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Relation granulation and algebraic structure based on concept lattice in complex information systems

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Abstract

Normally, there may exist some kind of relationship among different attribute values such as order relationship, similarity relationship or other more complicated relationship hidden in complex information systems. In the case, the binary relation on the universe is probably a kind of more general binary relation rather than equivalence relation, tolerance relation, order relation, etc. For the case, the paper tries to take concept lattice as theoretical foundation, which is appropriate very well for analyzing and processing binary relations, and finally proposes a new rough set model from the perspective of sub-relations. In the model, one general binary relation can be decomposed into several sub-relations, which can be viewed as granules to study algebraic structure and offer solutions to problems such as reduction, core. The algebraic structure mentioned above can organized all of relation granulation results in the form of lattice structure. In addition, the computing process based on concept lattice is often accompanied by high time complexity, aiming at the problem, the paper attempts to overcome it by introducing granular computing, and further converts complex information systems into relatively simple ones. In general, the paper is a new attempt and exploring to the fusion of rough set and concept lattice, and also offers a new idea for the expansion of rough set from the perspective of relation granulation.

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References

  1. Belohlavek R (2007) A note on variable threshold concept lattices: threshold-based operators are reducible to classical concept forming operators. Inf Sci 177:3186–3191

    Article  MathSciNet  Google Scholar 

  2. Birkhoff G (1967) Lattice theory, vol 25, 3rd edn. American Mathematical Society, Providence

    MATH  Google Scholar 

  3. Chen JK, Li JJ, Lin YJ, Lin GP, Ma ZM (2015) Relations of reduction between covering generalized rough sets and concept lattices. Inf Sci 304:16–27

    Article  MathSciNet  Google Scholar 

  4. Deogun JS, Saquer J (2004) Monotone concepts for formal concept analysis. Discret Appl Math 144:70–78

    Article  MathSciNet  Google Scholar 

  5. Dubois D, Prade H (1990) Rough fuzzy sets and fuzzy rough sets. Int J Gen Syst 17:191–209

    Article  Google Scholar 

  6. Ganter B, Wille R (1999) Formal concept analysis: mathematical foundations. Springer, Berlin

    Book  Google Scholar 

  7. Greco S, Matarazzo B, Slowinski R (2002) Rough approximation by dominance relations. Int J Intell Syst 17(2):153–171

    Article  Google Scholar 

  8. Hu QH, Yu DR, Liu JF, Wu CX (2008) Neighborhood rough set based heterogeneous feature subset selection. Inf Sci 178:3577–3594

    Article  MathSciNet  Google Scholar 

  9. Kang XP, Li DY, Wang SG, Qu KS (2012) Formal concept analysis based on fuzzy granularity base for different granulations. Fuzzy Set Syst 203:33–48

    Article  MathSciNet  Google Scholar 

  10. Kang XP, Li DY, Wang SG, Qu KS (2013) Rough set model based on formal concept analysis. Inf Sci 222:611–625

    Article  MathSciNet  Google Scholar 

  11. Kang XP, Li DY, Wang SG (2012) Research on domain ontology in different granulations based on concept lattice. Knowl Based Syst 27:152–161

    Article  Google Scholar 

  12. Kang XP, Miao DQ (2016) A variable precision rough set model based on the granularity of tolerance relation. Knowl Based Syst 102:103–115

    Article  Google Scholar 

  13. Kang XP, Miao DQ (2016) A study on information granularity in formal concept analysis based on concept-bases. Knowl Based Syst 105:147–159

    Article  Google Scholar 

  14. Kent RE (1996) Rough concept analysis: a synthesis of rough sets and formal concept analysis. Fund Inf 27:169–181

    MathSciNet  MATH  Google Scholar 

  15. Lang GM, Li QG, Cai MJ, Yang T (2015) Characteristic matrixes-based knowledge reduction in dynamic covering decision information systems. Knowl Based Syst 85:1–26

    Article  Google Scholar 

  16. Lang GM, Li QG, Yang T (2014) An incremental approach to attribute reduction of dynamic set-valued information systems. Int J Mach Learn Cybern 5:775–788

    Article  Google Scholar 

  17. Lee HS (2001) An optimal algorithm for computing the max-min transitive closure of a fuzzy similarity matrix. Fuzzy Set Syst 123(1):129–136

    Article  MathSciNet  Google Scholar 

  18. Leung Y, Li DY (2003) Maximal consistent block techniques for rule acquisition in incomplete information systems. Inf Sci 153:85–106

