Advertisement

Granular Computing

, Volume 4, Issue 3, pp 313–322 | Cite as

Attribute reduction based on the Boolean matrix

  • Yunpeng Shi
  • Yang Huang
  • Changzhong WangEmail author
  • Qiang He
Original Paper

Abstract

Attribute reduction is an important preprocessing step in machine learning and pattern recognition. This paper introduces condition-attribute Boolean matrix and decision-attribute Boolean matrix and proposes a new attribute reduction model based on Boolean operations according to the concept of neighborhood rough set. Some operation rules of Boolean vectors are defined and an uncertainty measure, named attribute support function, is proposed to evaluate the importance degree of candidate attributes with respect to decision attributes. An attribute reduction algorithm based on the proposed measure is designed. Ten data sets selected from public data sources are used to compare the proposed algorithm with some existing algorithms. The experimental results show that the proposed reduction algorithm is feasible and effective.

Keywords

Rough set Attribute reduction Boolean vector Boolean matrix 

Notes

Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grants 61572082, 61673396, and 61473111, the Foundation of Educational Committee of Liaoning Province (LZ2016003), and the Natural Science Foundation of Liaoning Province (20170540012, 20170540004).

References

  1. An S, Shi H, Hu Q, Li X, Dang J-W (2014) Fuzzy rough regression with application to wind speed prediction. Inf Sci 282:388–400MathSciNetCrossRefGoogle Scholar
  2. An S, Hu Q, Pedrycz W, Zhu P, Eric C, Tsang C (2016) Data-distribution-aware fuzzy rough set model and its application to robust classification. IEEE Trans Cybern 46(12):3073–3085Google Scholar
  3. Chen D, Zhang L, Zhao S, Hu Q, Zhu P (2013) A novel algorithm for finding reducts with fuzzy rough sets. IEEE Trans Fuzzy Syst 20(2):385–389CrossRefGoogle Scholar
  4. Chen Y, Zhang Z, Zheng J, Ma Y, Xue Y (2017) Gene selection for tumor classification using neighborhood rough sets and entropy measures. J Biomed Inform 67:59–68CrossRefGoogle Scholar
  5. Dai J, Xu Q (2013) Attribute selection based on information gain ratio in fuzzy rough set theory with application to tumor classification. Appl Soft Comput 13(1):211–221CrossRefGoogle Scholar
  6. Dai J, Hu H, Wu W, Qian Y, Huang D (2017) Maximal discernibility pairs based approach to attribute reduction in fuzzy rough sets. IEEE Trans Fuzzy Syst.  https://doi.org/10.1109/TFUZZ.2017.2768044 CrossRefGoogle Scholar
  7. Dubois D, Prade H (1990) Rough fuzzy sets and fuzzy rough sets. Int J Gen Syst 17:191–208zbMATHCrossRefGoogle Scholar
  8. Greco S, Matarazzo B, Slowinski R (2002) Rough approximation by dominance relations. Int J Intell Syst 17:153–171zbMATHCrossRefGoogle Scholar
  9. Hu Q, Yu D, Liu J, Wu C (2008) Neighborhood-rough-set based heterogeneous feature subset selection. Inf Sci 178(18):3577–3594MathSciNetzbMATHCrossRefGoogle Scholar
  10. Huang B, Li H (2018) Distance-based information granularity in neighborhood-based granular space. Granul Comput 3(2):93–110CrossRefGoogle Scholar
  11. Huang B, Guo C, Zhuang Y, Li H, Zhou X (2014) Intuitionistic fuzzy multi-granulation rough sets. Inf Sci 277:299–320zbMATHCrossRefGoogle Scholar
  12. Kim D (2001) Data classification based on tolerant rough set. Pattern Recogn 34(8):1613–1624zbMATHCrossRefGoogle Scholar
  13. Lang G, Li Q, Cai M, Yang T, Xiao Q (2017a) Incremental approaches to knowledge reduction based on characteristic matrices. Int J Mach Learn Cybern 8(1):203–222CrossRefGoogle Scholar
  14. Lang G, Miao D, Cai M, Zhang Z (2017b) Incremental approaches for updating reducts in dynamic covering information systems. Knowl Based Syst 134:85–104CrossRefGoogle Scholar
  15. Li J, Ren Y, Mei C, Qian Y, Yang X (2016) A comparative study of multigranulation rough sets and concept lattices via rule acquisition. Knowl Based Syst 91:152–164CrossRefGoogle Scholar
