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Approximation via a double-matroid structure. (English) Zbl 1418.68206
Summary: Approximation is an important issue in rough set theory. In this study, we consider approximation by the matroidal approach. First, we study three lattices induced by an information system. Two of the three lattices are selected as the macrostructure and microstructure for approximation, respectively. Second, based on the two lattices, we define double-matroid lattices, where the upper and lower approximations with respect to an information system are depicted. Since the two lattices are geometric, we actually present approximation by the matroidal approach. Finally, we study the connection between our double-matroid lattices and granular partition lattices. Specifically, the comparison of these two structures is presented in both micro-level and macro-level.

MSC:
68T37 Reasoning under uncertainty in the context of artificial intelligence
05B35 Combinatorial aspects of matroids and geometric lattices
06C10 Semimodular lattices, geometric lattices
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