A Review of Rough Set Models.pdfVIP

Decision-Theoretic Rough Set Models Yiyu Yao Department of Computer Science, University of Regina, Regina, Saskatchewan, Canada S4S 0A2 E-mail: yyao@cs.uregina.ca Abstract. Decision-theoretic rough set models are a probabilistic exten- sion of the algebraic rough set model. The required parameters for defin- ing probabilistic lower and upper approximations are calculated based on more familiar notions of costs (risks) through the well-known Bayesian decision procedure. We review and revisit the decision-theoretic models and present new results. It is shown that we need to consider additional issues in probabilistic rough set models. Keywords. Bayesian decision theory, decision-theoretic rough sets, prob- abilistic rough sets, variable precision rough sets 1 Introduction Ever since the introduction of rough set theory by Pawlak in 1982 [10, 11, 13], many proposals have been made to incorporate probabilistic approaches into the theory [14, 29–31]. They include, for example, rough set based probabilistic classification [24], 0.5 probabilistic rough set model [15], decision-theoretic rough set models [32, 33], variable precision rough set models [6, 35], rough membership functions [12], parameterized rough set models [14, 17], and Bayesian rough set models [2, 18, 19]. The results of these studies increase our understanding of the rough set theory and its domain of applications. The decision-theoretic rough set models [29, 32, 33] and the variable precision rough set models [6, 35, 36] were proposed in the early 1990’s. The two models are formulated differently in order to generalize the 0.5 probabilistic rough set model [15]. In fact, they produce the same rough set approximations [29, 30]. Their main differences lie in their respective treatment of the required param- eters used in defining the lower and upper probabilistic approximations. The decision-theoretic models systematically calculate the parameters based on a loss function through the Bayesian decision proce