    Article  MathSciNet  Google Scholar 

  19. Li JH, Kumar CA, Mei CL, Wang XZ (2017) Comparison of reduction in formal decision contexts. Int J Approx Reason 80:100–122

    Article  MathSciNet  Google Scholar 

  20. 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

    Article  Google Scholar 

  21. Li JH, Mei CL, Wang LD, Wang JH (2015a) On inference rules in decision formal contexts. Int J Comput Intell Syst 8(1):175–186

    Article  MathSciNet  Google Scholar 

  22. Li JH, Mei CL, Xu WH, Qian YH (2015b) Concept learning via granular computing: a cognitive viewpoint. Inf Sci 298:447–467

    Article  MathSciNet  Google Scholar 

  23. Li JH, Huang CC, Qi JJ, Qian YH, Liu WQ (2017) Three-way cognitive concept learning via multi-granularity. Inf Sci 378:244–263

    Article  Google Scholar 

  24. Li JH, Mei CL, Wang JH, Zhang X (2014) Rule-preserved object compression in formal decision contexts using concept lattices. Knowl Based Syst 71:435–445

    Article  Google Scholar 

  25. Li TJ, Wu WZ (2011) Attribute reduction in formal contexts: a covering rough set approach. Fund Inf 111:15–32

    MathSciNet  MATH  Google Scholar 

  26. Lin GP, Liang JY, Qian YH (2014) Topological approach to multigranulation rough sets. Int J Mach Learn Cybern 5:233–243

    Article  Google Scholar 

  27. Liu M, Shao MW, Zhang WX, Wu C (2007) Reduct method for concept lattices based on rough set theory and its application. Comput Math Appl 53(9):1390–1410

    Article  MathSciNet  Google Scholar 

  28. Ma JM, Leung Y, Zhang WX (2014) Attribute reductions in object-oriented concept lattices. Int J Mach Learn Cybern 5:789–813

    Article  Google Scholar 

  29. Mi JS, Leung Y, Wu WZ (2010) Approaches to attribute reduct in concept lattices induced by axialities. Knowl Based Syst 23(6):504–511

    Article  Google Scholar 

  30. Oosthuizen GD (1994) Rough sets and concept lattices. In: Ziarko WP (ed) Rough Sets, and fuzzy sets and knowledge discovery (RSKD’93). Springer, London, pp 24–31

    Chapter  Google Scholar 

  31. Pawlak Z (1982) Rough sets. Int J Comput Inf Sci 11(5):341–356

    Article  Google Scholar 

  32. Pawlak Z (1991) Rough sets: theoretical aspects of reasoning about data. Kluwer Academic Publishers, Boston

    Book  Google Scholar 

  33. Pei D, Mi JS (2011) Attribute reduction in decision formal context based on homomorphism. Int J Mach Learn Cybern 2:289–293

    Article  Google Scholar 

  34. Qian YH, Zhang H, Sang YL, Liang JY (2014) Multigranulation decision-theoretic rough sets. Int J Approx Reason 55:225–237

    Article  MathSciNet  Google Scholar 

  35. Qian YH, Liang JY, Pedrycz W, Dang CY (2010) Positive approximation: an accelerator for attribute reduction in rough set theory. Artif Intell 174:597–618

    Article  MathSciNet  Google Scholar 

  36. Qian YH, Liang JY, Pedrycz W, Dang CY (2011) An efficient accelerator for attribute reduction from incomplete data in rough set framework. Pattern Recogn 44:1658–1670

    Article  Google Scholar 

  37. Qu KS, Zhai YH (2006) Posets, inclusion degree theory and FCA. Chin J Comput 29(2):219–226

    MathSciNet  Google Scholar 

  38. Qu KS, Zhai YH, Liang JY, Chen M (2007) Study of decision implications based on formal concept analysis. Int J Gen Syst 36(2):147–156

    Article  MathSciNet  Google Scholar 

  39. Skowron A, Stepaniuk J (1996) Tolerance approximation spaces. Fund Inf 27:245–253

    MathSciNet  MATH  Google Scholar 

  40. Shafer G (1976) A mathematical theory of evidence. Princeton University Press, Princeton

    MATH  Google Scholar 

  41. Shao MW, Yang HZ, Wu WZ (2015) Knowledge reduction in formal fuzzy contexts. Knowl Based Syst 73:265–275

    Article  Google Scholar 

  42. Tan AH, Li JJ, Lin GP (2015) Connections between covering-based rough sets and concept lattices. Int J Approx Reason 56:43–58

    Article  MathSciNet  Google Scholar 

  43. Wang CZ, Wu CX, Chen DG (2008) A systematic study on attribute reduction with rough sets based on general binary relations. Inf Sci 178(9):2237–2261

