Journal of Shandong University(Engineering Science) ›› 2022, Vol. 57 ›› Issue (5): 20-27.doi: 10.6040/j.issn.1671-9352.7.2021.216

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α-lower and upper approximation reductions in inconsistent interval-valued decision systems

ZHANG Xiao-yu1, LI Tong-jun1,2*   

  1. 1. School of Information Engineering, Zhejiang Ocean University, Zhoushan 316022, Zhejiang, China;
    2. Key Laboratory of Oceanographic Big Data Mining &
    Application of Zhejiang Province, Zhoushan 316022, Zhejiang, China
  • Published:2022-06-21

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Abstract: The focus is on the attribute reductions of inconsistent interval-valued decision systems based on α-tolerance relation. With respect to one kind of α-tolerance relations in inconsistent interval-valued decision systems, notions of α-lower and upper approximate reductions are defined, which keep the lower and upper approximations of all the decision classes unchanged, respectively. Subsequently, the equivalences among the α-upper approximate reduction and α-generalized decision reduction, α-uncertainty maintained reduction, and between α-lower approximate reduction and α-certainty maintained reduction are proved. Meanwhile, the relationships between α-lower approximate reduction and α-upper approximate reduction are discussed in detail, and verified by some examples.

Key words: rough set, inconsistent interval-valued decision system, α-tolerance relation, α-upper approximate reduction, α-lower approximate reduction

CLC Number: 

