|Table of Contents|

Uncertainty measurement for interval set decision informationtables based on conditional information entropy(PDF)

《南京理工大学学报》(自然科学版)[ISSN:1005-9830/CN:32-1397/N]

Issue:
2019年04期
Page:
393-401
Research Field:
Publishing date:

Info

Title:
Uncertainty measurement for interval set decision informationtables based on conditional information entropy
Author(s):
Zhang YimengJia XiuyiTang Zhenmin
School of Computer Science and Engineering,Nanjing University of Science andTechnology,Nanjing 210094,China
Keywords:
rough set theory uncertainty measurement interval set decision tables approximation sets granular computing
PACS:
TP391
DOI:
10.14177/j.cnki.32-1397n.2019.43.04.003
Abstract:
This paper aims at studying uncertainty measures for interval set decision information tables based on conditional information entropy. A binary similarity relation,called δ-interval similarity relation in an interval set decision table is proposed to depict the relationships of objects. Based on this relation,the extended uncertainty measures from Pawlak rough set model,namely,approximate accuracy and approximate roughness,are defined in interval set decision information tables. According to the analysis of δ-interval approximate accuracy and δ-interval approximate roughness,they are not sensitive to the variation of granular structure. A new uncertainty measure called δ-interval decision conditional entropy is proposed by combining with conditional information entropy in interval set decision tables. The associated properties of δ-interval approximate accuracy,δ-interval approximate roughness and δ-interval decision conditional entropy are analyzed and proved. Through an actual example,the proposed δ-interval decision conditional entropy can measure the uncertainty of interval set decision tables effectively and accurately.

References:

[1] Pawlak Z. Rough sets[J]. International Journal of Computer & Information Sciences,1982,11(5):341-356.
[2]Yao Yiyu. Information granulation and rough set approximation[J]. International Journal of Intelligent Systems,2001,16(1):87-104.
[3]Xu Weihua,Zhang Xianyao,Zhang Wenxiu. Knowledge granulation,knowledge entropy and knowledge uncertainty measure in ordered information systems[J]. Applied Soft Computing,2009,9(4):1244-1251.
[4]Jia Xiuyi,Liao Wenhe,Tang Zhenmin,et al. Minimum cost attribute reduction in decision-theoretic rough set models[J]. Information Sciences,2013,219:151-167.
[5]Zhang Yimeng,Jia Xiuyi,Tang Zhenmin. Minimum cost attribute reduction in incomplete systems under decision-theoretic rough set model[C]//Proceedings of Fuzzy Systems and Knowledge Discovery. Piscataway,NJ:IEEE,2016:940-944.
[6]Dai Jianhua,Tian Haowei,Wang Wentao,et al. Decision rule mining using classification consistency rate[J]. Knowledge-Based Systems,2013,43(2):95-102.
[7]Jia Xiuyi,Rao Ya,Shang Ling,et al. Similarity-based attribute reduction in rough set theory:a clustering perspective[J]. International Journal of Machine Learning and Cybernetics,2019.
[8]王宇,杨志荣,杨习贝. 决策粗糙集属性约简:一种局部视角方法[J]. 南京理工大学学报,2016,40(4):444-449.
[9]Leung Y,Fischer M M,Wu Weizhi,et al. A rough set approach for the discovery of classification rules in interval-valued information systems[J]. International Journal of Approximate Reasoning,2008,47(2):233-246.
[10]Gediga G,Duntsch I. Rough approximation quality revisited[J]. Artificial Intelligence,2001,132(2):219-234.
[11]Dai Jianhua,Xu Qing. Approximations and uncertainty measures in incomplete information systems[J]. Information Sciences,2012,198:62-80.
[12]Shannon C E,Weaver W. The mathematical theory of communication[J]. Bell Labs Technical Journal,1950,3(9):31-32.
[13]Duntsch I,Gediga G. Uncertainty measures of rough set prediction[J]. Artificial Intelligence,1998,106(1):109-137.
[14]Beaubouef T,Petry F E,Arora G. Information-theoretic measures of uncertainty for rough sets and rough relational databases[J]. Information Sciences,1998,109(1-4):185-195.
[15]Yao Yiyu,Zhao Liquan. A measurement theory view on the granularity of partitions[J]. Information Sciences,2012,213(23):1-13.
[16]Liang Jiye,Shi Zhongzhi. The information entropy,rough entropy and knowledge granulation in rough set theory[J]. International Journal of Uncertainty,Fuzziness and Knowledge-Based Systems,2004,12(1):37-46.
[17]Liang Jiye,Shi Zhongzhi,Li Deyu,et al. Information entropy,rough entropy and knowledge granulation in incomplete information systems[J]. International Journal of General Systems,2006,35(6):641-654.
[18]Qian Yuhua,Liang Jiye. Combination entropy and combination granulation in rough set[J]. International Journal of Uncertainty,Fuzziness and Knowledge-Based Systems,2008,16(2):179-193.
[19]Dai Jianhua,Wang Wentao,Xu Qing,et al. Uncertainty measurement for interval-valued decision systems based on extended conditional entropy[J]. Knowledge-Based Systems,2012,27:443-450.
[20]Dai Jianhua,Wang Wentao,Mi Jusheng. Uncertainty measurement for interval-valued information systems[J]. Information Sciences,2013,251(4):63-78.
[21]Yao Yiyu,Liu Qing. A generalized decision logic in interval-set-valued information tables[C]//Proceedings of International Workshop on New Directions in Rough Sets,Data Mining and Granular-Soft Computing. Berlin,Germany:Springer-Verlag,1999.
[22]Zhang Qinghua,Wang Jin,Wang Guoyin,et al. Approximation set of the interval set in pawlak’s space[J]. The Scientific World Journal,2014(11):317-329.
[23]Yao Yiyu. Interval-set algebra for qualitative knowledge representation[C]//Proc of the 5th International Conference on Computing & Information. Sudbury:IEEE,1993:370-374.
[24]林耀进,李进金,吴顺祥. 区间集值信息系统中的粗糙集理论[J]. 控制与决策,2011,26(11):1611-1615.
Lin Yaojin,Li Jinjin,Wu Shunxiang. Rough set theory in interval and set-valued information systems[J]. Control and Decision,2011,26(11):1611-1615.
[25]Wang Hong,Yue Hongbo. Entropy measures and granularity measures for interval and set-valued information systems[J]. Soft Computing,2016,20(9):3489-3495.
[26]王国胤,于洪,杨大春. 基于条件信息熵的决策表约简[J]. 计算机学报,2002,25(7):759-766.
Wang Guoyin,Yu Hong,Yang Dachun. Decision table reduction based on conditional information entropy[J]. Chinese Journal of Computers,2002,25(7):759-766.

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Last Update: 2019-09-30