Soft Computing

, Volume 22, Issue 22, pp 7553–7569 | Cite as

Efficient parallel algorithm for computing rough set approximation on GPU

  • Si-Yuan JingEmail author
  • Gong-Liang Li
  • Kai Zeng
  • Wei Pan
  • Cai-Ming Liu


Computation of rough set approximation (RSA) is a critical step for attribute reduction and knowledge acquisition in rough set theory. Continuously improving computation efficiency of RSA is very meaningful, because it can enhance user experience of existing applications. Furthermore, it is helpful to apply rough sets to some fields with high performance requirement. Graphics processing unit (GPU) has gained a lot of attention from scientific communities for its applicability in high-performance computing. Different from existing works, this paper tries to apply GPU to accelerate a state-of-the-art serial algorithm of RSA computation, which is based on radix sorting. Three key steps of the serial algorithm are parallel designed, including object sorting, computation of equivalence classes, and computation of RSA. The experimental results show that the parallel method can accelerate the computation process efficiently.


Rough set theory Parallel computing Rough set approximation GPU 



This study was funded by the National Science Foundation of China (Grand No. 61702128); the Scientific Research Fund of Sichuan Provincial Department (Grand No. 17ZA0201); the Scientific Research Fund of Leshan Normal University (Grand No. Z1325).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.


