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On the structure of generalized rough sets. (English) Zbl 1096.03065

In this paper links are established between the theory of rough sets and the field of topology, where lower and upper approximation operators play the role of interior and closure operators, respectively. The term “generalized” refers to the fact that the approximation space under consideration is induced by a relation which is not necessarily an equivalence relation. However, the propositions and theorems stated in the paper require the relation to be at least reflexive and often also symmetrical and/or transitive. The author sets his contribution apart from previous work by not restricting the universe to be finite.

MSC:

03E72 Theory of fuzzy sets, etc.
54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)
68T30 Knowledge representation
68T37 Reasoning under uncertainty in the context of artificial intelligence
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References:

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