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A simple multigranulation rough set approach is to approximate the target through a family of binary relations. Optimistic and pessimistic multigranulation rough sets are two typical examples of such approach. However, these two multigranulation rough sets do not take frequencies of occurrences of containments or intersections into account. To solve such problem, by the motivation of the multiset, the model of the multiple multigranulation rough set is proposed, in which both lower and upper approximations are multisets. Such two multisets are useful when counting frequencies of occurrences such that objects belong to lower or upper approximations with a family of binary relations. Furthermore, not only the concept of approximate distribution reduct is introduced into multiple multigranulation rough set, but also a heuristic algorithm is presented for computing reduct. Finally, multiple multigranulation rough set approach is tested on eight UCI (University of California-Irvine) data sets. Experimental results show: 1. the approximate quality based on multiple multigranulation rough set is between approximate qualities based on optimistic and pessimistic multigranulation rough sets; 2. by comparing with optimistic and pessimistic multigranulation rough sets, multiple multigranulation rough set needs more attributes to form a reduct.

Different from classical rough set, Multigranulation Rough Set (MGRS) is frequently designed for approximating target through using multiple results of information granulation. Presently, though many forms of MGRS have been intensively explored, most of them are constructed based on the homogeneous information granulation with respect to different scales or levels. They lack the multi-view which involves the results of heterogeneous information granulation. To fill such a gap, a Triple-G MGRS is developed. Such a Triple-G is composed of three different heterogeneous information granulations:(1) neiGhborhood based information granulation; (2) Gap based information granulation; (3) Granular ball based information granulation. Neighborhood provides a parameterized mechanism while gap and granular ball offer two representative data-adaptive strategies for performing information granulation. Immediately, both optimistic and pessimistic MGRS can be re-constructed. Furthermore, the problem of attribute reduction is also addressed based on the proposed models. Not only the forward greedy searching is used for deriving the Triple-G MGRS related reducts, but also an attribute grouping based accelerator is reported for further speeding up the process of searching reducts. The experimental results over 20 UCI data sets demonstrate the follows: (1) from the viewpoint of the generalization performance, the reducts obtained by our Triple-G MGRS is superior to those obtained by previous researches; (2) attribute grouping does speed up the process of searching reducts.

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