Granular computing and dual Galois connection

A covering model for granular computing in a set-theoretic setting is studied in this paper. Under this model, a zooming-in operator is redefined. Combinations of the zooming-in and zooming-out operators form two pairs of approximation operators of the original and the granulated universe of discourse. Their properties are examined in detail. For the two pairs of lower and upper approximation operators, it is proved that the duality is always true. For a generalized approximation space, the approximation representations are just the combination operators formed on the basis of the zooming-out and zooming-in operators. Relationships between these combination operators and the dual Galois connection are also analyzed.