  1. Balamash AS, Pedrycz W, -Hmouz RA et al (2017) Granular classifiers and their design through refinement of information granules. Soft Comput 21(10):2745–2759CrossRefGoogle Scholar
  2. Chen HM, Li TR, Ruan D et al (2013) A rough-set-based incremental approach for updating approximations under dynamic maintenance environments. IEEE Trans Knowl Data Eng 25(2):274–284CrossRefGoogle Scholar
  3. Cheng Y (2011) The incremental method for fast computing the rough fuzzy approximations. Data Knowl Eng 70(1):84–100CrossRefGoogle Scholar
  4. David K, Hwu WM (2010) Programming massively parallel processors: a hand-on approach. Morgan Kaufmann Publishers Inc., San FranciscoGoogle Scholar
  5. Dean J, Ghemawat S (2008) Mapreduce: simplified data processing on large clusters. Commun ACM 51(1):107–113CrossRefGoogle Scholar
  6. Deng DY, Yan DX, Wang JY (2010) Parallel reducts based on attribute significance. In: Yu J, Greco S, Lingras P et al (eds) Rough Set and Knowledge Technology, vol 6401. Lecture Notes in Computer Science. Springer, Berlin, pp 336–343CrossRefGoogle Scholar
  7. Fan A, Zhao H, Zhu W (2016) Test-cost-sensitive attribute reduction on heterogeneous data for adaptive neighborhood model. Soft Comput 20(12):4813–4824CrossRefGoogle Scholar
  8. Harris M, Sengupta S, Owens JD (2007) Parallel prefix sum (scan) with CUDA. In: Nguyen H (ed) GPU gems 3. Addison Wesley, ReadingGoogle Scholar
  9. Hu QH, Xie ZX, Yu DR (2007) Hybrid attribute reduction based on a novel fuzzy-rough model and information granulation. Pattern Recognit 40(22):3509–3521CrossRefGoogle Scholar
  10. Hu QH, Yu DR, Liu JF et al (2008) Neighborhood rough set based heterogeneous feature subset selection. Inf Sci 178(18):3577–3594MathSciNetCrossRefGoogle Scholar
  11. Jensen R, Shen Q (2004) Fuzzy-rough attribute reduction with application to web categorization. Fuzzy Sets Syst 131(3):469–485MathSciNetCrossRefGoogle Scholar
  12. Jing SY (2014) A hybrid genetic algorithm for feature subset selection in rough set theory. Soft Comput 18(7):1373–1382CrossRefGoogle Scholar
  13. Jing SY, Ali S, She K et al (2013) State-of-the-art research study for green cloud computing. J Supercomput 65(1):445–468CrossRefGoogle Scholar
  14. Li TR, Ruan D, Wets G et al (2007) A rough sets based characteristic relation approach for dynamic attribute generalization in data mining. Knowl Based Syst 20(5):485–494CrossRefGoogle Scholar
  15. Li SY, Li TR, Zhang ZX et al (2015) Parallel computing of approximations in dominance-based rough sets approach. Knowl Based Syst 87:202–211CrossRefGoogle Scholar
  16. Liang JY, Qian YH (2008) Information granules and entropy theory in information systems. Sci China Ser F Inf Sci 51(10):1427–1444MathSciNetCrossRefGoogle Scholar
  17. Liang JY, Wang F, Dang CY et al (2012) An efficient rough feature selection algorithm with a multi-granulation view. Int J Approx Reason 53:912–926MathSciNetCrossRefGoogle Scholar
  18. Lindholm E, Nickolls J, Oberman S (2008) Nvidia tesla: a unified graphics and computing architecture. IEEE Micro 28(2):39–55CrossRefGoogle Scholar
  19. Min F, He HP, Qian YH et al (2011) Test-cost-sensitive attribute reduction. Inf Sci 181(22):4928–4942CrossRefGoogle Scholar
  20. Min F, Hu QH, Zhu W (2014) Feature selection with test cost constraint. Int J Approx Reason 55(1):167–179MathSciNetCrossRefGoogle Scholar
  21. Pawlak Z (1991) Rough sets, theoretical aspects of reasoning about data. Kluwer Academic Publishers, DordrechtzbMATHGoogle Scholar
  22. Pawlak Z, Skowron A (2007a) Rough sets and Boolean reasoning. Inf Sci 177(1):41–73MathSciNetCrossRefGoogle Scholar
  23. Pawlak Z, Skowron A (2007b) Rough sets: some extensions. Inf Sci 177(1):28–40MathSciNetCrossRefGoogle Scholar
  24. Pawlak Z, Skowron A (2007c) Rudiments of rough sets. Inf Sci 177(1):3–27MathSciNetCrossRefGoogle Scholar
  25. Pedrycz W (2001) Granular computing: an introduction. In: IFSA world congress & NAFIPS international conferenceGoogle Scholar
  26. Pedrycz W, Al-Hmouz R, Balamash AS et al (2017) Modeling with linguistic entities and linguistic descriptors: a perspective of granular computing. Soft Comput 21(7):1833–1845CrossRefGoogle Scholar
  27. Qian YH, Liang JY, Dang CY (2010a) Incomplete multigranulation rough set. IEEE Trans Syst Man Cybern Part A 40(2):420–431CrossRefGoogle Scholar
  28. Qian YH, Liang JY, Pedrycz W et al (2010b) Positive approximation: an accelerator for attribute reduction in rough set theory. Artif Intell 174(9–10):597–618MathSciNetCrossRefGoogle Scholar
  29. Qian J, Miao DQ, Zhang ZH (2011) Knowledge reduction algorithms in cloud computing. Chin J Comput 34(12):2332–2342CrossRefGoogle Scholar
  30. Qian J, Miao DQ, Zhang ZH et al (2014) Parallel attribute reduction algorithms using MapReduce. Inf Sci 279:671–690MathSciNetCrossRefGoogle Scholar
  31. Ryoo S, Rodrigues CI, Baghsorkhi SS et al (2008) Optimization principles and application performance evaluation of a multi-threaded GPU using CUDA. In: Proceedings of the PPoPP’08, pp 73–82Google Scholar
  32. Satish N, Harris M, Garland M (2009) Designing efficient sorting algorithms for manycore GPUs. In: Proceedings of the IPDPS’09, pp 1–10Google Scholar
  33. Susmaga R (2004) Tree-like parallelization of reduct and construct computation. In: Tsumoto S et al (eds) RSCTC 2004, LNAI 3066, Springer, Berlin, pp 455–464CrossRefGoogle Scholar
  34. Tang JG, She K, Min F, Zhu W (2013) A matroidal approach to rough set theory. Theor Comput Sci 471:1–11MathSciNetCrossRefGoogle Scholar
  35. Tay FEH, Shen L (2002) Economic and financial prediction using rough sets model. Eur J Oper Res 141(3):641–659CrossRefGoogle Scholar
  36. Tsumoto S (2004) Mining diagnostic rules from clinical databases using rough sets and medical diagnostic model. Inf Sci 162(2):65–80MathSciNetCrossRefGoogle Scholar
  37. Wang GY, Yu H, Yang DC (2002) Decision table reduction based on conditional information entropy. Chin J Comput 25(7):759–766MathSciNetGoogle Scholar
  38. Xu ZY, Liu ZP, Yang BR et al (2006) A quick attribute reduction algorithm with complexity of max(\(O|C, U|, O|C|^{2}|U/C|\)). Chi J Comput 29(3):391–399Google Scholar
  39. Yu J, Yang Y (2016) Minimal attribute reduction with rough set based on compactness discernibility information tree. Soft Computing 20(6):2233–2243CrossRefGoogle Scholar
  40. Zeng K (2016) Preference mining using neighborhood rough set model on two universes. Comput Intell Neurosci (Public online) Google Scholar
  41. Zhang JB, Li TR, Ruan D et al (2012) A parallel method for computing rough set approximations. Inf Sci 194:209–223CrossRefGoogle Scholar
  42. Zhang JB, Wong JS, Pan Y et al (2015) A parallel matrix-based method for computing approximations in incomplete information systems. IEEE Trans Knowl Data Eng 27(2):326–339CrossRefGoogle Scholar
  43. Zhang JB, Zhu Y, Li TR et al (2016) Efficient parallel Boolean matrix based algorithms for computing composite rough set approximations. Inf Sci 329:287–302CrossRefGoogle Scholar
  44. Zhu W (2007a) Topological approaches to covering rough sets. Inf Sci 177(6):1499–1508MathSciNetCrossRefGoogle Scholar
  45. Zhu W (2007b) Generalized rough sets based on relations. Inf Sci 177(22):4997–5011MathSciNetCrossRefGoogle Scholar
  46. Zhu XZh, Zhu W, Fan XN (2017) Rough set methods in feature selection via submodular function. Soft Comput 21(13):3699–3711CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Computer ScienceLeshan Normal UniversityLeshanChina
  2. 2.Sichuan Province University Key Laboratory of Internet Natural Language Intelligent ProcessingLeshan Normal UniversityLeshanChina
  3. 3.Institute of Computing ApplicationsChina Academy of Engineering PhysicsMianyangChina
  4. 4.Faculty of Information EngineeringGuizhou Institute of TechnologyGuiyangChina
  5. 5.School of ComputerChina West Normal UniversityNanchongChina

Personalised recommendations