On relationship between probabilistic rough set and Bayesian risk decision over two universes

Abstract

We consider a problem of Bayesian risk decision based on probabilistic rough set over two universes. It is a new extension of classical probabilistic rough set on the same universe. We give four rough set models on probabilistic approximation space over two universes. Then we study the interrelationship between Bayesian risk decision and probabilistic rough set models over two universes. The results show that there must exist a kind of Bayesian minimum risk decision problem corresponding to one of the probabilistic rough set models over two universes. In fact, the conclusion also includes some generalized probabilistic rough set models on the same universe by other authors. And at the same time, the principal and validity of the Bayesian risk decision based on probabilistic rough set over two universes are tested by a numerical example of the medical diagnosis systems in detail. The probabilistic rough set approach over two universes gives an effective assistant for decision makers in the context of risk and uncertainty.

Keywords:

• Bayesian risk decision
• probabilistic rough set
• two universes

Acknowledgements

We are grateful to the reviewers for the valuable comments and recommendations. This work was partly supported by the National Natural Science Foundation of China (71161016, 71071113, 70671004), a Foundation for the Author of National Excellent Doctoral Dissertation of PR China (200782), the Shuguang Plan of Shanghai Education Development Foundation and Shanghai Education Committee (08SG21), Shanghai Pujiang Program, and Shanghai Philosophical and Social Science Program (2010BZH003), the Fundamental Research Funds for the Central Universities.