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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Attribute reduction is a critical topic in the field of rough set theory. Currently, to further enhance the stability of the derived reduct, various attribute selectors are designed based on the framework of ensemble selectors. Nevertheless, it must be pointed out that some limitations are concealed in these selectors: (1) rely heavily on the distribution of samples; (2) rely heavily on the optimal attribute. To generate the reduct with higher stability, a novel beam-influenced selector (BIS) is designed based on the strategies of random partition and beam. The scientific novelty of our selector can be divided into two aspects: (1) randomly partition samples without considering the distribution of samples; (2) beam-based selections of features can save the selector from the dependency of the optimal attribute. Comprehensive experiments using 16 UCI data sets show the following: (1) the stability of the derived reducts may be significantly enhanced by using our selector; (2) the reducts generated based on the proposed selector can provide competent performance in classification tasks.

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