Abstract
The approximation theory is studied via rough sets, fuzzy sets and topological spaces (more precisely, Frechet spaces). Rough set theory is a set theory via knowledge bases. This set theory is extended to fuzzy sets and Frechet topological spaces. By these results one can show that the classification preserves the approximation. We also showed that within the approximation theory, fuzzy set and Frechet topology are intrinsically equivalent notions. Finally, we show that even though approximation is a compromised solution, the three theories allow one to draw an exact solution whenever there are adequate approximations. This implies that these three approaches are good approximation theories.
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