Abstract
Multigranulation rough set model (MGRS) uses multiple equivalence relations on the universe to calculate the approximations, which can solve problem in mutigranulation spaces. In practical applications, information systems often dynamically update due to the variation of objects, attributes or attribute values. Incremental approach is an effective method to calculate approximations for dynamically updated information system. However, existing incremental updating approximations in MGRS mainly focus on single-dimensional variation of objects, attributes or attribute values respectively, without considering multi-dimensional variation of objects, attributes and attribute values. In this paper, we propose matrix-based incremental updating approximations in multigranulation rough set under two-dimensional variation of objects, attributes and attribute values. One is the simultaneous variation of objects and attributes (VOA). The other is the simultaneous variation of objects and attribute values (VOV). First, we give the incremental approaches to update the relevant matrices for the dynamically updated information system due to VOA and VOV. Second, based on the updated matrices, we propose two matrix-based incremental algorithms to update approximations. Finally, examples and experimental results demonstrate the effectiveness of the proposed algorithms for incremental updating approximations in multigranulation rough set under two-dimensional variation.
Similar content being viewed by others
References
Qian YH, Liang JY, Yao YY (2010) MGRS: a multi-granulation rough set. Inf Sci 180(6):949–970
Pawlak Z (1982) Rough sets. Int J Paral Program 11(5):341–356
Xu WH, Guo YT (2016) Generalized multigranulation double-quantitative decision-theoretic rough set. Knowl. Based Syst 105:190–205
Li JH, Huang CC, Qi JJ, Qian YH, Liu WQ (2017) Three-way cognitive concept learning via multi-granularity. Inf Sci 378:244–263
Sun BZ, Ma WM, Xiao X (2017) Three-way group decision making based on multigranulation fuzzy decision-theoretic rough set over two universes. Internat J Approx Reason 81:87–102
Yao YY, She YH (2016) Rough set models in multigranulation spaces. Inf Sci 327:40–56
Feng T, Mi JS (2015) Variable precision multigranulation decision-theoretic fuzzy rough sets. Knowl. Based Syst 91:93–101
Yang XB, Song XN, Dou HL, Yang JY (2011) Multi-granulation rough set: from crisp to fuzzy case. Ann Fuzzy Math Inf Sci 1(1):55–70
Xu WH, Wang QR, Zhang XT (2011) Multi-granulation fuzzy rough sets in a fuzzy tolerance approximation space. Int J Fuzzy Syst 13(4):246–259
Lin GP, Qian YH, Li JJ (2012) NMGRS: neighborhood-based multigranulation rough sets. Internat J Approx Reason 53(7):1080–1093
Lin GP, Liang JY, Qian YH (2013) Multigranulation rough sets: from partition to covering. Inf Sci 241:101–118
Xu WH, Sun WX, Zhang XY, Zhang WX (2012) Multiple granulation rough set approach to ordered information systems. Int J Gen Syst 41(5):475–501
Li JH, Ren Y, Mei CL, Qian YH, Yang XB (2016) A comparative study of multigranulation rough sets and concept lattices via rule acquisition. Knowl Based Syst 91:152–164
Qian YH, Liang XY, Lin GP, Guo Q, Liang JY (2017) Local multigranulation decision-theoretic rough sets. Internat J Approx Reason 82:119–137
Luo C, Li TR, Yi Z, Fujita H (2016) Matrix approach to decision-theoretic rough sets for evolving data. Knowl. Based Syst. 99:123–134
Hao C, Li JH, Fan M, Liu WQ, Tsang Eric CC (2017) Optimal scale selection in dynamic multi-scale decision tables based on sequential three-way decisions. Inf Sci 415:213–232
Zhang YY, Li TR, Luo C, Zhang JB, Chen HM (2016) Incremental updating of rough approximations in interval-valued information systems under attribute generalization. Inf Sci 373:461–475
Yu JH, Chen MH, Xu WH (2017) Dynamic computing rough approximations approach to time-evolving information granule interval-valued ordered information system. Appl Soft Comput 60:18–29
Luo C, Li TR, Chen HM, Fujita H, Yi Z (2018) Incremental rough set approach for hierarchical multicriteria classification. Inf Sci 429:72–87
