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Matroidal approaches to rough sets via closure operators. (English) Zbl 1246.68233
Summary: This paper studies rough sets from the operator-oriented view by matroidal approaches. We firstly investigate some kinds of closure operators and conclude that the Pawlak upper approximation operator is just a topological and matroidal closure operator. Then we characterize the Pawlak upper approximation operator in terms of the closure operator in Pawlak matroids, which are first defined in this paper, and are generalized to fundamental matroids when partitions are generalized to coverings. A new covering-based rough set model is then proposed based on fundamental matroids and properties of this model are studied. Lastly, we refer to the abstract approximation space, whose original definition is modified to get a one-to-one correspondence between closure systems (operators) and concrete models of abstract approximation spaces. We finally examine the relations of four kinds of abstract approximation spaces, which correspond exactly to the relations of closure systems.

MSC:
68T37 Reasoning under uncertainty in the context of artificial intelligence
05B35 Combinatorial aspects of matroids and geometric lattices
06A15 Galois correspondences, closure operators (in relation to ordered sets)
54A05 Topological spaces and generalizations (closure spaces, etc.)
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