Abstract
In the previous decision-theoretic rough sets (DTRS), its loss function values are precise. This paper extends the precise values of loss functions to a more realistic stochastic environment. The stochastic loss functions are induced to decision-theoretic rough set theory based on the bayesian decision theory. A model of stochastic decision-theoretic rough set theory (SDTRS) is built with respect to the minimum bayesian expected risk. The corresponding propositions and criteria of SDTRS are also analyzed. Furthermore, we investigate two special SDTRS models under the uniform distribution and the normal distribution, respectively. Finally, an empirical study of Public-Private Partnerships (PPP) project investment validates the reasonability and effectiveness of the proposed models.
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