1.Institute of Computer Science and Technology,Chongqing University of Posts and Telecommunications,Chongqing 400065 2.School of Electronic Engineering,Xidian University,Xian 710071
Abstract：Since some uncertainty measures of rough sets are unreasonable under some circumstances, a basic rule set of uncertainty measure of rough set is proposed from the perspective of intuition. All the uncertainty measures except the quadratic fuzziness satisfy the basic rule set. The uncertainty measures satisfying the basic rule set still have unreasonability, and thus an extended rule set is further developed. The fuzzy entropy and revised fuzziness are the uncertainty measures satisfying the extended rule set, while the roughness, rough entropy and linear fuzziness are not. The results provide theoretical basis of the reasonability or unreasonability for the existing uncertainty measures, and it is a foundation for designing new uncertainty measures.
[1] Li Deyi, Liu Changyu, Du Yi, et al. Artificial Intelligence with Uncertainty. Journal of Software, 2004, 15(11): 1583-1594 (in Chinese) (李德毅,刘常昱,杜 鹢,等.不确定性人工智能.软件学报, 2004, 15(11): 1583-1594) [2] Pawlak Z. Rough Sets: Theoretical Aspects of Reasoning about Data. Boston, USA: Kluwer Academic Publishers, 1991 [3] Dubois D, Prade H. Rough Fuzzy Sets and Fuzzy Rough Sets. International Journal of General Systems, 1990, 17(2/3): 191-209 [4] Chakrabarty K, Biswas R, Nanda S. Fuzziness in Rough Sets. Fuzzy Sets and Systems, 2000, 110(2): 247-251 [5] Liang Jiye, Chin K S, Dang C Y, et al. A New Method for Measuring Uncertainty and Fuzziness in Rough Set Theory. International Journal of General Systems, 2002, 31(4): 331-342 [6] Banerjee M, Pal S K. Roughness of a Fuzzy Set. Information Sciences: An International Journal, 1996, 93(3/4): 235-246 [7] Huynh V N, Nakamori Y. A Roughness Measure for Fuzzy Sets. Informatics and Computer Science: An International Journal, 2005, 173(1/2/3): 255-275 [8] Pawlak Z. Rough Sets. International Journal of Computer and Information Sciences, 1982, 11: 341-356
[9] Wieman M J. Measuring Uncertainty in Rough Set Theory. International Journal of General Systems, 1999, 28(4/5): 283-297 [10] Miao Duoqian, Wang Jue. On the Relationships between Information Entropy and Roughness of Knowledge in Rough Set Theory. Pattern Recognition and Artificial Intelligence, 1998, 11(1): 34-40 (in Chinese) (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.模式识别与人工智能, 1998, 11(1): 34-40) [11] Liang Jiye, Shi Zhongzhi. The Information Entropy, Rough Entropy and Knowledge Granulation in Rough Set Theory. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2004, 12(1): 37-46 [12] Liang Jiye, Shi Zhongzhi, Li Deyu, et al. Information Entropy, Rough Entropy and Knowledge Granulation in Incomplete Information Systems. International Journal of General Systems, 2006, 35(6): 641-654 [13] Liang Jiye, Li Deyu. Uncertainty and Knowledge Acquisition in Information Systems. Beijing, China: Science Press, 2005 (in Chinese) (梁吉业,李德玉.信息系统中的不确定性与知识获取.北京:科学出版社, 2005) [14] Beaubouef T, Petry F E, Arora G. Information-Theoretic Measures of Uncertainty for Rough Sets and Rough Relational Databases. Information Sciences, 1998, 109(1/2/3/4): 185-195 [15] Wang Guoyin, Zhang Qinghua. Uncertainty of Rough Sets in Different Knowledge Granularities. Chinese Journal of Computers, 2008, 31(9): 1588-1598 (in Chinese) (王国胤,张清华.不同知识粒度下粗糙集的不确定性研究.计算机学报, 2008, 31(9): 1588-1598) [16] Wang Guoyin. Rough Set Theory and Knowledge Acquisition. Xian, China: Xian Jiaotong University Press, 2001 (in Chinese) (王国胤.Rough集理论与知识获取.西安:西安交通大学出版社, 2001) [17] Wang Guoyin, Yu Hong, Yang Dachun. Decision Table Reduction Based on Conditional Information Entropy. Chinese Journal of Computers, 2002, 25(7): 759-766 (in Chinese) (王国胤,于 洪,杨大春.基于条件信息熵的决策表约简.计算机学报, 2002, 25(7): 759-766) [18] Düntsch I, Gediga G. Uncertainty Measures of Rough Set Prediction. Artificial Intelligence, 1998, 106(1): 109-137 [19] Liang Jiye, Qian Yuhua. Information Granules and Entropy Theory in Information Systems. Science in China: Series E, 2008, 38(12): 2048-2065 (in Chinese) (粱吉业,钱宇华.信息系统中的信息粒与熵理论.中国科学E辑, 2008, 38(12): 2048-2065)
2010, Vol. 23 
