Abstract
Multigranulation rough set is an extension of classical rough set, and optimistic multigranulation and pessimistic multigranulation are two special cases of it.βmultigranulation rough set is a more generalized multigranulation rough set. In this paper, we first introduce fuzzy rough theory intoβmultigranulation rough set to construct aβmultigranulation fuzzy rough set, which can be used to deal with continuous data; then some properties are discussed. Reduction is an important issue of multigranulation rough set, and an algorithm of granular space reduction toβmultigranulation fuzzy rough set for preserving positive region is proposed. To test the algorithm, experiments are taken on five UCI data sets with different values ofβ. The results show the effectiveness of the proposed algorithm.
Highlights
Qian et al [1,2,3] proposed a multigranulation rough set, which is constructed on a family of granular structures and is different from Pawlak’s rough set [4,5,6,7]
Granular space reduction is an important issue of multigranulation rough set and it is recently researched by many scholars [20,21,22,23,24]
We focus on the problem to deal with β multigranulation rough set
Summary
Qian et al [1,2,3] proposed a multigranulation rough set, which is constructed on a family of granular structures and is different from Pawlak’s rough set [4,5,6,7]. The word “optimistic” means that at least one of the granulation spaces can be used for approximating while the word “pessimistic” means that all of the granulation spaces should be used for approximating In these two models, all of the binary relations, or granulation spaces, are presented simultaneously; optimistic and pessimistic are two special cases of multigranulation rough set. Xu et al generalized multigranulation fuzzy rough sets to tolerance approximation space to construct optimistic and pessimistic multigranulation fuzzy rough sets models [14].
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