Incomplete Multi-granulation Reduction Based on Discernibility Matrix
LIU Kai1,2, TAN Anhui1,2, GU Shenming1,2
1. School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan 316022 2. Key Laboratory of Oceanographic Big Data Mining and Appli-cation of Zhejiang Province, Zhejiang Ocean University, Zhou-shan 316022
Abstract For the incomplete data with missing attribute values, the multi-granularity reduction structures of incomplete information systems and incomplete decision systems are constructed from the perspective of discernibility matrix. Firstly, the reduction attributes of incomplete information systems based on pessimistic and optimistic multi-granularity approximations are discussed, and three types of multi-granularity discernibility matrices of incomplete information systems and incomplete decision systems are constructed. Then, it is theoretically proved that all the multi-granularity reductions of incomplete information systems and incomplete decision systems can be computed accurately by the disjunctive and conjunctive logical operations of the constructed discernibility matrices. Finally, examples are given to demonstrate the effectiveness and practicability of the proposed method.
Fund:National Natural Science Foundation of China(No. 62076221,61976194)
Corresponding Authors:
TAN Anhui, Ph.D. associate professor. His research interests include granular computing and data mining.
About author:: LIU Kai, master student. His research interests include granular computing and data mining.GU Shenming, master, professor. His research interests include granular computing, data mining and deep learning.
[1] QIAN Y H, LIANG J Y, YAO Y Y, et al. MGRS: A Multi-granulation Rough Set. Information Sciences, 2010, 180(6): 949-970. [2] QIAO Y H, LIANG J Y, DANG C Y. Incomplete Multigranulation Rough Set. IEEE Transactions on Systems, Man, and Cybernetics(Systems and Humans), 2010, 40(2): 420-431. [3] TAN A H, WU W Z, LI J J, et al. Evidence-Theory-Based Numerical Characterization of Multigranulation Rough Sets in Incom-plete Information Systems. Fuzzy Sets and Systems, 2016, 294: 18-35. [4] 徐 怡,孙伟康,王 泉.邻域多粒度粗糙集知识更新增量算法.小型微型计算机系统, 2020, 41(5): 908-918. (XU Y, SUN W K, WANG Q. Incremental Algorithm for Know-ledge Updating of Neighborhood Multigranulation Rough Set. Journal of Chinese Computer Systems, 2020, 41(5): 908-918.) [5] 翁 冉,王俊红,魏 巍,等.基于区分矩阵的多粒度属性约简.南京航空航天大学报, 2019, 51(5): 636-642. (WENG R, WANG J H, WEI W, et al. Multi-granulation Attribute Reduction Based on Discernibility Matrix. Journal of Nanjing University of Aeronautics and Astronautics, 2019, 51(5): 636-642.) [6] 赵思雨,钱 婷,魏 玲.基于决策表的多粒度粗糙集属性约简研究.陕西师范大学学报(自然科学版), 2019, 47(3): 73-78. (ZHAO S Y, QIAN T, WEI L. The Attribute Reduction in MGRS Based on a Decision Table. Journal of Shaanxi Normal University (Natural Science Edition), 2019, 47(3): 73-78.) [7] 万 青,马盈仓,魏 玲.基于多粒度的多源数据知识获取.