Double-Level Absolute Reduction for Multi-granulation Rough Sets
DENG Dayong1, HUANG Houkuan2
1.Xingzhi College, Zhejiang Normal University, Jinhua 321004 2.School of Computer and Information Technology, Beijing Jiaotong University, Beijing 100044
Abstract：Multi-granulation rough set is a rough set model for heterogenous data in essence. However, it is still not employed to deal with heterogenous data. From the viewpoints of absolute attribute reduction, double-level absolute reduction for multi-granulation rough sets is proposed, including multi-granulation absolute recducts and multi-granulation absolute granulation reducts, and properties of double-level absolute reduction are analyzed from the perspective of heterogenous data. The algorithms for double-level absolute reduction are presented. Theoretical analysis and example show the validation of multi-granulation absolute reducts, multi-granulation absolute granulation reducts and double-level absolute reducts.
[1] PAWLAK Z.Rough Sets.International Journal of Computer and Information Sciences, 1982, 11(5): 341-356. [2] PAWLAK Z, SKOWRON A.Rudiments of Rough Sets.Information Sciences, 2007, 177(1): 3-27. [3] ZIAKO W.Variable Precision Rough Sets Model. Journal of Compu-ter and System Sciences, 1993, 46(1): 39-59. [4] 冯 林,李天瑞,余志强.连续值属性决策表中的可变精度粗糙集模型及属性约简.计算机科学, 2010, 37(9): 205-208. (FENG L, LI T R, YU Z Q.Attributes Reduction Based on the Variable Precision Rough Set in Decision Tables Containing Conti-nuous-Valued Attributes.Computer Science, 2010, 37(9): 205-208.) [5] ZHU W, WANG F Y.Reduction and Axiomization of Covering Ge-neralized Rough Sets.Information Sciences, 2003,152: 217-230. [6] 张灵均,徐久成,李双群,等.相斥邻域的覆盖粗糙集实值属性约简.山东大学学报(理学版), 2012, 47(1): 77-82. (ZHANG L J, XU J C, LI S Q, et al. Numerical Attribute Reduction of Mutex Neighborhood Covering Rough Set Theory. Journal of Shandong University(Natural Science), 2012, 47(1): 77-82.) [7] YAO Y Y, WONG S K M.A Decision Theoretic Framework for Approximating Concepts. International Journal of Man-Machine Studies, 1992, 37(6): 793-809. [8] 刘 盾,姚一豫,李天瑞.三枝决策粗糙集.计算机科学, 2011, 38(1): 246-250. (LIU D, YAO Y Y, LI T R.Three-Way Decision-Theoretic Rough Sets. Computer Science, 2011, 38(1): 246-250.) [9] DUBOIS D, PRADE H. Rough Fuzzy Sets and Fuzzy Rough Sets. International Journal of General Systems, 1990, 17(2/3): 191-209. [10] 徐菲菲,苗夺谦,魏 莱,等.基于互信息的模糊粗糙集属性约简.电子与信息学报, 2008, 30(6): 1372-1375. (XU F F, MIAO D Q, WEI L, et al.Mutual Information-Based Algorithm for Fuzzy-Rough Attribute Reduction. Journal of Electronics & Information Technology, 2008, 30(6): 1372-1375.) [11] LIN T Y.Neighborhood Systems: A Qualitative Theory for Fuzzy and Rough Sets[M/OL].[2016-06-25]. http://xanadu.cs.sjsu.edu/~tylin/publications/paperList/94.pdf. [12] HU Q H, ZHANG L, ZHANG D, et al. Measuring Relevance between Discrete and Continuous Features Based on Neighborhood Mutual Information. Expert Systems with Applications: An International Journal, 2011, 38(9): 10737-10750. [13] SHI K Q, ZHAO J L .Function S-Rough Sets and Security-Authentication of Hiding Law.Science in China(Information Science),2008, 51(7): 924-935. [14] SHI K Q, YAO B X. Function S-Rough Sets and Law Identifica-tion. Science in China(Information Science), 2008, 51(5): 499-510. [15] QIAN Y H, LIANG J Y, YAO Y Y, et al.MGRS: A Multi-granulation Rough Set. Information Sciences, 2010, 180(6): 949-970. [16] 张 明,唐振民,徐维艳,等.可变多粒度粗糙集模型.模式识别与人工智能, 2012, 25(4): 709-720. (ZHANG M, TANG Z M, XU W Y, et al. Variable Multigranulation Rough Set Model.Pattern Recognition and Artificial Intelligence, 2012, 25(4): 709-720.) [17] 邓大勇,陈 林.并行约简与F-粗糙集 // 苗夺谦,王国胤,姚一豫,等,编.云模型与粒计算.北京:科学出版社, 2012: 210-228. (DENG D Y, CHEN L. Parallel Reducts and F-Rough Sets // MIAO D Q, WANG G Y, YAO Y Y, et al., eds. Cloud Model and Granular Computing.Beijing, China: Science Press, 2012: 210-228.) [18] 陈 林.粗糙集中不同粒度层次下的并行约简及决策.硕士学位论文.金华:浙江师范大学, 2013. (CHEN L.Parallel Reducts and Decision in Various Levels of Granularity.Master Dissertation.Jinhua,China: Zhejiang Normal University, 2013.) [19] 邓大勇,裴明华,黄厚宽.F-粗糙集方法对概念漂移的度量.浙江师范大学学报(自然科学版), 2013, 36(3): 303-308. (DENG D Y, PEI M H, HUANG H K. The F-Rough Sets Approaches to the Measures of Concept Drift. Journal of Zhejiang Normal University(Natural Sciences), 2013, 36(3): 303-308.) [20] 邓大勇,徐小玉,黄厚宽.基于并行约简的概念漂移探测.计算机研究与发展, 2015, 52(5): 1071-1079. (DENG D Y, XU X Y, HUANG H K.Concept Drifting Detection for Categorical Evolving Data Based on Parallel Reducts. Journal of Computer Research and Development,2015,52(5): 1071-1079.) [21] 顾力平,杨习贝.基于一般二元关系的多粒度粗糙集模型.南京航空航天大学学报, 2013, 45(1): 124-129. (GU L P, YANG X B. Multigranulation Rough Set Models Based on General Binary Relations. Journal of Nanjing University of Aeronautics & Astronautics, 2013, 45(1): 124-129.) [22] 李 聪.多粒度模糊粗糙集研究.数学杂志, 2016, 36(1): 124-134.
(LI C. The Study on Multi-granulation Fuzzy Rough Set. Journal of Mathematics, 2016, 36(1): 124-134.) [23] 桑妍丽,钱宇华.一种悲观多粒度粗糙集中的粒度约简算法.模式识别与人工智能, 2012, 25(3): 361-366. (SAN Y L, QIAN Y H.A Granular Space Reduction Approach to Pessimistic Multi-granulation Rough Sets.Pattern Recognition and Artificial Intelligence, 2012, 25(3): 361-366.) [24] 桑 林,李续武.基于可变相容粒空间的多粒度覆盖粗糙集模型.计算机技术与发展, 2015, 25(8): 35-38. (SANG L,LI X W.Multi-granule Covering Rough Sets Model Based on Variable Precision Tolerant-Granule Space.Computer Technology and Development, 2015, 25(8): 35-38.) [25] 安 虹.区间值信息系统多粒度粗糙集拓展模型的知识约简.硕士学位论文.临汾:山西师范大学, 2014. (AN H.Knowledge Reduction Based on Multigranulation Rough Set Extended Model in Interval Valued Information System.Master Dissertation. Linfen, China: Shanxi Normal University, 2014.)
2016, Vol. 29 
