Matrix-Based Approaches for Updating Approximations in Multigranulation Rough Set While Adding and Deleting Attributes

Abstract

With advanced technology in medicine and biology, data sets containing information could be huge and complex that sometimes are difficult to handle. Dynamic computing is an efficient approach to solve some problems. Since multigranulation rough sets were proposed, many algorithms have been designed for updating approximations in multigranulation rough sets, but they are not efficient enough in terms of computational time. The purpose of this study is to further reduce the computational time of updating approximations in multigranulation rough sets. First, searching regions in data sets for updating approximations in multigranulation rough sets are shrunk. Second, matrix-based approaches for updating approximations in multigranulation rough set are proposed. The incremental algorithms for updating approximations in multigranulation rough sets are then designed. Finally, the efficiency and validity of the designed algorithms are verified by experiments.

Object-First Incremental Algorithms for Updating Approximations in Multi-Granulation Fuzzy Probabilistic Rough Sets Over Two Universes

“…But the structure of Hu's algorithm is single granulation that limits its application scope in multi-granulation information system. Meanwhile, some scholars proposed some incremental algorithms based on the MRS theory in [36]- [39], but these traditional incremental algorithms still need to traverse a large amount of data during updating approximations. Therefore, it is necessary to design the incremental algorithms based on the MFPRS over two universes, which need to extend Hu's incremental algorithm from single granulation to multiple granulations, and need to be more efficiency than the traditional incremental algorithms mentioned above.…”

Attribute Reduction of Boolean Matrix in Neighborhood Rough Set Model

“…However, discretizing the continuous values exists some uncertainty and may lose some essential information. To solve this problem, many rough set models have been proposed, such as fuzzy rough sets [3][4][5][6], covering rough sets [7][8][9], semimonolayer cover rough set [10], neighborhood rough sets [11][12][13][14], granule-based rough sets [15][16][17]. Neighborhood rough set is a feasible model to handle continuous values without discretization.…”

Relative relation matrix-based approaches for updating approximations in multigranulation rough sets

“…Yang et al [38] proposed a dynamic update method when the granular structures increase. Yu et al [41,42] proposed vector-based and matrixbased approaches to compute the approximations in MGRS, respectively. Hu et al [4] paid attention to the dynamic updating approximations in MGRS while refining or coarsening attribute values.…”