Boolean Matrix Approach for Multi-scale Covering Decision Information System
CHEN Yingsheng1, LI Jinjin1,2, LIN Rongde1, CHEN Dongxiao1
1. Fujian Province University Key Laboratory of Computational Science, School of Mathematical Sciences, Huaqiao University, Quanzhou 362021 2. School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000
Abstract：In multi-scale decision information system, one condition attribute corresponding to a certain scale forms a partition of the universe. A multi-scale covering decision information system (MSCDS) is proposed and the partition is generalized to a covering. A boolean matrix method is applied to simplify the complexity of information expression in this system. Firstly, boolean matrix is employed to describe the covering decision information system, including upper and lower approximations, consistency and generalized decision function. Secondly, the definitions of MSCDS, consistency and generalized decision invariant of the system are expressed in boolean matrix method. Finally, the boolean matrix method is utilized to define the significance of a combination scale with both consistency and inconsistency, and the relevant algorithms and examples of optimal granularity selection of MSCDS are presented.
[1] ZADEH L A. Fuzzy Sets and Information Granularity // GUPTA M, RAGADE R, YAGER R, eds. Advances in Fuzzy Set Theory and Applications. Amsterdam, The Netherlands: North-Holland Publishing, 1979: 3-18. [2] LIN T Y. Introduction to the Special Issue on Rough Sets. International Journal of Approximate Reasoning, 1996, 15(4): 287-289. [3] YAO Y Y. A Partition Model of Granular Computing // PETERS J F, SKOWRON A, eds. Transactions on Rough Sets I. Berlin, Germany: Springer, 2004: 232-253. [4] YAO Y Y, SHE Y H. Rough Set Models in the Multigranulation Spaces. Information Sciences, 2016, 327: 40－56. [5] PAWLAK Z. Rough Set. International Journal of Computer and Information Sciences, 1982, 11(5): 341－356. [6] JIA X Y, SHANG L, ZHOU B, et al. Generalized Attribute Reduction in Rough Set Theory. Knowledge-Based Systems, 2016, 91: 204-218. [7] FAN X D, ZHAO W D, WANG C Z, et al. Attribute Reduction Based on Max-Decision Neighborhood Rough Set Model. Knowledge-Based Systems, 2018, 151: 16-23. [8] LIN Y Y, LI J J, TAN A H, et al. Granular Matrix Based Know-ledge Reductions of Formal Fuzzy Contexts. International Journal of Machine Learning and Cybernetics, 2020, 11: 643-656. [9] HU B Q, WONG H, YIU K F C, et al. The Aggregation of Multiple Three-Way Decision Spaces. Knowledge-Based Systems, 2016, 98:241-249. [10] HUANG J X, YU P Q, LI W K. Updating the Reduct in Fuzzy β-Covering via Matrix Approaches While Adding and Deleting Some Objects of the Universe. Information, 2020, 11(1). DOI: 10.3390/info11010003. [11] CHEN D G, WANG C Z, HU Q H. A New Approach to Attribute Reduction of Consistent and Inconsistent Covering Decision Systems with Covering Rough Sets. Information Sciences, 2007, 177(17):3500-3518. [12] DONG Z, SUN M, YANG Y Y. Fast Algorithms of Attribute Reduction for Covering Decision Systems with Minimal Elements in Discernibility Matrix. International Journal of Machine Learning and Cybernetics, 2016, 7: 297-310. [13] WANG C Z, SHAO M W, SUN B Q, et al. An Improved Attribute Reduction Scheme with Covering Based Rough Sets. Applied Soft Computing, 2015, 26: 235-243. [14] CHEN J K, LIN Y J, LIN G P, et al. Attribute Reduction of Co-vering Decision Systems by Hypergraph Model. Knowledge-Based Systems, 2017, 118: 93-104. [15] TAN A H, LI J J, LIN Y J, et al. Matrix-Based Set Approximations and Reductions in Covering Decision Information Systems. International Journal of Approximate Reasoning, 2015, 59: 68-80. [16] WU W Z, LEUNG Y. Theory and Applications of Granular Labelled Partitions in Multi-scale Decision Tables. Information Sciences, 2011, 181(18): 3878-3897. [17] LI F,HU B Q. A New Approach of Optimal Scale Selection to Multi-scale Decision Table. Information Sciences, 2017, 381: 193-208. [18] HUANG Z H, LI J J, DAI W Z, et al. Generalized Multi-scale Decision Tables with Multi-scale Decision Attributes. International Journal of Approximate Reasoning, 2019, 115: 194-208. [19] 吴伟志,庄宇斌,谭安辉,等.不协调广义多尺度决策系统的尺度组合.模式识别与人工智能, 2018, 31(6): 485-494. (WU W Z, ZHUANG Y B, TAN A H, et al. Scale Combinations in Inconsistent Generalized Multi-scale Decision Systems. Pattern Recognition and Artificial Intelligence, 2018, 31(6): 485-494.) [20] LI F,HU B Q,WANG J. Stepwise Optimal Scale Selection for Multi-scale Decision Tables via Attribute Significance. Knowledge-Based Systems, 2017, 129: 4-16. [21] 顾沈明,胡 超,吴伟志,等.多标记序信息系统的不确定性研究.南京大学学报(自然科学), 2015, 51(2): 377-383. (GU S M, HU C, WU W Z, et al . Uncertainty Measure in Multi-scale Order Information Systems. Journal of Nanjing University(Natural Sciences), 2015, 51(2): 377-383.) [22] 戴志聪,吴伟志.不完备多粒度序信息系统的粗糙近似.南京大学学报(自然科学), 2015, 51(2): 361-367. (DAI Z C, WU W Z. Rough Approximations in Incomplete Multi-granular Ordered Information Systems. Journal of Nanjing University(Natural Sciences), 2015, 51(2): 361-367.) [23] SHE Y H, LI J H, YANG H L. A Local Approach to Rule Induction in Multi-scale Decision Tables. Knowledge-Based Systems, 2015, 89: 398-410. [24] GUAN J W, BELL D A, GUAN Z. Matrix Computation for Information Systems. Information Sciences, 2001, 131(1/2/3/4): 129-156. [25] 李少阳,李巧艳,宋卫妮.粗糙集上下近似的矩阵刻画及应用.计算机工程与应用, 2015, 51(20): 107-111. (LI S Y, LI Q Y, SONG W N. Matrix Description and Applications of Upper and Lower Approximation of Rough Set. Computer Engineering and Applications, 2015, 51(20): 107-110.) [26] 王 磊,李天瑞.基于矩阵的粗糙集上下近似的计算方法.模式识别与人工智能, 2011, 24(6): 756-762. (WANG L, LI T R. Matrix-Based Computational Method for Upper and Lower Approximations of Rough Sets. Pattern Recognition and Artificial Intelligence, 2011, 24(6): 756-762.) [27] MA L W. The Investigation of Covering Rough Sets by Boolean Matrices. International Journal of Approximate Reasoning, 2018, 100: 69-84.
2020, Vol. 33 
