Probabilistic model criteria with decision-theoretic rough sets

In dealing with risk in real decision problems, decision-theoretic rough sets with loss functions aim to obtain optimization decisions by minimizing the overall risk with Bayesian decision procedures. Two parameters generated by loss functions divide the universe into three regions as the decision of acceptance, deferment and rejection. In this paper, we discuss the semantics of loss functions, and utilize the differences of losses replace actual losses to construct a new four-level approach of probabilistic rules choosing criteria. Ten types of probabilistic rough set models can be generated by the four-level approach and form two groups of models: two-way probabilistic decision models and three-way probabilistic decision models. A reasonable decision with these criteria is demonstrated by an illustration of oil investment. (C) 2011 Elsevier Inc. All rights reserved.