    Article  MathSciNet  Google Scholar 

  44. Wang LD, Liu XD (2008) Concept analysis via rough set and AFS algebra. Inf Sci 178(21):4125–4137

    Article  MathSciNet  Google Scholar 

  45. Wei L, Qi JJ (2010) Relation between concept lattice reduct and rough set reduct. Knowl Based Syst 23(8):934–938

    Article  Google Scholar 

  46. Wei L, Wan Q (2016) Granular transformation and irreducible element judgment theory based on pictorial diagrams. IEEE Trans Cybern 46(2):380–387

    Article  Google Scholar 

  47. Wille R (1982) Restructuring lattice theory: an approach based on hierarchies of concepts. Ordered sets. Springer, The Netherlands

    MATH  Google Scholar 

  48. Wu WZ, Leung Y, Mi JS (2009) Granular computing and knowledge reduction in formal contexts. IEEE Trans Knowl Data Eng 21(10):1461–1474

    Article  Google Scholar 

  49. Xu WH, Li WT (2016) Granular computing approach to two-way learning based on formal concept analysis in fuzzy datasets. IEEE Trans Cybern 46(2):366–379

    Article  MathSciNet  Google Scholar 

  50. Yang XB, Yang JY, Wu C, Yu DJ (2008) Dominance-based rough set approach and knowkledge reductions in incomplete ordered information system. Inf Sci 178(4):1219–1234

    Article  Google Scholar 

  51. Yao YY, Chen YH (2006) Rough set approximations in formal concept analysis. LNCS Trans Rough Sets V 4100:285–305

    Article  MathSciNet  Google Scholar 

  52. Yao YY (1998) Relational interpretations of neighborhood operators and rough set approximation operators. Inf Sci 111(1–4):239–259

    Article  MathSciNet  Google Scholar 

  53. Yao YY (2016) Rough-set analysis: interpreting RS-definable concepts based on ideas from formal concept analysis. Inf Sci 346–347:442–462

    Article  MathSciNet  Google Scholar 

  54. Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353

    Article  Google Scholar 

  55. Zadeh LA (1997) Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. Fuzzy Set Syst 90(2):111–127

    Article  MathSciNet  Google Scholar 

  56. Zhang B, Zhang L (1992) Theory and applications of problem solving. Elsevier Science Publishers, North-Holland

    MATH  Google Scholar 

  57. Zhang WX, Ma JM, Fan SQ (2007) Variable threshold concept lattices. Inf Sci 177:4883–4892

    Article  MathSciNet  Google Scholar 

  58. Zhang XH, Miao DQ, Liu CH, Le ML (2016) Constructive methods of rough approximation operators and multigranulation rough sets. Knowl Based Syst 91:114–125

    Article  Google Scholar 

  59. Zhang XH, Dai JH, Yu YC (2015) On the union and intersection operations of rough sets based on various approximation spaces. Inf Sci 292:214–229

    Article  MathSciNet  Google Scholar 

  60. Zhang XH, Zhou B, Li P (2012) A general frame for intuitionistic fuzzy rough sets. Inf Sci 216:34–49

    Article  MathSciNet  Google Scholar 

  61. Zhu W (2007) Generalized rough sets based on relations. Inf Sci 177(22):4997–5011

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

Authors would like to thank the anonymous reviewers very much for their professional comments and valuable suggestions to improve the manuscript. This work is supported by National Natural Science Foundation of China (Nos. 61603278, 61673301, 61603173) and National Postdoctoral Science Foundation of China (No. 2014M560352).

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Authors and Affiliations

  1. Key Laboratory of Embedded System and Service Computing, Ministry of Education, Tongji University, Shanghai, 201804, China

    Xiangping Kang & Duoqian Miao

  2. China National Tobacco Corporation, Shanxi Branch, Taiyuan, 030000, Shanxi, China

    Xiangping Kang

  3. School of Mathematics and Statistics, Minnan Normal University, Zhangzhou, 363000, Fujian, China

    Guoping Lin

  4. School of Computer Science and Technology, Shandong University, Jinan, 250101, China

    Yong Liu

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  1. Xiangping Kang
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Correspondence to Xiangping Kang.

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Kang, X., Miao, D., Lin, G. et al. Relation granulation and algebraic structure based on concept lattice in complex information systems. Int. J. Mach. Learn. & Cyber. 9, 1895–1907 (2018). https://doi.org/10.1007/s13042-017-0698-0

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  • DOI: https://doi.org/10.1007/s13042-017-0698-0

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