连续值信息系统的不确定性度量
Uncertainty Measures for Continuous-Valued Information Systems
DOI: 10.12677/CSA.2017.74047, PDF, HTML, XML,  被引量 下载: 1,620  浏览: 5,534 
作者: 许 鑫*：烟台大学计算机与控制工程学院，山东 烟台
关键词: 连续值信息系统；粗糙集；不确定性度量；熵；Continuous-Valued Information Systems； Rough Sets； Uncertainty Measure； Entropy
摘要: 不确定性的度量方法是人工智能研究的重要课题之一，受到国内外专家学者的广泛关注，相关研究成果已经成功的应用于数据挖掘，决策分析，模式识别与人工智能领域中。通过二元关系与熵，对连续值信息系统中的不确定性度量进行了系统研究。基于经典Pawlak粗糙集理论中的近似精度、知识粒度与信息熵，提出了连续值信息系统的粗糙度、知识粒度与知识熵，并对三种度量方式进行了比较分析。三种不确定性度量方式的提出，为连续值信息系统知识约简与表示的研究提供了理论基础。
Abstract: Approach to uncertainty measures is one of the hottest topics in area of artificial intelligence, which attracts attention from many researchers. Relevant research results have been applied in data mining, decision analysis, pattern recognition and artificial intelligence. In this paper, the uncertainty measures of continuous-valued information systems have been investigated system-atically by using binary relation and entropy. Based on the approximation accuracy, knowledge granulation and information entropy in Pawlak rough set theory, we propose the rough accuracy, knowledge granulation and knowledge entropy in continuous-valued information systems. We also have the comparative study about three measures in the paper. The proposed uncertainty measures for continuous-valued information systems could provide the theoretical foundation for knowledge reduction and representation in continuous information systems.
文章引用：许鑫. 连续值信息系统的不确定性度量[J]. 计算机科学与应用, 2017, 7(4): 388-397. https://doi.org/10.12677/CSA.2017.74047

参考文献

[1] Düntsch, I. and Gediga, G. (1998) Uncertainty Measures of Rough Set Prediction. Artificial Intelligence, 106, 109-137.
https://doi.org/10.1016/S0004-3702(98)00091-5
[2] Wierman, M. (1999) Measuring Uncertainty in Rough Set Theory. International Journal of General Systems, 28, 283-297.
https://doi.org/10.1080/03081079908935239
[3] Beaubouef, T., Petry, F.E. and Arora, G. (1998) Information-Theoretic Measures of Uncertainty for Rough Sets and Rough Relational Databases. Information Sciences, 109, 185-195.
https://doi.org/10.1016/S0020-0255(98)00019-X
[4] Qian, Y.H., Liang, J.Y. and Wang, F. (2009) A New Method for Measuring the Uncertainty in Incomplete Information Systems. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 17, 855-880.
https://doi.org/10.1142/S0218488509006303
[5] Liang, J.Y. and Shi, Z.Z. (2004) The Information Entropy, Rough Entropy and Knowledge Granulation in Rough Set Theory. International Journal of General Systems, 12, 37-46.
https://doi.org/10.1142/s0218488504002631
[6] Yao, Y.Y. and Zhao, L.Q. (2012) A Measurement Theory View on the Granularity of Partitions. Information Sciences, 213, 1-13.
https://doi.org/10.1016/j.ins.2012.05.021
[7] 刘财辉, 苗夺谦, 岳晓冬, 赵才荣. 知识不确定性度量及其关系研究[J]. 计算机科学, 2015, 41(3): 66-70.
[8] 张楠, 苗夺谦, 岳晓冬. 区间值信息系统的知识约简[J]. 计算机研究与发展, 2010, 47(8): 1362-1371.
[9] 苗夺谦. Rough Set理论及其在机器学习中的应用研究[D]: [博士学位论文]. 北京: 中国科学院自动化研究所, 1997.
[10] 苗夺谦, 王珏. 粗糙集理论中概念与运算的信息表示[J]. 软件学报, 1999, 10(2): 113-116.
[11] 苗夺谦, 范世栋. 知识的粒度计算及其应用[J]. 系统工程理论与实践, 2002, 22(1): 48-56.
[12] Wang, G. (2003) Rough Reduction in Algebra View and Information View. International Journal of Intelligent Systems, 18, 679-688.
https://doi.org/10.1002/int.10109
[13] 黄兵, 周献中, 史迎春. 基于一般二元关系的知识粗糙熵与粗集粗糙熵[J]. 系统工程理论与实践, 2004, 24(1): 93-96.
[14] Liang, J., Shi, Z., Li, D. and Wierman, M. (2006) Information Entropy, Rough Entropy and Knowledge Granularity in Incomplete Information Systems. International Journal of General Systems, 35, 641-654.
https://doi.org/10.1080/03081070600687668
[15] Feng, Q.R., Miao, D.Q., Zhou, J. and Cheng, Y. (2010) A Novel Measure of Knowledge Granularity in Rough Sets. International Journal of Granular Computing, Rough Sets and Intelligent Systems, 1, 233-251.
https://doi.org/10.1504/IJGCRSIS.2010.029580
[16] 冯琴荣. 基于多维数据模型的粒计算方法研究[D]: [博士学位论文]. 上海: 同济大学, 2009.
[17] 王国胤, 苗夺谦, 吴伟志, 梁吉业. 不确定信息的粗糙集表示和处理[J]. 重庆邮电大学学报(自然科学版), 2010, 22(5): 541-544.
[18] Xu, W.H., Zhang, X.Y. and Zhang, W.X. (2009) Knowledge Granulation, Knowledge Entropy and Knowledge Uncertainty Measure in Ordered Information Systems. Applied Soft Computing, 9, 1244-1251.
https://doi.org/10.1016/j.asoc.2009.03.007
[19] 王国胤, 张清华, 马希骜, 杨青山. 知识不确定性问题的粒计算模型[J]. 软件学报, 2011, 22(4): 676-694.
[20] Dai, J.H., Wang, W.T., Xu, Q. and Tian, H.W. (2012) Uncertainty Measurement for Interval-Valued Decision Systems Based on Extended Conditional Entropy. Knowledge-Based Systems, 27, 443-450.
https://doi.org/10.1016/j.knosys.2011.10.013
[21] Guan, Y.Y., Wang, H.K., Wang, Y. and Yang, F. (2009) Attribute Reduction and Optimal Decision Rules Acquisition for Continuous Valued Information Systems. Information Sciences, 179, 2974-2984.
https://doi.org/10.1016/j.ins.2009.04.017
[22] Yao, Y.Y. and Zhao, L.Q. (2012) A Measurement Theory View on the Granularity of Partitions. Information Sciences, 213, 1-13.
https://doi.org/10.1016/j.ins.2012.05.021
[23] 张楠. 区间值信息系统与知识空间的粒计算方法研究[D]: [博士学位论文]. 上海: 同济大学, 2012.
[24] 苗夺谦, 王珏. 粗糙集理论中知识粗糙性与信息熵关系的讨论[J]. 模式识别与人工智能, 1998, 11(1): 34-40.