  • TP18
[1] PAWLAK Z. Rough sets[J]. International Journal of Computer & Information Sciences, 1982, 11(5):341-356.
[2] 张文修, 吴伟志, 梁吉业, 等. 粗糙集论与理方法[M]. 北京: 科学出版社, 2001. ZHANG Wenxiu, WU Weizhi, LIANG Jiye, et al. Rough set theory and approach[M]. Beijing: Science Press, 2001.
[3] 张文修, 梁怡, 吴伟志. 信息系统与知识发现[M]. 北京: 科学出版社, 2003. ZHANG Wenxiu, LIANG Yi, WU Weizhi. Information systems and knowledge discovery[M]. Beijing: Science Press, 2003.
[4] YAO Yiyu, ZHAO Yan. Attribute reduction in decision-theoretic rough set models[J]. Information Sciences, 2008, 178(17):3356-3373.
[5] 张文修, 米据生, 吴伟志. 不协调目标信息系统的知识约简[J]. 计算机学报, 2003, 26(1):12-18. ZHANG Wenxiu, MI Jusheng, WU Weizhi. Knowledge reductions in inconsistent information systems[J]. Chinese Journal of Computers, 2003, 26(1):12-18.
[6] 徐伟华, 张晓燕, 张文修. 优势关系下不协调目标信息系统的上近似约简[J]. 计算机工程, 2009, 35(18):191-193. XU Weihua, ZHANG Xiaoyan, ZHANG Wenxiu. Upper approximation reduction in inconsistent target information system based on dominance relations[J]. Computer Engineering, 2009, 35(18):191-193.
[7] 徐伟华, 张晓燕, 张文修. 优势关系下不协调目标信息系统的下近似约简[J]. 计算机工程与应用, 2009, 45(16):66-68. XU Weihua, ZHANG Xiaoyan, ZHANG Wenxiu. Lower approximation reduction in inconsistent information systems based on dominance relations[J]. Computer Engineering and Applications, 2009, 45(16):66-68.
[8] 李同军, 张文修, 马建敏. 基于粗糙集的形式背景属性约简及属性特征[J]. 计算机科学, 2006, 33(9):178-180. LI Tongjun, ZHANG Wenxiu, MA Jianmin. Attribute reductions and attribute features of formal contexts based on a type of rough sets[J]. Computer Science, 2006, 33(9):178-180.
[9] KRYSZKIEWICZ M. Rules in incomplete information systems[J]. Information Sciences, 1999, 113(3/4):271-292.
[10] KRYSZKIEWICZ M. Rough set approach to incomplete information systems[J]. Information Sciences, 1998, 112(1/2/3/4):39-49.
[11] MIAO Duoqian, ZHANG Nan,YUE Xiaodong. Knowledge reduction in interval-valued information systems[C] //Proceedings of the 8th IEEE International Conference on Cognitive Informatics. Washington: IEEE Computer Society, 2009: 320-327.
[12] 刘鹏惠, 陈子春, 秦克云. 区间值信息系统的决策属性约简[J]. 计算机工程与应用, 2009, 45(28):148-150. LIU Penghui, CHEN Zichun, QIN Keyun. Decision attribute reduction of interval-valued information system[J]. Computer Engineering and Applications, 2009, 45(28):148-150.
[13] DAI Jianhua, WEI Bingjie, ZHANG Xiaohong, et al. Uncertainty measurement for interval-valued information systems based on α-weak similarity[J]. Knowledge-Based Systems, 2017, 136:159-171.
[14] DAI Jianhua, HU Hu, ZHENG Guojie, et al. Attribute reduction in interval-valued information systems based on information entropies[J]. Frontiers of Information Technology & Electronic Engineering, 2016, 17(9):919-928.
[15] LEUNG Y, FISCHER M M, WU W Z, 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.
[16] QIAN Yuhua, LIANG Jiye, DANG Chuangyin. Interval ordered information systems[J]. Computers and Mathematics with Applications, 2008, 56(8):1994-2009.
[17] YANG Xibei, YU Dongjun, YANG Jingyu, et al. Dominance-based rough set approach to incomplete interval-valued information system[J]. Data & Knowledge Engineering, 2009, 68(11):1331-1347.
[18] YANG Xibei, QI Yong, YU Dongjun, et al. α-dominance relation and rough sets in interval-valued information systems[J]. Information Sciences, 2015, 294(5):334-347.
[19] YANG Lei, ZHANG Xiaoyan, XU Weihua, et al. Attribute reduction based on improving DIT in interval-valued ordered information system[J]. The Journal of Engineering, 2020, 2020(13):429-437.
[20] ZHANG Xiao, MEI Changlin, CHEN Degang, et al. Multi-confidence rule acquisition and confidence-preserved attribute reduction in interval-valued decision systems[J]. International Journal of Approximate Reasoning, 2014, 55(8):1787-1804.
[21] LIN Bingyan, ZHANG Xiaoyan. Relative reduction of incomplete interval-valued decision information systems associated with evidence theory[J]. Journal of Information Sciences and Engineering, 2019, 35(6):1377-1396.
[22] ZHANG Jia, ZHANG Xiaoyan, XU Weihua. Attribute reduction in interval-valued fuzzy ordered decision tables via evidence theory[J]. The Journal of Engineering, 2018, 2018(16):1475-1482.
[23] 张楠, 许鑫, 童向荣, 等. 不协调区间值决策系统的知识约简[J]. 小型微型计算机系统, 2017, 38(7):1585-1589. ZHANG Nan, XU Xin, TONG Xiangrong, et al. Knowledge reduction in inconsistent interval-valued decision systems[J]. Journal of Chinese Computer Systems, 2017, 38(7):1585-1589.
[24] 张楠, 许鑫, 童向荣, 等. 不协调区间值决策系统的分布约简[J]. 计算机科学, 2017, 44(9):78-82,104. ZHANG Nan, XU Xin, TONG Xiangrong, et al. Distribution reduction in inconsistent interval-valued decision systems[J]. Computer Science, 2017, 44(9):78-82,104.
[25] 尹继亮, 张楠, 赵立威, 等. 区间值决策系统的局部属性约简[J]. 计算机科学, 2018, 45(7):178-185. YIN Jiliang, ZHANG Nan, ZHAO Liwei, et al. Local attribute reduction in interval-valued decision systems[J]. Computer Science, 2018, 45(7):178-185.
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