基于关系矩阵的区间集粗糙近似

doi:10.6040/j.issn.1671-9352.4.2019.142

摘要/Abstract

摘要： 基于矩阵的直观性和矩阵运算的简便性引入区间向量,给出了区间集一种新的表达形式,探讨了区间向量的相关性质,给出了区间向量与关系矩阵的运算法则。在经典粗糙集中,给出了基于关系矩阵的粗糙下、上近似的等价表示,进而利用关系矩阵和区间向量提出了基于关系矩阵的区间集粗糙下、上近似,构造了基于关系矩阵计算区间集粗糙下、上近似的方法,给出了其相应的算法,并通过实例说明了该方法的简便性与有效性。

关键词: 关系矩阵, 区间向量, 区间集, 区间集粗糙近似

Abstract: Based on the intuition of a matrix and the simplicity of the matrix operations, this paper introduces the interval vector, which gives a new representation of an interval set, and the related properties of them are investigated. The operations between the interval vector and the relation matrix are discussed. On the basis of relation matrices, the equivalent representations of the rough lower and upper approximations are depicted for the classical rough sets. By using the operations between the relation matrix and interval vectors, the interval-set rough lower and upper approximations are shown in the view of relation matrices. An approach and the related algorithm to obtain the interval-set rough lower and upper approximations according to a relation matrix are also given. An example is used to show the simplicity and effectiveness of the algorithm.

Key words: relation matrix, interval vector, interval set, interval-set rough approximations

中图分类号:

TP18

常凡凡,马建敏. 基于关系矩阵的区间集粗糙近似[J]. 《山东大学学报(理学版)》, 2020, 55(3): 98-106.

CHANG Fan-fan, MA Jian-min. Interval-set rough approximations based on a relation matrix[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(3): 98-106.

