TY - CHAP

T1 - Fuzzy similarity relation as a basis for rough approximations

AU - Greco, Salvatore

AU - Matarazzo, Benedetto

AU - Slowinski, Roman

PY - 1998

Y1 - 1998

N2 - The rough sets theory proposed by Pawlak was originally founded on the idea of approximating a given set by means of indiscernibility binary relation, which was assumed to be an equivalence relation (reflexive, symmetric and transitive). With respect to this basic idea, two main theoretical developments have been proposed: some extensions to a fuzzy context (e.g. Dubois and Prade, Slowinski and Stefanowski, Yao) and some extensions of the indiscernibility relation by means of more general binary relations (e.g. Nieminen, Lin, Marcus, Polkowski, Skowron and Zytkow, Skowron and Stepaniuk, Slowinski, Slowinski and Vanderpooten, Yao and Wong). In the latter extensions, we wish to point out the proposal of Slowinski and Vanderpooten who introduced and characterized a general definition of rough approximations using a similarity relation which is a reflexive binary relation, relaxing the assumption of symmetry and transitivity.

AB - The rough sets theory proposed by Pawlak was originally founded on the idea of approximating a given set by means of indiscernibility binary relation, which was assumed to be an equivalence relation (reflexive, symmetric and transitive). With respect to this basic idea, two main theoretical developments have been proposed: some extensions to a fuzzy context (e.g. Dubois and Prade, Slowinski and Stefanowski, Yao) and some extensions of the indiscernibility relation by means of more general binary relations (e.g. Nieminen, Lin, Marcus, Polkowski, Skowron and Zytkow, Skowron and Stepaniuk, Slowinski, Slowinski and Vanderpooten, Yao and Wong). In the latter extensions, we wish to point out the proposal of Slowinski and Vanderpooten who introduced and characterized a general definition of rough approximations using a similarity relation which is a reflexive binary relation, relaxing the assumption of symmetry and transitivity.

U2 - 10.1007/3-540-69115-4_39

DO - 10.1007/3-540-69115-4_39

M3 - Chapter (peer-reviewed)

SN - 9783540646556

T3 - Lecture notes in computer science

SP - 283

EP - 289

BT - Rough sets and current trends in computing

A2 - Polkowski, Lech

A2 - Skowron, Andrzej

PB - Springer

CY - Berlin, Germany

ER -