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中文摘要：
以一族等价关系所构成的多粒度空间为研究对象，在乐观和悲观多粒度粗糙集模型的基础上，给出两种多粒度粗糙隶属度函数以重构乐观和悲观多粒度粗糙集。从多粒度空间中一族等价关系的交集和并集出发，定义多粒度空间上的两种知识粒度，并将这两种知识粒度作为启发式信息，分别构建启发式算法以删除多粒度空间中的冗余粒空间。
英文摘要：
In this paper, the muhigranulation space, which is derived from a family of the equivalence relations, is deeply explored. Based on the optimistic and pessimistic muhigranulation rough sets, two different multigranulation rough membership functions are proposed to re - construct optimistic and pessimistic multigran- ulation rough sets. Moreover, from the viewpoints of intersection and union of equivalence relations, two differ- ent definitions of knowledge granulations are proposed in multigranulation space. Such two knowledge granula- tions are regarded as the heuristic information to construct algorithms, from which the redundant granulation spaces can be deleted in multigranulation space.
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