Attribute reducts of multi-granulation information system

  • Qingzhao Kong
  • Xiawei Zhang
  • Weihua XuEmail author
  • Shutong Xie


In recent years, more and more methods and theories of multi-granulation information systems have been explored. However, there is very limited investigation on the attribute reducts of multi-granulation rough sets. Therefore, the main objective of this paper is to draw attention to the attribute reducts of multi-granulation information system. For any subset of information system, we usually characterize it by its upper and lower approximations. In order to calculate the upper and lower approximations faster, we must reduce the redundant information of the information system. According to the preceding analysis, we first introduce three types of attribute reduct, which are called arbitrary union reduct, neighborhood union reduct and neighborhood intersection reduct, respectively. Then many basic and important results of these reducts are deeply explored. In order to apply the theories of attribute reducts to deal with practical issues, we develop three algorithms so as to compute multi-granulation upper and lower approximations. Next, we further study the interrelationships among these attribute reducts. Finally, we present a multi-granulation information system with respect to thirty students’ exam scores and calculate the corresponding attribute reducts by using the algorithms listed in the paper.


Rough sets Multi-granulation Reduct Lower and upper approximations 



The authors are very grateful to the reviewers and editors for their valuable suggestions. This work is partially supported by National Natural Science Foundation of China (Nos.61472463, 61772002, 61402064), Fundamental Research Funds for the Central Universities (XDJK2019B029), Natural Science Foundation of Fujian Province (Nos. 2017J01763, 2017J01468, 2016J01310, 2016J01735, 2018J01538) and Research Startup Foundation of Jimei University (NO. ZQ2017004), Foundation of Education Department of Fujian Province, China (No. JAT160369).


