TY - GEN
T1 - A non-boolean lattice derived by double indiscernibility
AU - Gunji, Yukio Pegio
AU - Haruna, Taichi
PY - 2010
Y1 - 2010
N2 - 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.
AB - 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.
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U2 - 10.1007/978-3-642-14467-7_11
DO - 10.1007/978-3-642-14467-7_11
M3 - Conference contribution
AN - SCOPUS:77955822773
SN - 3642144667
SN - 9783642144660
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 211
EP - 225
BT - Transactions on Rough Sets XII
T2 - Rough Set and Knowledge Technology Conference, RSKT 2008
Y2 - 1 May 2008 through 1 May 2008
ER -