JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2018, Vol. 53 ›› Issue (8): 1-8.doi: 10.6040/j.issn.1671-9352.4.2018.184

    Next Articles

Local optimal granularity selections in generalized multi-scale decision systems

GU Shen-ming1,2, LU Jin-lu2, WU Wei-zhi1,2, ZHUANG Yu-bin2   

  1. 1. Key Laboratory of Oceanographic Big Data Mining &
    Application of Zhejiang Province, Zhejiang Ocean University, Zhoushan 316022, Zhejiang, China;
    2. School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan 316022, Zhejiang, China
  • Received:2018-04-15 Online:2018-08-20 Published:2018-07-11

Abstract: People tend to choose the appropriate level of granularity to solve problems in application. In the classical multi-scale decision systems, during the process of constructing the levels of granularity, some fixed levels of granularity are selected manually for attribute values. Aiming at generalized multi-scale decision systems in this paper, the levels of granularity are constructed by using the scale combination of attribute values. Furthermore, the selection problems of local optimal granularity are studied. The concept of generalized multi-scale decision systems is introduced firstly. Then, notions of the optimal granularity and the local optimal granularity in consistent generalized multi-scale decision system are defined, and the algorithms for finding optimal granularities and the local optimal granularities are described. Finally, the generalized decisions are introduced to inconsistent generalized multi-granular decision systems, the generalized optimal granularity and the generalized local optimal granularity are defined, and the algorithms for finding the generalized optimal granularity and the generalized local optimal granularity are also investigated.

Key words: decision system, local optimal granularity, multi-scale, generalized multi-scale

CLC Number: 