  16. Li J, Aswani Kumar C, Mei C, Wang X (2017) Comparison of reduction in formal decision contexts. Int J Approx Reason 80:100–122MathSciNetzbMATHCrossRefGoogle Scholar
  17. Liang J, Wang F, Dang C, Qian Y (2014) A group incremental approach to attribute selection applying rough set technique. IEEE Trans Knowl Data Eng 26(2):294–304CrossRefGoogle Scholar
  18. Lin T (1997) Neighborhood systems: application to qualitative fuzzy and rough sets. In: Wang PP (ed) Advances in machine intelligence and soft computing. Department of Electrical Engineering, Duke University, Durham, pp 132–155Google Scholar
  19. Lin Y, Hu Q, Liu J, Li J, Wu X (2017) Streaming feature selection for multi-label learning based on fuzzy mutual information. IEEE Trans Fuzzy Syst 25(6):1491–1507CrossRefGoogle Scholar
  20. Liu H, Gegov A, Cocea M (2016) Rule-based systems: a granular computing perspective. Granul Comput 1(4):259–274CrossRefGoogle Scholar
  21. Mandal P, Ranadive AS (2018) Multi-granulation interval-valued fuzzy probabilistic rough sets and their corresponding three-way decisions based on interval-valued fuzzy preference relations. Granul Comput.  https://doi.org/10.1007/s41066-018-0090-9 zbMATHCrossRefGoogle Scholar
  22. Min F, Zhu W (2012) Attribute reduction of data with error ranges and test costs. Inf Sci 211:48–67MathSciNetzbMATHCrossRefGoogle Scholar
  23. Pawlak Z (1982) Rough sets. Int J Comput Inform Sci 11(5):341–356zbMATHCrossRefGoogle Scholar
  24. Pawlak Z, Skowron A (2006) Rudiments of rough sets. Inf Sci 177:3–27MathSciNetzbMATHCrossRefGoogle Scholar
  25. Pedrycz W, Chen S (2011) Granular computing and intelligent systems: design with information granules of high order and high type. Springer, HeidelbergCrossRefGoogle Scholar
  26. Pedrycz W, Chen S (2015a) Granular computing and decision-making: interactive and iterative approaches. Springer, HeidelbergCrossRefGoogle Scholar
  27. Pedrycz W, Chen S (2015b) Information granularity, big data, and computational intelligence. Springer, HeidelbergCrossRefGoogle Scholar
  28. Qian Y, Liang J, Yao Y, Dang C (2010) MGRS: a multi-granulation rough set. Inf Sci 180:949–970MathSciNetzbMATHCrossRefGoogle Scholar
  29. Qian Y, Liang J, Pedrycz W, Dang C (2011) An efficient accelerator for attribute reduction from incomplete data in rough set framework. Pattern Recogn 44(8):1658–1670zbMATHCrossRefGoogle Scholar
  30. She Y, He X, Ma L (2017a) On the structure of metric spaces related to pre-rough logic. Int J Mach Learn Cybern 8(2):537–546CrossRefGoogle Scholar
  31. She Y, He X, Shi H, Qian Y (2017b) A multiple-valued logic approach for multigranulation rough set model. Int J Approx Reason 82:270–284MathSciNetzbMATHCrossRefGoogle Scholar
  32. Sun L, Xu J, Tian Y (2012) Feature selection using rough entropy-based uncertainty measures in incomplete decision systems. Knowl Based Syst 36:206–216CrossRefGoogle Scholar
  33. Sun B, Ma W, Chen X (2015) Fuzzy rough set on probabilistic approximation space over two universes and its application to emergency decision-making. Expert Syst 32(4):507–521CrossRefGoogle Scholar
  34. Sun B, Ma W, Qian Y (2017) Multi-granulation fuzzy rough set over two universes and its application to decision making. Knowl Based Syst 123:61–74CrossRefGoogle Scholar
  35. Wang B, Liang J, Qian Y (2014) Determining decision makers’ weights in group ranking: a granular computing method. Int J Mach Learn Cybern 6(3):511–521CrossRefGoogle Scholar
  36. Wang C, Qi Y, Shao Y et al (2016a) A fitting model for feature selection with fuzzy rough sets. IEEE Trans Fuzzy Syst 25(4):741–753CrossRefGoogle Scholar
  37. Wang C, Shao M, He Q, Qian Y, Qi Y (2016b) Feature subset selection based on fuzzy neighborhood rough sets. Knowl Based Syst 111(1):173–179CrossRefGoogle Scholar
  38. Wang C, Hu Q, Wang X, Chen D, Qian Y (2017a) Feature selection based on neighborhood discrimination index. IEEE Trans Neural Netw Learn Syst.  https://doi.org/10.1109/TNNLS.2710422 CrossRefGoogle Scholar
  39. Wang C, He Q, Shao M, Xua Y, Hu Q (2017b) A unified information measure for general binary relations. Knowl Based Syst 135(1):18–28CrossRefGoogle Scholar
