TY - CHAP
T1 - Algebra and topology for dominance-based rough set approach
AU - Greco, Salvatore
AU - Matarazzo, B.
AU - Slowinski, R.
PY - 2010
Y1 - 2010
N2 - Dominance-based rough sets generalize classical indiscernibility based rough sets by handling ordered value sets of attributes and monotonic relationships between values of condition and decision attributes. Dominance based rough sets permit, in particular, a natural hybridization of fuzziness and roughness, which are complementary concepts of vagueness. In this article, we characterize the Dominance-based Rough Set Approach (DRSA) from the point of view of its mathematical foundations, taking into account algebraic structures and topological properties. We present algebraic representations of DRSA in terms of generalizations of several algebras already used to represent the classical rough set approach, namely: bipolar de Morgan Brouwer-Zadeh distributive lattice, bipolar Nelson algebra, bipolar Heyting algebra, bipolar double Stone algebra, bipolar three-valued Łukasiewicz algebra, bipolar Wajsberg algebra.We also present an algebraic model for ordinal classification. With respect to topological properties, using the concept of a bitopological space, we extend on DRSA the results obtained for classical rough sets.
AB - Dominance-based rough sets generalize classical indiscernibility based rough sets by handling ordered value sets of attributes and monotonic relationships between values of condition and decision attributes. Dominance based rough sets permit, in particular, a natural hybridization of fuzziness and roughness, which are complementary concepts of vagueness. In this article, we characterize the Dominance-based Rough Set Approach (DRSA) from the point of view of its mathematical foundations, taking into account algebraic structures and topological properties. We present algebraic representations of DRSA in terms of generalizations of several algebras already used to represent the classical rough set approach, namely: bipolar de Morgan Brouwer-Zadeh distributive lattice, bipolar Nelson algebra, bipolar Heyting algebra, bipolar double Stone algebra, bipolar three-valued Łukasiewicz algebra, bipolar Wajsberg algebra.We also present an algebraic model for ordinal classification. With respect to topological properties, using the concept of a bitopological space, we extend on DRSA the results obtained for classical rough sets.
U2 - 10.1007/978-3-642-05183-8_3
DO - 10.1007/978-3-642-05183-8_3
M3 - Chapter (peer-reviewed)
SN - 9783642051821
VL - 265
T3 - Studies in computational intelligence
SP - 43
EP - 78
BT - Advances in intelligent information systems
A2 - Ras, Z.
A2 - Tsay, L.
PB - Springer
CY - Berlin
ER -