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Erschienen in:
2010 | OriginalPaper | Buchkapitel
A Non-boolean Lattice Derived by Double Indiscernibility
verfasst von : Yukio-Pegio Gunji, Taichi Haruna
Erschienen in: Transactions on Rough Sets XII
Verlag: Springer Berlin Heidelberg
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The central notion of a rough set is the indiscernibility that is based on an equivalence relation. Because an equivalence relation shows strong bondage in an equivalence class, it forms a Galois connection and the difference between the upper and lower approximations is lost. Here, we introduce two different equivalence relations, one for the upper approximation and one for the lower approximation, and construct a composite approximation operator consisting of different equivalence relations. We show that a collection of fixed points with respect to the operator is a lattice and there exists a representation theorem for that construction.