|
Dominance-based rough set approach (DRSA) is an extension of rough set theory for multi-criteria decision analysis (MCDA), introduced by Greco, Matarazzo and Słowiński.〔 Greco, S., Matarazzo, B., Słowiński, R.: Rough sets theory for multi-criteria decision analysis. European Journal of Operational Research, 129, 1 (2001) 1–47〕〔 Greco, S., Matarazzo, B., Słowiński, R.: Multicriteria classification by dominance-based rough set approach. In: W.Kloesgen and J.Zytkow (eds.), Handbook of Data Mining and Knowledge Discovery, Oxford University Press, New York, 2002〕〔 Słowiński, R., Greco, S., Matarazzo, B.: Rough set based decision support. Chapter 16 (): E.K. Burke and G. Kendall (eds.), Search Methodologies: Introductory Tutorials in Optimization and Decision Support Techniques, Springer-Verlag , New York (2005) 475–527〕 The main change comparing to the classical rough sets is the substitution of the indiscernibility relation by a dominance relation, which permits to deal with inconsistencies typical to consideration of criteria and preference-ordered decision classes. ==Multicriteria classification (sorting)== Multicriteria classification (sorting) is one of the problems considered within MCDA and can be stated as follows: given a set of objects evaluated by a set of criteria (attributes with preference-order domains), assign these objects to some pre-defined and preference-ordered decision classes, such that each object is assigned to exactly one class. Due to the preference ordering, improvement of evaluations of an object on the criteria should not worsen its class assignment. The sorting problem is very similar to the problem of classification, however, in the latter, the objects are evaluated by regular attributes and the decision classes are not necessarily preference ordered. The problem of multicriteria classification is also referred to as ordinal classification problem with monotonicity constraints and often appears in real-life application when ordinal and monotone properties follow from the domain knowledge about the problem. As an illustrative example, consider the problem of evaluation in a high school. The director of the school wants to assign students (''objects'') to three classes: ''bad'', ''medium'' and ''good'' (notice that class ''good'' is preferred to ''medium'' and ''medium'' is preferred to ''bad''). Each student is described by three criteria: level in Physics, Mathematics and Literature, each taking one of three possible values ''bad'', ''medium'' and ''good''. Criteria are preference-ordered and improving the level from one of the subjects should not result in worse global evaluation (class). As a more serious example, consider classification of bank clients, from the viewpoint of bankruptcy risk, into classes ''safe'' and ''risky''. This may involve such characteristics as "return on equity (ROE)", "return on investment (ROI)" and "return on sales (ROS)". The domains of these attributes are not simply ordered but involve a preference order since, from the viewpoint of bank managers, greater values of ROE, ROI or ROS are better for clients being analysed for bankruptcy risk . Thus, these attributes are criteria. Neglecting this information in knowledge discovery may lead to wrong conclusions. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Dominance-based rough set approach」の詳細全文を読む スポンサード リンク
|