  1. Abualigah L, Khader A, Hanandeh E (2018) Hybrid clustering analysis using improved krill herd algorithm. Appl Intell 48(11):4047–4071CrossRefGoogle Scholar
  2. Abualigah L, Khader A, Hanandeh E (2018) A combination of objective functions and hybrid krill herd algorithm for text document clustering analysis. Eng Appl Artif Intell 73:111–125CrossRefGoogle Scholar
  3. Abualigah L, Khader A, Hanandeh E (2018) A novel weighting scheme applied to improve the text document clustering techniques. Innovative computing, optimization and its applications. Springer, Cham, pp 305–320CrossRefGoogle Scholar
  4. Abualigah L, Khader A, Hanandeh E (2018) A hybrid strategy for krill herd algorithm with harmony search algorithm to improve the data clustering. intelligent decision technologies, preprintGoogle Scholar
  5. Abualigah L, Khader A, Hanandeh E (2017) A new feature selection method to improve the document clustering using particle swarm optimization algorithm. J Comput Sci 25:456–466CrossRefGoogle Scholar
  6. Abualigah L, Khader A, Hanandeh E, Gandomi A (2017) A novel hybridization strategy for krill herd algorithm applied to clustering techniques. Appl Soft Comput 60:423–435CrossRefGoogle Scholar
  7. Abualigah L, Khader A, Al-Betar M, Hanandeh E (2017) A new hybridization strategy for krill herd algorithm and harmony search algorithm applied to improve the data clustering. Management 9:11Google Scholar
  8. Abualigah L, Khader A (2017) Unsupervised text feature selection technique based on hybrid particle swarm optimization algorithm with genetic operators for the text clustering. J Supercomput 73(11):4773–4795CrossRefGoogle Scholar
  9. Abualigah L, Khader A, Al-Betar M, Alomari O (2017) Text feature selection with a robust weight scheme and dynamic dimension reduction to text document clustering. Expert Syst Appl 84:24–36CrossRefGoogle Scholar
  10. Abualigah L, Hanandeh E (2015) Applying genetic algorithms to information retrieval using vector space model. Int J Comput Sci Eng Appl 5(1):19Google Scholar
  11. Al-Betar M, Abualigah L (2017) Big data and E-government: a review. In: The 8th IEEE international conference on information technology (ICIT). Amman, JordanGoogle Scholar
  12. Bonikowski Z, Bryniarski E, Wybraniec U (1998) Extensions and intentions in the rough set theory. Inf Sci 107:149–167MathSciNetCrossRefzbMATHGoogle Scholar
  13. Baszczyński J, Slowiński R, Szelag M (2011) Sequential covering rule induction algorithm for variable consistency rough set approaches. Inf Sci 181(5):987–1002MathSciNetCrossRefGoogle Scholar
  14. Cattaneo G (1998) Abstract approximate spaces for rough theories. In: Polkowski Skowron (ed) Rough sets in knowledge discovery 1: methodology and applications. Physicaverlag, Heidelberg, pp 59–98Google Scholar
  15. Chen D, hang W, Yeung D, Tsang E (2006) Rough approximation on a complete completely distributive lattice with applications to generalized rough sets. Inf Sci 176:1829–1848MathSciNetCrossRefzbMATHGoogle Scholar
  16. Chen D, Wang C, Hu Q (2007) A new approach to attribute reduction of consistent and inconsistent covering decision systems with covering rough sets. Inf Sci 177(17):3500–3518MathSciNetCrossRefzbMATHGoogle Scholar
  17. Chen D, Hu Q, Yang Y (2011) Parameterized attribute reduction with Gaussian kernel based fuzzy rough sets. Inf Sci 181(23):5169–5179CrossRefzbMATHGoogle Scholar
  18. Chen J, Li J, Lin Y, Lin G, Ma Z (2015) Relations of reduction between covering generalized rough sets and concept lattices. Inf Sci 304:16–27MathSciNetCrossRefzbMATHGoogle Scholar
  19. Diker M, Ugur A (2012) Textures and covering based rough sets. Inf Sci 184(1):44–63MathSciNetCrossRefzbMATHGoogle Scholar
  20. Ge X, Li Z (2011) Definable subsets in covering approximation spaces. Int J Comput Math Sci 5(1):31–34MathSciNetGoogle Scholar
  21. Kong Q, Xu W (2018) The comparative study of covering rough sets and multi-granulation rough sets. Soft Comput. Google Scholar
  22. Kong Q, Xu W (2018) Operation properties and algebraic application of covering rough sets. Fundam Inf 160:385–408MathSciNetCrossRefzbMATHGoogle Scholar
  23. Kong Q, Zhang X, Xu W (2018) Operation properties and algebraic properties of multi-covering rough sets. Granul Comput. zbMATHGoogle Scholar
  24. Kong Q, Wei Z (2017) Further study of multi-granulation fuzzy rough sets. J Intell Fuzzy Syst 32:2413–2424CrossRefzbMATHGoogle Scholar
  25. Kong Q, Wei Z (2015) Covering-based fuzzy rough sets. J Intell Fuzzy Syst 29:2405–2411CrossRefzbMATHGoogle Scholar
  26. Li J, Ren Y, Mei C, Qian Y, Yang X (2016) A comparative study of multi-granulation rough sets and concept lattices via rule acquisition. Knowl Based Syst 91:152–164CrossRefGoogle Scholar
  27. Li J, Huang C, Qi J, Qian Y, Liu W (2017) Three-way cognitive concept learning via multi-granularity. Inf Sci 378:244–263CrossRefGoogle Scholar