  40. Wang G, Li Y, Li X (2017c) Approximation performance of the nonlinear hybrid fuzzy system based on variable universe. Granul Comput 2:1–12CrossRefGoogle Scholar
  41. Wang G, Yang J, Xu J (2017d) Granular computing: from granularity optimization to multi-granularity joint problem solving. Granul Comput 2:1–16CrossRefGoogle Scholar
  42. Wang C, He Q, Shao M, Hu Q (2018) Feature selection based on maximal neighborhood discernibility. Int J Mach Learn Cybern.  https://doi.org/10.1007/s13042-017-0712-6 CrossRefGoogle Scholar
  43. Wu W, Zhang W (2002) Neighborhood operator systems and approximations. Inf Sci 144(14):201–217MathSciNetzbMATHCrossRefGoogle Scholar
  44. Xu W, Li W (2016a) Granular computing approach to two-way learning based on formal concept analysis in fuzzy datasets. IEEE Trans Cybern 46(2):366–379MathSciNetCrossRefGoogle Scholar
  45. Xu Z, Wang H (2016b) Managing multi-granularity linguistic information in qualitative group decision making: an overview. Granul Comput 1(1):21–35CrossRefGoogle Scholar
  46. Xu W, Yu J (2017a) A novel approach to information fusion in multi-source datasets: a granular computing viewpoint. Inf Sci 378:410–423CrossRefGoogle Scholar
  47. Xu W, Li W, Zhang X (2017b) Generalized multigranulation rough sets and optimal granularity selection. Granul Comput 4(2):271–288CrossRefGoogle Scholar
  48. Yang X, Qi Y, Yu D, Yu H, Yang J (2015) α-Dominance relation and rough sets in interval-valued information systems. Inf Sci 294:334–347MathSciNetzbMATHCrossRefGoogle Scholar
  49. Yang Y, Chen D, Wang H, Eric C, Tsang C, Zhang D (2017a) Fuzzy rough set based incremental attribute reduction from dynamic data with sample arriving. Fuzzy Sets Syst 312:66–86MathSciNetzbMATHCrossRefGoogle Scholar
  50. Yang Y, Chen D, Wang H (2017b) Active sample selection based incremental algorithm for attribute reduction with rough sets. IEEE Trans Fuzzy Systems 25(4):825–838CrossRefGoogle Scholar
  51. Yao Y (1998) Relational interpretations of neighborhood operators and rough set approximation operators. Inf Sci 101:239–259MathSciNetzbMATHCrossRefGoogle Scholar
  52. Yao Y, Mi J, Li Z (2011) Attribute reduction based on generalized fuzzy evidence theory in fuzzy decision systems. Fuzzy Sets Syst 170(1):64–75MathSciNetzbMATHCrossRefGoogle Scholar
  53. Zhang H, Yang S (2016) Inclusion measure for typical hesitant fuzzy sets, the relative similarity measure and fuzzy entropy. Soft Comput 20(4):1277–1287MathSciNetzbMATHCrossRefGoogle Scholar
  54. Zhang H, Yang S (2017) Feature selection and approximate reasoning of large-scale set-valued decision tables based on alpha-dominance-based quantitative rough sets. Inf Sci 378:328–347CrossRefGoogle Scholar
  55. Zhang X, Zhou B, Li P (2012) A general frame for intuitionistic fuzzy rough sets. Inf Sci 216:34–49MathSciNetzbMATHCrossRefGoogle Scholar
  56. Zhao S, Tsang C, Chen D (2010) Building a rule-based classifier by using fuzzy rough set technique. IEEE Trans Knowl Data Eng 22(5):624–638CrossRefGoogle Scholar
  57. Zhao S, Chen H, Li C, Du X, Sun H (2015) A novel approach to building a robust fuzzy rough classifier. IEEE Trans Fuzzy Syst 23(4):769–786CrossRefGoogle Scholar
  58. Zhao H, Wang P, Hu Q (2016) Cost-sensitive feature selection based on adaptive neighborhood granularity with multi-level confidence. Inf Sci 366:134–149MathSciNetCrossRefGoogle Scholar
  59. Zhu P, Hu Q (2013) Adaptive neighborhood granularity selection and combination based on margin distribution optimization. Inf Sci 249:1–12MathSciNetzbMATHCrossRefGoogle Scholar
  60. Zhu W, Wang F (2007) On three types of covering-based rough sets. IEEE Trans Knowl Data Eng 19(8):1131–1144CrossRefGoogle Scholar
  61. Ziarko W (1993) Variable precision rough sets model. J Comput Syst Sci 46:139–159MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsBohai UniversityJinzhouPeople’s Republic of China
  2. 2.College of ScienceBeijing University of Civil Engineering and ArchitectureBeijingPeople’s Republic of China

Personalised recommendations