南京大学学报(自然科学版) ›› 2015, Vol. 51 ›› Issue (2): 377383.
顾沈明 * , 胡 超, 吴伟志, 王 霞
Gu Shenming*, Hu Chao, Wu Weizhi, Wang Xia
摘要: 在许多场合下,要把论域中的每一个对象或元素区分开来是没有必要的.用粒计算的观点来看,由小的部分可以组成较大的粒.而在不同粒度层次上,人们常常用层次结构的方法来观察或处理数据.由于不同尺度对数据有不同的分割,也就会得到不同层次的信息粒度.这些不同的信息粒度常常用不同的标记来标注.本文先介绍了多标记信息系统的概念,为了引入序关系而重新定义了保序的信息变换函数,并给出了多标记序信息系统的概念.在多标记序信息系统中,利用新的保序的信息变换函数,可以获得知识粒度的一个层次结构.在每一个层次中,利用优势关系可以定义优势类和劣势类,并定义了知识粒的下近似、上近似,进而定义了粗糙度、信息熵、粗糙熵等概念.在不同层次之间,分别讨论了下近似、上近似、粗糙度、信息熵和粗糙熵随着粒度粗细变化而变化的有关性质,在不同的标记粒度层次下探索的知识不确定性的变化规律.
[1] 李德毅,刘常昱,杜 鷁等.不确定性人工智能.软件学报,2004,15(11):1583~1594. [2] 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. [3] Zadeh L A. Fuzzy sets. Information and Control, 1965, 8: 338~353. [4] Pawlak Z. Rough sets. International Journal of Computer and Information Science, 1982, 11(5):341~356. [5] 张 钹,张 铃.问题求解理论及应用.北京:清华大学出版社,1990: 1~476. [6] 张文修,吴伟志,梁吉业等.粗糙集理论与方法.北京:科学出版社,2001:15~90. [7] Chakrabarty k, Biswas R, Nanda S. Fuzziness in rough sets. Fuzzy Sets and Systems, 2000, 110: 247~251. [8] Banerjee M, Pal S K. Roughness of a fuzzy set. Information Sciences, 1996, 93: 235~246. [9] Huynh V H, Nakamori Y. A roughness measure for fuzzy sets. Information Sciences, 2005, 73: 255~275. [10] 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):1~8. [11] Wang G Y, Zhao J, An J J, et al. A comparative study of algebra view point and information view point in attribute reduction. Fundamenta Informaticae, 2005,68(3):289~301. [12] Liang J Y, Chin K S, Dang C Y. A new method for measuring uncertainty and fuzziness in rough set theory. International Journal of General Systems, 2002,31(4):331~342. [13] 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: 1~118. [14] 苗夺谦,范世栋.知识的粒度计算及其应用.系统工程理论与实践,2002,22(1):48~56. [15] 苗夺谦,王 珏.粗糙集理论中概念与运算的信息表示.软件学报,1999,10(2):113~116. [16] 苗夺谦,王国胤,刘 清等.粒计算:过去、未来和展望.北京:科学出版社,2007: 1~388. [17] Mi J S, Leung Y, Wu W Z. An uncertainty measure in partition-based fuzzy rough sets. International Journal of General Systems, 2005,34:77~90. [18] Greco S, Matarazzo B, Slowingski R. Rough approximation of a preference relation by dominance relation. European Journal of Operational Research, 1999,117:63~83. [19] Greco S, Matarazzo B, Slowingski R. Rough sets theory for multicriteria decision analysis. European Journal of Operational Research, 2001,129:1~47. [20] Greco S, Matarazzo B, Slowinski R. Rough approximation by dominance relations. International Journal of Inteligent Systems, 2002,17( 2):153~171. [21] Greco S, Inuiguchi M, Slowinski R. Fuzzy rough sets and multiple-premise gradual decision rules. International Journal of Approximate Reasoning, 2006,41:179~211. [22] Yang X B, Yu D J, Yang J Y, et al. Dominance-based rough set approach to incomplete interval-valued information system. Data & Knowledge Engineering, 2009,68:1331~1347. [23] Xu W H, Zhang X Y, Zhang W X. Knowledge granulation, knowledge entropy and knowledge uncertainty measure in ordered information systems. Applied Soft Computing, 2009,9:1244~1251. [24] 顾沈明,叶晓敏,吴伟志.多标记粒度不完备信息系统的粗糙近似.南京大学学报(自然科学),2013,49(2):250~257. [25] Wu W Z, Leung Y. Theory and applications of granular labeled partitions in multi-scale decision tables. Information Sciences, 2011, 181: 3878~3897. [26] 顾沈明,吴伟志,徐优红.不完备多标记信息系统中粒度研究.南京大学学报(自然科学),2013,49(5):567~573. [27] Gu S M, Wu W Z. On knowledge acquisition in multi-scale decision systems. International Journal of Machine Learning and Cybernetics, 2013,4(5):477~486. [28] 张文修,米据生,吴伟志.不协调目标信息系统的知识约简. 计算机学报,2003, 26(1): 12~18. [29] Shao M W, Zhang W X. Dominance relation and rules in an incomplete ordered information system. International Journal of Intelligent Systems, 2005,20:13~27. [30] 徐伟华.序信息系统与粗糙集.北京:科学出版社,2013: 1~214. |
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