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Multigranulation covering rough sets based on the union of minimal descriptions of elements
LIU Caihui, CAI Kecan
Department of Mathematics & Computer Science, Gannan Normal University, Ganzhou 341000, China
Abstract: To generalize multigranulation rough sets to a covering-based approximation space, this paper proposes three kinds of covering-based multigranulation rough sets by employing the conditional probability between the target concept and the union of the minimal descriptions of elements. Based on new definitions, some basic properties of these models were investigated and their relationships with some existing covering-based multigranulation rough sets are revealed. The inter-relationship among the three new models is also explored. The discussions show that the proposed models are a special form of text model, as well as extensions of some existing covering-based multigranulation rough sets.
Key words: rough sets     multigranulation     conditional probability     covering     minimal description

1 经典多粒度粗糙集的基本概念

2 基于最小描述并集的多粒度覆盖粗糙集及性质

, 则称XC1, C2，…, Cn描述下的平均多粒度覆盖粗糙集，否则称X是可定义集。

, 则称XC1, C2，…, Cn描述下的乐观多粒度覆盖粗糙集，否则称X是可定义集。

, 则称XC1, C2，…, Cn描述下的悲观多粒度覆盖粗糙集，否则称X是可定义集。

X={1, 2, 5, 8}，则

1) 当α=1时，有

2) 当β=0时，有

1)

2)

3)

X={1, 2}, α=0.6，β=0.3, 则有

3 3种模型的关系

1) α=1时，有 (X)= (X)

2) β=0时，有 (X)= (X)

1)

2) 成立。

4 结论

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DOI: 10.11992/tis.201605034

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#### 文章信息

LIU Caihui, CAI Kecan

Multigranulation covering rough sets based on the union of minimal descriptions of elements

CAAI Transactions on Intelligent Systems, 2016, 11(4): 534-538
http://dx.doi.org/10.11992/tis.201605034