  • TP18
[1] ZADEH L A. Fuzzy sets and information granularity[J]. Fuzzy Sets, Fuzzy Logic and Fuzzy Systems, 1996, 6:443-448.
[2] LIN T Y. Granular computing: structures, representations, and applications[C] // WANG G Y, LIU Q, YAO Y Y, et al. Rough Sets, Fuzzy Sets, Data Mining, Granular Computing. Berlin: Springer, 2003: 16-24.
[3] YAO Y Y. Granular computing: basic issues and possible solutions[C] // Proc of the 5th Joint Conference on Information Science. Berlin: Springer, 2000: 186-189.
[4] YAO J T, VASILAKOS A V, PEDRYCZ W. Granular computing: perspectives and challenges[J]. IEEE Transactions on Cybernetics, 2013, 43(6):1977-1989.
[5] 梁吉业,钱宇华,李德玉,等. 大数据挖掘的粒计算理论与方法[J]. 中国科学(信息科学), 2015, 45(11):1355-1369. LIANG Jiye, QIAN Yuhua, LI Deyu, et al. Theory and method of granular computing for big data mining[J]. Science China(Information Sciences), 2015, 45(11):1355-1369.
[6] 徐计, 王国胤, 于洪. 基于粒计算的大数据处理[J]. 计算机学报, 2015, 38(8):1497-1517. XU Ji, WANG Guoyin, YU Hong. Review of big data processing based on granular computing[J]. Chinese Journal of Computers, 2015, 38(8):1497-1517.
[7] 刘清, 邱桃荣, 刘斓. 基于非标准分析的粒计算研究[J]. 计算机学报, 2015, 38(8):1618-1627. LIU Qing, QIU Taorong, LIU Lan. The research of granular computing based on nonstandard analysis[J]. Chinese Journal of Computers, 2015, 38(8):1618-1627.
[8] PAWLAK Z. Rough sets[J]. International Journal of Computer and Information Science, 1982, 11(5):341-356.
[9] ZADEH L A. Fuzzy sets[J]. Information and Control, 1965, 8:338-353.
[10] 张铃,张钹. 基于商空间的问题求解:粒度计算的理论基础[M]. 北京:清华大学出版社, 2014. ZHANG Ling, ZHANG Bo. Quotient space based problem solving: a theoretical foundation of granular computing[M]. Beijing: Tsinghua University Press, 2014.
[11] INUIGUCHI M, HIRANO S, TSUMOTO S. Rough set theory and granular computing[M]. Berlin: Springer, 2002.
[12] LIN T Y, YAO Y Y, ZADEH L A. Data mining, rough sets and granular computing[M]. New York: Physica-Verlag, 2002.
[13] 苗夺谦,李德毅,姚一豫,等. 不确定性与粒计算[M]. 北京:科学出版社,2011. MIAO Duoqian, LI Deyi, YAO Yiyu, et al. Uncertainty and granular computing[M]. Beijing: Science Press, 2011.
[14] PEDRYCZ W, SKOWRON A, KREINOVICH V. Handbook of granular computing[M]. New York: Wiley, 2008.
[15] YANG X B, QIAN Y H, YANG J Y. Hierarchical structures on multigranulation spaces[J]. Journal of Computer Science and Technology, 2012, 27:1169-1183.
[16] 李金海, 吴伟志. 形式概念分析的粒计算方法及其研究展望[J]. 山东大学学报(理学版), 2017, 52(7):1-12. LI Jinhai, WU Weizhi. Granular computing approach for formal concept analysis and its research outlooks[J]. Journal of Shandong University(Natural Science), 2017, 52(7):1-12.
[17] 马媛媛, 孟慧丽, 徐久成, 等. 基于粒计算的正态粒集下的格贴近度[J]. 山东大学学报(理学版), 2014, 49(8):107-110. MA Yuanyuan, MENG Huili, XU Jiucheng, et al. Normal distribution of lattice close-degree based on granular computing[J]. Journal of Shandong University(Natural Science), 2014, 49(8):107-110.
[18] QIAN Y H, LIANG J Y, YAO Y Y, et al. MGRS: a multi-granulation rough set[J]. Information Sciences, 2010, 180(6):949-970.
[19] QIAN Y H, LIANG J Y, DANG C Y. Incomplete multi-granulation rough set[J]. IEEE Transactions on Systems, Man and Cybernetics, 2010, 40(2):420-431.
[20] YANG X B, SONG X N, CHEN Z H, et al. On multigranulation rough sets in incomplete information system[J]. International Journal of Machine Learning and Cybernetics 2012, 3(3):223-232.
[21] SUN B Z, MA W M, QIAN Y H. Multigranulation fuzzy rough set over two universes and its application to decision making[J]. Knowledge-Based Systems, 2017, 123:61-74.
[22] WU W Z, LEUNG Y. Theory and applications of granular labelled partitions in multi-scale decision tables[J]. Information Sciences, 2011, 181(18):3878-3897.
[23] WU W Z, LEUNG Y. Optimal scale selection for multi-scale decision tables[J]. International Journal of Approximate Reasoning, 2013, 54(8):1107-1129.
[24] 吴伟志, 陈颖, 徐优红, 等. 协调的不完备多粒度标记决策系统的最优粒度选择[J]. 模式识别与人工智能, 2016, 29(2):108-115. WU Weizhi, CHEN Ying, XU Youhong, et al. Optimal granularity selections in consistent incomplete multi-granular labeled decision systems[J]. Pattern Recognition and Artificial Intelligence, 2016, 29(2):108-115.
[25] GU S M, WU W Z. On knowledge acquisition in multi-scale decision systems[J]. International Journal of Machine Learning and Cybernetics, 2013, 4(5):477-486.
[26] GU S M, WU W Z. Knowledge acquisition in inconsistent multi-scale decision systems[C] // YAO J T, RAMANNA S, WANG G Y, et al. Lecture Notes in Computer Science. Berlin: Springer, 2011, 6954:669-678.
[27] LI F, HU B Q, WANG J. Stepwise optimal scale selection for multi-scale decision tables via attribute significance[J]. Knowledge-Based Systems, 2017,129:4-16.
[28] LI F, HU B Q. A new approach of optimal scale selection to multi-scale decision tables[J]. Information Sciences, 2017, 381:193-208.
[1] PAN Qingfei1, SHAN Wei2*, WU Jianliang3. A spectral stochastic multi-scale finite element method for
the exterior problem of the Helmholtz equation
[J]. J4, 2011, 46(6): 37-40.
[2] QU Xiao-bo,FENG Cun-feng,ZHANG Xue-yao,XUE Liang . Multi-scale image analysis applied to distinguish primary iron of cosmic rays in the knee region [J]. J4, 2008, 43(5): 19-23 .
Full text



No Suggested Reading articles found!