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.
|Title of host publication
|Knowledge discovery in databases: proceedings of the 11th european conference
|J. Kok, J. Koronacki, R. Lopez de Mantaras, S. Matwin, D. Mladenic, A. Skowron
|Place of Publication
|Number of pages
|Published - 2007
|Lecture notes in computer science