山东大学学报(理学版), 2020, 55(1): 41-50. (WAN Q, MA Y C, WEI L. Knowledge Acquisition of Multi-source Data Based on Multigranularity. Journal of Shandong University(Natural Science), 2020, 55(1): 41-50.) [8] 薛占熬,赵丽平,张 敏,等.多粒度支持直觉模糊粗糙集的多属性决策方法.模式识别与人工智能, 2019, 32(8): 677-690. (XUE Z A, ZHAO L P, ZHANG M, et al. Multi-attribute Decision-Making Method Based on Multi-granulation Support Intuitioni-stic Fuzzy Rough Sets. Pattern Recognition and Artificial Intelligence, 2019, 32(8): 677-690.) [9] 梁美社,米据生,侯成军,等.基于局部广义多粒度粗糙集的多标记最优粒度选择.模式识别与人工智能, 2019, 32(8): 718-725. (LIANG M S, MI J S, HOU C J, et al. Optimal Granulation Selection for Multi-label Data Based on Local Generalized Multi-granulation Rough Set. Pattern Recognition and Artificial Intelligence, 2019, 32(8): 718-725.) [10] 李雪岩,李学伟,蒋 君.基于知识粒度特征的多目标粗糙集属性约简算法[J/OL].[2020-05-25]. https://doi.org/10.13195/j.kzyjc.2019.0490. (LI X Y, LI X W, JIANG J. Multi Objective Rough Set Attribute Reduction Algorithm Based on the Characteristics of Knowledge Granularity[J/OL].[2020-05-25]. https://doi.org/10.13195/j.kzyjc.2019.0490.) [11] 陈静雯,马福民,张腾飞,等.基于最大粒的悲观邻域多粒度粗糙集规则获取算法.模式识别与人工智能, 2017, 30(11): 1048-1056. (CHEN J W, MA F M, ZHANG T F, et al. Rule Acquisition Algorithm for Neighborhood Multi-granularity Rough Sets Based on Maximal Granule. Pattern Recognition and Artificial Intelligence, 2017, 30(11): 1048-1056.) [12] 胡成祥,赵国柱.优势关系多粒度粗糙集中近似集动态更新方法.中国科学技术大学学报, 2017, 47(1): 40-47. (HU C X, ZHAO G Z. A Dominance-Based Multigranulation Rough Sets Approach for Dynamic Updating Approximations. Journal of University of Science and Technology of China, 2017, 47(1): 40-47.) [13] 胡志勇,米据生,冯 涛,等.双论域下多粒度模糊粗糙集上下近似的包含关系.智能系统学报, 2019, 14(1): 115-120. (HU Z Y, MI J S, FENG T, et al. Inclusion Relation of Upper and Lower Approximations of Multigranularity Fuzzy Rough Set in Two Universes. CAAI Transactions on Intelligent Systems, 2019, 14(1): 115-120.) [14] SKOWRON A, RAUSZER C. The Discernibility Matrices and Func-tions in Information Systems // SL＇OWIN＇SKI R ed. Intelligent Decision Support. Berlin, Germany: Springer, 1992: 331-362. [15] 苗夺谦,胡桂荣.知识约简的一种启发式算法.计算机研究与发展, 1999, 36(6): 681-684. (MIAO D Q, HU G R. A Heuristic Algorithm for Reduction of Knowledge. Journal of Computer Research and Development, 1999, 36(6): 681-684.) [16] 毛 华,武振宇.利用关联矩阵探究属性约简方法.小型微型计算机系统, 2019, 40(8): 1617-1621. (MAO H, WU Z Y. Using Association Matrix to Explore Attribute Reduction. Journal of Chinese Computer Systems, 2019, 40(8): 1617-1621.) [17] 吕跃进,程林海,张 玉,等.区间粗糙数信息系统的覆盖分类冗 余度与属性约简[J/OL]. [2020-05-25]. https://doi.org/10.13195/j.kzyjc.2019.0744. (LÜ Y J, CHENG L H, ZHANG Y, et al. Coverage Classification Redundancy and Attribute Reduction of Interval Rough Number Information System[J/OL]. [2020-05-25]. https://doi.org/10.13195/j.kzyjc.2019.0744.) [18] TAN A H, WU W Z, LI J J, et al. Reduction Foundation with Multigranulation Rough Sets Using Discernibility. Artificial Intelligence Review, 2020, 53(4): 2425-2452. [19] KRYSZKIEWICZ M. Rough Set Approach to Incomplete Information Systems. Information Sciences, 1998, 112(1/2/3/4): 39-49.
2020, Vol. 33 
