Non-Boolean Lattice Derived by Double Indiscernibility
نویسندگان
چکیده
The central notion of a rough set is indiscernibility based on equivalence relation. Since equivalence relation shows strong bondage in an equivalence class, it forms a Galois connection and the difference between upper and lower approximations is lost. We here introduce two different equivalence relations, the one for upper approximation, and the other for lower approximation, and construct 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 that there exists a representation theorem for that construction.
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