anhui University, Hefei 230601, China
3
School of Computer Science and Technology, Anhui University, Hefei 230601, China
precision multigranulation decision-theoretic fuzzy rough set. Moreover, Yang et al. [8] and Xu et al. [9] constructed multigranulation rough set based on the fuzzy approximation space. Lin et al. [10, 11] discussed two kinds of neighborhood-based multigranulation rough set and three kinds of covering based multigranulation rough set.
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