Yu JH, Xu WH (2017) Incremental knowledge discovering in interval-valued decision information system with the dynamic data. Int J Mach Learn Cybern 8(3):849–864
Luo C, Li TR, Chen HM, Fujita H, Yi Z (2016) Efficient updating of probabilistic approximations with incremental objects. Knowl Based Syst 109:71–83
Chen HM, Li TR, Ruan D, Lin JH, Hu CX (2013) A rough-set based incremental approach for updating approximations under dynamic maintenance environments. IEEE Trans Knowl Data Eng 25(2):274–284
Hu J, Li TR, Zeng AP (2015) An incremental learning approach for updating approximations in rough set model over dual-universes. Int J Intell Syst 30(8):923–947
Hu J, Li TR, Luo C, Fujita H, Li SY (2017) Incremental fuzzy probabilistic rough sets over two universes. Int J Approx Reason 81:28–48
Sang YL, Liang JY, Qian YH (2016) Decision-theoretic rough sets under dynamic granulation. Knowl Based Syst 91:84–92
Shu WH, Qian WB (2015) An incremental approach to attribute reduction from dynamic incomplete decision systems in rough set theory. Data Knowl Eng 100:116–132
Zhang CC, Dai JH, Chen JL (2020) Knowledge granularity based incremental attribute reduction for incomplete decision systems. Int J Mach Learn Cybern 11:1141–1157
Liu D, Li TR, Zhang JB (2015) Incremental updating approximations in probabilistic rough sets under the variation of attributes. Knowl Based Syst 73:81–96
Zhang YY, Li TR, Luo C, Zhang JB, Chen HM (2016) Incremental updating of rough approximations in interval-valued information systems under attribute gener-alization. Inf Sci 373:461–475
Ju HR, Yang XB, Song XN, Qi YS (2014) Dynamic updating multigranulation fuzzy rough set: approximations and reducts. Int J Mach Learn Cybern 5(6):981–990
Zeng AP, Li TR, Hu J, Chen HM, Luo C (2017) Dynamical updating fuzzy rough approximations for hybrid data under the variation of attribute values. Inf Sci 378:363–388
Li SY, Li TR (2015) Incremental update of approximations in dominance-based rough sets approach under the variation of attribute values. Inf Sci 294:348–361
Chen HM, Li TR, Luo C, Horng SJ, Wang GY (2015) A decision-theoretic rough set approach for dynamic data mining. IEEE Trans Fuzzy Syst 23(6):1958–1970
Dai JH, Hu H, Wu WZ, Qian YH, Huang DB (2018) Maximal-discernibility-pair-based approach to attribute reduction in fuzzy rough sets. IEEE Trans Fuzzy Syst 26(4):2174–2187
Dai JH (2013) Rough set approach to incomplete numerical data. Inf Sci 241:43–57
Zhang JB, Wong JS, Pan Y, Li TR (2015) A parallel matrix-based method for computing approximations in incomplete information systems. IEEE Trans Knowl Data Eng 27(2):326–339
Tan AH, Li JJ, Lin YJ, Lin GP (2015) Matrix-based set approximations and reductions in covering decision information systems. Int J Approx Reason 59:68–80
Zhang JB, Li TR, Chen HM (2014) Composite rough sets for dynamic data mining. Inf Sci 257(2):81–100
Wang S, Li TR, Luo C, Fujita H (2016) Efficient updating rough approximations with multi-dimensional variation of ordered data. Inf Sci 372:690–708
Hu CX, Liu SX, Liu GX (2017) Matrix-based approaches for dynamic updating approximations in multigranulation rough sets. Knowl Based Syst 122:51–63
UCI machine learning repository, http://www.ics.uci.edu/mlearn/MLRepository.html. Accessed 2018
Acknowledgements
The author would like to thank the editors and the anonymous reviewers for their valuable comments and suggestions to improve the paper. This work was supported by the National Natural Science Foundation of China (No. 62076002), the Natural Science Foundation of Anhui Province, China (No. 2008085MF194, 1908085MF188), the Higher Education Natural Science Foundation of Anhui Province, China (No. KJ2013A015).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Xu, Y., Wang, Q. & Sun, W. Matrix-based incremental updating approximations in multigranulation rough set under two-dimensional variation. Int. J. Mach. Learn. & Cyber. 12, 1041–1065 (2021). https://doi.org/10.1007/s13042-020-01219-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13042-020-01219-y