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Extensions and intensions in the rough set theory. (English) Zbl 0934.03069

The paper presents some basic properties of approximation spaces being a generalization of the classical approximation spaces introduced by Zdzisław Pawlak in rough set theory. These approximation spaces have been also defined and investigated by some other authors. Instead of partition of the universe a covering is considered; elements of the partition are called neighborhoods. The main results in the paper are related to characterization of neighborhoods. In particular it is shown that the following properties of neighborhoods are equivalent: to be representative, to be exact and to be minimal. Necessary and sufficient conditions for a poset defined by a covering to be a lattice are formulated using the above-mentioned notions.

MSC:

03E72 Theory of fuzzy sets, etc.
68T30 Knowledge representation
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