南京大学学报(自然科学版) ›› 2015, Vol. 51 ›› Issue (2): 377–383.

• • 上一篇    下一篇

多标记序信息系统的不确定性研究


顾沈明 * , 胡 超, 吴伟志, 王 霞   

  • 出版日期:2015-03-06 发布日期:2015-03-06
  • 作者简介:(浙江海洋学院数理与信息学院,舟山,316022)
  • 基金资助:
    国家自然科学基金 (61272021, 61075120, 61202206, 61173181),浙江省自然科学基金重点项目(LZ12F03002),海洋科学浙江省重中之重学科开放课题(20130109)

Uncertainty measures in multi-label ordered information systems


Gu Shenming*, Hu Chao, Wu Weizhi, Wang Xia   

  • Online:2015-03-06 Published:2015-03-06
  • About author:(School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan, 316022)

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. 

Abstract: In many real-life applications, it is impossible or unnecessary to distinguish individual objects or elements in universe of discourses. With the view point of granular computing, the notion of a granule may be interpreted as one of the numerous small particles forming a larger unit. Human beings often observe objects or deal with data hierarchically structured at different levels of granulations. There are different granules at different levels of scale in data sets having hierarchical structures. These different granulations often use different labels to mark. The purpose of this study is to analyze representations of granules and uncertainty measures in multi-label ordered information systems. The concept of multi-label information systems is first reviewed. The notion of granular information transformation functions between ordered sets is redefined in multi-label information systems. These functions are ordered preserving. Then, the concept of multi-label ordered information systems is introduced. By employing the new functions of granular information transformation, hierarchical structures of granules with different levels of granulations are derived in multi-label ordered information systems. At each level of granulations, dominance classes and dominated classes determined by dominance relations are also produced. Lower and upper approximations of any subset of the universe of discourse constructed by both dominance classes and dominated classes in multi-label ordered information systems are further explored, and their properties are examined. Finally, uncertainty measures such as roughness, information entropy and rough entropy of an object set at each level of granulations are also presented as usual way in multi-label ordered information systems. Monotonic properties of these uncertainty measures with different levels of granulations are analyzed.

[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.
No related articles found!
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!