A Study on Bayesian Decision Theoretic Rough Set

Abstract

The concept of rough set was first developed by Pawlak (1982). After that it has been successfully applied in many research fields, such as pattern recognition, machine learning, knowledge acquisition, economic forecasting and data mining. But the original rough set model cannot effectively deal with data sets which have noisy data and latent useful knowledge in the boundary region may not be fully captured. In order to overcome such limitations, some extended rough set models have been put forward which combine with other available soft computing technologies. Many researchers were motivated to investigate probabilistic approaches to rough set theory. Variable precision rough set model (VPRSM) is one of the most important extensions. Bayesian rough set model (BRSM) (Slezak & Ziarko, 2002), as the hybrid development between rough set theory and Bayesian reasoning, can deal with many practical problems which could not be effectively handled by original rough set model. Based on Bayesian decision procedure with minimum risk, Yao (1990) puts forward a new model called decision theoretic rough set model (DTRSM) which brings new insights into the probabilistic approaches to rough set theory. Throughout this paper, the concept of decision theoretic rough set is studied and also a new concept of Bayesian decision theoretic rough set is introduced. Lastly a comparative study is done between Bayesian decision theoretic rough set and Rough set defined by Pawlak (1982).