  28. Lin G, Liang J, Qian Y (2013) Multigranulation rough sers: from partition to covering. Inf Sci 241:101–118CrossRefzbMATHGoogle Scholar
  29. Liu C, Wang M (2011) Covering fuzzy rough set based on multi-granulation. In: International conference on uncertainty reasoning and knowledge engineering. pp 146–149Google Scholar
  30. Liu C, Miao D, Qian J (2014) On multi-granulation covering rough sets. Int J Approx Reason 55:1404–1418MathSciNetCrossRefzbMATHGoogle Scholar
  31. Liu G, Zhu W (2008) The algebraic structures of generalized rough set theory. Inf Sci 178:4105–4113MathSciNetCrossRefzbMATHGoogle Scholar
  32. Liu G, Sai Y (2009) A comparison of two types of rough sets induced by coverings. Int J Approx Reason 50:521–528MathSciNetCrossRefzbMATHGoogle Scholar
  33. Pawlak Z (1982) Rough sets. Int J Comput Inf Sci 11(5):341–356CrossRefzbMATHGoogle Scholar
  34. Qian Y, Liang J, Yao Y, Dang C (2010) MGRS: a multi-granulation rough set. Inf Sci 180:949–970MathSciNetCrossRefzbMATHGoogle Scholar
  35. Qian Y, Liang J (2006) Rough set method based on multi-granulations, In: The 5th IEEE international conference on congnitive informatics. Beijing, ChinaGoogle Scholar
  36. She Y, he X (2003) On the structure of the multigranulation rough set model. Knowl Based Syst 151:81–92Google Scholar
  37. Shi Z, Gong Z (2010) The futher investigation of covering-based rough sets: uncertainty characterization, similarity measure and generalized models. Inf Sci 180(19):3745–3763CrossRefzbMATHGoogle Scholar
  38. Skowron A, Stepaniuk J (1996) Tolerance approximation spaces. Fundam Inf 27:245–253MathSciNetzbMATHGoogle Scholar
  39. Slowinski R, Vanderpooten D (2000) A generalized definition of rough approximations based on similarity. IEEE Trans Knowl Data Eng 12:331–336CrossRefGoogle Scholar
  40. Tan A, Li J, Lin Y (2015) Matrix-based set approximations and reductions in covering decision systems. Int J Approx Reason 59:68–80MathSciNetCrossRefzbMATHGoogle Scholar
  41. Tsang E, Chen D, Yeung D (2008) Approximations and reducts with covering generalized rough sets. Comput Math Appl 56:279–289MathSciNetCrossRefzbMATHGoogle Scholar
  42. Wang C, He Q, Chen D, Hu Q (2014) A novel method for attribute reduction of covering decision systems. Inf Sci 254:181–196MathSciNetCrossRefzbMATHGoogle Scholar
  43. Wang C, Shao M, Sun B (2015) An improved attribute reduction scheme with covering based rough sets. Appl Soft Comput 26:235–243CrossRefGoogle Scholar
  44. Wang C, Shao M, He Q, Qian Y, Qi Y (2016) Feature subset selection based on fuzzy neighborhood rough sets. Knowl Based Syst 111(1):173–179CrossRefGoogle Scholar
  45. Wang C, Hu Q, Wang X, Chen D, Qian Y (2017) Feature selection based on neighborhood discrimination index. IEEE Trans Neural Netw Learn Syst. Google Scholar
  46. Wang C, He Q, Shao M, Xua Y, Hu Q (2017) A unified information measure for general binary relations. Knowl Based Syst 135(1):18–28CrossRefGoogle Scholar
  47. Xu W, Li Y, Liao X (2012) Approaches to attribute reductions based on rough set and matrix computation in inconsistent ordered information systems. Knowl Based Syst 41(5):78–91CrossRefGoogle Scholar
  48. Xu W, Wang Q, Zhang X (2011) Multi-granulation fuzzy rough sets in a fuzzy tolerance approximation space. Int J Fuzzy Syst 13:246–259MathSciNetGoogle Scholar
  49. Xu W, Wang Q, Zhang X (2013) Multi-granulation rough sets based on tolerance relations. Soft Comput 17(7):1241–1252CrossRefzbMATHGoogle Scholar
  50. Xu W, Wang Q, Luo S (2014) Multi-granulation fuzzy rough sets. J Intell Fuzzy Syst 26:1323–1340MathSciNetzbMATHGoogle Scholar
  51. Xu W, Li W, Zhang X (2017) Generalized multigranulation rough sets and optimal granularity selection. Granul Comput. Google Scholar
  52. Yang X, Song X, Dou H, Yang J (2011) Multigranulation rough set: from crisp to fuzzy case. Ann Fuzzy Math Inf 1:55–70zbMATHGoogle Scholar
  53. Yao Y (2011) Information granulation and rough set approximation. Int J Intell Syst 16(1):87–104CrossRefzbMATHGoogle Scholar
  54. Yao Y (1998) Constructive and algebraic methods of the theory of rough sets. Inf Sci 109:21–47MathSciNetCrossRefzbMATHGoogle Scholar
  55. Zakowski W (1983) Approximations in the space (\(u,\pi \)). Demonstr Math 16:761–769zbMATHGoogle Scholar
  56. Zhang X, Kong Q (2016) On four types of multi-covering rough sets. Fundam Inf 147:457–476MathSciNetCrossRefzbMATHGoogle Scholar
  57. Zhu W, Wang F (2003) Reduction and axiomization of covering generalized rough sets. Inf Sci 152:217–230MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • Qingzhao Kong
    • 1
  • Xiawei Zhang
    • 2
  • Weihua Xu
    • 3
    Email author
  • Shutong Xie
    • 4
  1. 1.School of ScienceJimei UniversityXiamenChina
  2. 2.School of Applied MathematicsXiamen University of TechnologyXiamenChina
  3. 3.School of Mathematics and StatisticsSouthwest UniversityChongqingChina
  4. 4.School of Computer EngineeringJimei UniversityXiamenChina

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