参考文献

[1] PAWLAK Z. Rough sets[J]. International Journal of Computer and Information Science, 1982, 11(5):341-356.
[2] PAWLAK Z. Rough sets-theoretical aspects of reasoning about data[M]. London: Kluwer Academic Publishers, 1991.
[3] SWINIARSKI R W, SKOWRON A. Rough set methods in feature selection and recognition[J]. Pattern Recognition Letters. 2003, 24(6):833-849.
[4] 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: 81-86. ZHANG Wenxiu, LIANG Yi, WU Weizhi. Information systems and knowledge discovery[M]. Beijing: Science Press, 2003: 81-86.
[5] QIAN Y H, CHENG H H, WANG J T, et al. Grouping granular structures in human granulation intelligence[J]. Information Science, 2017, 382/383:150-169.
[6] 郑荔平, 胡敏杰, 杨红和, 等. 基于粗糙集的协同过滤算法研究[J]. 山东大学学报(理学版), 2019, 54(2):41-50. ZHENG Liping, HU Minjie, YANG Honghe, et al. Research on collaborative filtering algorithm based on rough set[J]. Journal of Shandong University(Natural Science), 2019, 54(2):41-50.
[7] GRECO S, MATARAZZO B, SLOWINSKI R. Rough approximation by dominance relations[J]. International Journal of Intelligent System, 2002, 17(2):153-171.
[8] MA Jianmin, ZOU Cunjun, PAN Xiaochen. Structured probabilistic rough set approximations[J]. International Journal of Approximate Reasoning, 2017, 90:319-332.
[9] 翟俊海, 张垚, 王熙照. 相容粗糙模糊集模型[J]. 山东大学学报理学版(理学版), 2014, 49(8):73-79. ZHAI Junhai, ZHANG Yao, WANG Xizhao. Tolerance rough fuzzy set model[J]. Journal of Shandong University(Natural Science), 2014, 49(8):73-79.
[10] ZIARKO W. Variable precision rough set model[J]. Journal of Computer and Systems Science, 1993, 46(1):39-59.
[11] PAWLAK Z, WONG S K M, ZIARKO W. Rough sets: probabilistic versus deterministic approach[J]. International Journal of Man-Machine Studies, 1988, 29(1):81-95.
[12] YAO Y Y. Probabilistic rough set approximation[J]. International Journal of Approximate Reasoning, 2008, 49(2):255-271.
[13] YAO Y Y, WONG S K M. A decision theoretic framework for approximating concepts[J]. International Journal of Man-Machine Studies, 1992, 37(6):793-809.
[14] SLEZAK D, ZIARKO W. The investigation of the Beyesian rough set model[J]. International Journal of Approximate Reasoning, 2005, 40:81-91.
[15] GRAYMALA-BUSSE J W, YAO Y Y. Probabilistic rule induction with the LERS data mining system[J]. International Journal of Intelligent Systems, 2011, 26(6):518-539.
[16] TSUMOTO S, TANAKA H. Primerose: probabilistic rule induction method based on rough sets and resampling methods[J]. Computational Intelligence, 1995, 11(2):389-405.
[17] DUBOIS D, PRADE H. Rough fuzzy sets and fuzzy rough set[J]. International Journal of General Systems, 1990, 17(1):191-208.
[18] WANG Chunyong. Topological characterizations of generalized fuzzy rough sets[J]. Fuzzy Sets and Systems, 2016, 312:109-125.
[19] 胡宝清. 基于区间集的三支决策粗糙集[M] // 刘盾, 李天瑞, 苗夺谦, 等. 三支决策与粒计算. 北京: 科学出版社, 2013: 182-183. HU Baoqing. Three decisions rough sets based on interval sets[M] // LIU Dun, LI Tianrui, MIAO Duoqian, et al. Three Decisions and Granular Computing. Beijing: Science Press, 2013: 182-183.
[20] GUAN J W, BELL D A, GUAN Z. Matrix computation for information systems[J]. Information Sciences, 2001, 131:129-156.
[21] LIU Guilong. The axiomatization of the rough set upper approximation operations[J]. Fundamenta Informaticae, 2006, 69(3):331-342.
[22] 王磊, 李天瑞. 基于矩阵的粗糙集上下近似的计算方法[J]. 模式识别与人工智能, 2011, 24(6):1-7. WANG Lei, LI Tianrui. Calculation method of upper and lower approximation of rough set based on matrix[J]. Pattern Recognition & Artificial Intelligence, 2011, 24(6):1-7.
[23] 刘财辉, 苗夺谦. 基于矩阵的粗糙集上、下近似求解算法[J]. 计算机应用研究, 2011, 28(5):1628-1630. LIU Caihui, MIAO Duoqian. Algorithm for upper and lower approximation of rough sets based on matrix[J]. Journal of Computer Applications, 2011, 28(5):1628-1630.
[24] ZHANG Junbo, ZHU Yun, PAN Yi, et al. Efficient parallel Boolean matrix based algorithms for computing composite rough set approximations[J]. Information Sciences, 2016, 329:287-302.
[25] 林姿琼, 王敬前, 祝峰. 矩阵方法计算覆盖粗糙集中最小、最大描述[J]. 山东大学学报(理学版), 2014, 49(8):97-101. LIN Ziqiong, WANG Jingqian, ZHU Feng. Computing minimal description and maximal description in covering-based rough sets through matrices[J]. Journal of Shandong University(Natural Science), 2018, 49(8):97-101.
[26] WANG Jingqian, ZHANG Xiaohong. Matrix approaches for some issues about minimal and maximal descriptions in covering-based rough sets[J]. International Journal of Approximate Reasoning, 2019, 104:126-143.
[27] HUANG Yanyong, LI Tianrui, LUO Chuan. Matrix-based dynamic updating rough fuzzy approximations for data mining[J]. Knowledge-Based Systems, 2017, 119:273-283.
[28] YAO Y Y. Interval-set algebra for qualitative knowledge representation[C] // Proceedings of the 5th International Conference on Computing and Information.Ontario:IEEE, 1993: 370-374.
[29] 马建敏, 景嫄, 姚红娟. 区间集概率粗糙集的单调性[J]. 模糊系统与数学, 2018, 32(4):180-190. MA Jianmin, JING Yuan, YAO Hongjuan. The monotonicity of interval-sets probabilistic rough sets[J]. Fuzzy Systems and Mathematics, 2018, 32(4):180-190.

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