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引用次数: 30
摘要
粗糙集的概念最早是由Pawlak(1982)提出的。之后,它被成功地应用于许多研究领域,如模式识别、机器学习、知识获取、经济预测和数据挖掘。但是原始的粗糙集模型不能有效地处理含有噪声数据的数据集,并且边界区域的潜在有用知识可能没有被完全捕获。为了克服这些局限性,一些扩展粗糙集模型结合了现有的软计算技术被提出。许多研究人员被激励去研究粗糙集理论的概率方法。变精度粗糙集模型(VPRSM)是其中最重要的扩展之一。贝叶斯粗糙集模型(BRSM) (Slezak & Ziarko, 2002)作为粗糙集理论与贝叶斯推理的混合发展,可以处理许多原始粗糙集模型无法有效处理的实际问题。Yao(1990)在最小风险贝叶斯决策过程的基础上提出了决策理论粗糙集模型(decision theory rough set model, DTRSM),为粗糙集理论的概率方法带来了新的见解。本文研究了决策理论粗糙集的概念,并引入了贝叶斯决策理论粗糙集的新概念。最后对贝叶斯决策理论粗糙集与Pawlak(1982)定义的粗糙集进行了比较研究。
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).