TY - CHAP

T1 - Statistical model for rough set approach to multicriteria classification

AU - Dembczynski, K.

AU - Greco, Salvatore

AU - Kotlowski, W.

AU - Slowinski, R.

PY - 2007

Y1 - 2007

N2 - In order to discover interesting patterns and dependencies in data, an approach based on rough set theory can be used. In particular, Dominance-based Rough Set Approach (DRSA) has been introduced to deal with the problem of multicriteria classification. However, in real-life problems, in the presence of noise, the notions of rough approximations were found to be excessively restrictive, which led to the proposal of the Variable Consistency variant of DRSA. In this paper, we introduce a new approach to variable consistency that is based on maximum likelihood estimation. For two-class (binary) problems, it leads to the isotonic regression problem. The approach is easily generalized for the multi-class case. Finally, we show the equivalence of the variable consistency rough sets to the specific risk-minimizing decision rule in statistical decision theory.

AB - In order to discover interesting patterns and dependencies in data, an approach based on rough set theory can be used. In particular, Dominance-based Rough Set Approach (DRSA) has been introduced to deal with the problem of multicriteria classification. However, in real-life problems, in the presence of noise, the notions of rough approximations were found to be excessively restrictive, which led to the proposal of the Variable Consistency variant of DRSA. In this paper, we introduce a new approach to variable consistency that is based on maximum likelihood estimation. For two-class (binary) problems, it leads to the isotonic regression problem. The approach is easily generalized for the multi-class case. Finally, we show the equivalence of the variable consistency rough sets to the specific risk-minimizing decision rule in statistical decision theory.

U2 - 10.1007/978-3-540-74976-9_18

DO - 10.1007/978-3-540-74976-9_18

M3 - Chapter (peer-reviewed)

SN - 9783540749752

VL - 4702

T3 - Lecture notes in computer science

SP - 164

EP - 175

BT - Knowledge discovery in databases: proceedings of the 11th european conference

A2 - Kok, J.

A2 - Koronacki, J.

A2 - Lopez de Mantaras, R.

A2 - Matwin, S.

A2 - Mladenic, D.

A2 - Skowron, A.

PB - Springer

CY - Berlin

ER -