Skip to main content
SpringerLink
Log in

A novel fuzzy rule extraction approach using Gaussian kernel-based granular computing

  • Regular Paper
  • Published:
Knowledge and Information Systems Aims and scope Submit manuscript

Abstract

In this paper, we present a novel fuzzy rule extraction approach by employing the Gaussian kernels and fuzzy concept lattices. First we introduce the Gaussian kernel to interval type-2 fuzzy rough sets to model fuzzy similarity relations and introduce a few concepts and theorems to improve the classification performance with fewer attributes accordingly. Based on this idea, we propose a novel attribute reduction algorithm, which can achieve better classification performance of deducing reduction subset of fewer attributes, and this will be used in the subsequent decision rule extraction. Then we justify the necessary and sufficient conditions of our fuzzy rule extraction approach through three implicit rule theorems and present a novel fuzzy decision rule extraction algorithm using fuzzy concept lattices and introduce the concepts of frequent nodes and candidate 2-tuples to our pruning strategy. Also, comparative performance experiments are carried out on the UCI datasets, and the results of both reduction subset size and classification ability show the advantages of our algorithm.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Ahmad SSS, Pedrycz W (2017) The development of granular rule-based systems: a study in structural model compression. Granul Comput 2(1):1–12

    Article  Google Scholar 

  2. Antonelli M, Ducange P, Lazzerini B, Marcelloni F (2016) Multi-objective evolutionary design of granular rule-based classifiers. Granul Comput 1(1):37–58

    Article  Google Scholar 

  3. Baixeries J, Sacarea C, Ojeda-Aciego M (2015) Formal concept analysis. Springer, Berlin

    Book  MATH  Google Scholar 

  4. Celik E, Gul M, Aydin N, Gumus AT, Guneri AF (2015) A comprehensive review of multi criteria decision making approaches based on interval type-2 fuzzy sets. Knowl Based Syst 85:329–341

    Article  Google Scholar 

  5. Chen SM, Chang YC, Pan JS (2013) Fuzzy rules interpolation for sparse fuzzy rule-based systems based on interval type-2 Gaussian fuzzy sets and genetic algorithms. IEEE Trans Fuzzy Syst 21(3):412–425

    Article  Google Scholar 

  6. Chen SM, Chien CY (2011) Parallelized genetic ant colony systems for solving the traveling salesman problem. Expert Syst Appl 38(4):3873–3883

    Article  Google Scholar 

  7. Chen SM, Kao PY (2013) TAIEX forecasting based on fuzzy time series, particle swarm optimization techniques and support vector machines. Inf Sci 247(15):62–71

    Article  MathSciNet  Google Scholar 

  8. Chen SM, Lee LW (2010) Fuzzy multiple criteria hierarchical group decision-making based on interval type-2 fuzzy sets. IEEE Trans Syst Man Cybern Part A Syst Hum 40(5):1120–1128

    Article  MathSciNet  Google Scholar 

  9. Chen SM, Wang CY (2013) Fuzzy decision making systems based on interval type-2 fuzzy sets. Inf Sci 242(Supplement2):1–21

    Article  MathSciNet  MATH  Google Scholar 

  10. Chen TY (2013) A signed-distance-based approach to importance assessment and multi-criteria group decision analysis based on interval type-2 fuzzy set. Knowl Inf Syst 35(1):193–231

    Article  Google Scholar 

  11. Deng Z, Choi KS, Cao L, Wang S (2017) T2FELA: type-2 fuzzy extreme learning algorithm for fast training of interval type-2 TSK fuzzy logic system. IEEE Trans Neural Netw Learn Syst 25(4):664–676

    Article  Google Scholar 

  12. Dubois D, Prade H (2016) Bridging gaps between several forms of granular computing. Granul Comput 1(2):115–126

    Article  Google Scholar 

  13. Fkih F, Omri MN (2016) IRAFCA: an \({O}(n)\) information retrieval algorithm based on formal concept analysis. Knowl Inf Syst 48(2):465–491

    Article  Google Scholar 

  14. Garibaldi JM, Guadarrama S (2011) Constrained type-2 fuzzy sets. In: Advances in type-2 fuzzy logic systems, pp 66–73

  15. Gonzalez C, Castro JR, Melin P, Castillo O (2016) An edge detection method based on generalized type-2 fuzzy logic. Soft Comput 20(2):773–784

    Article  Google Scholar 

  16. Hou J, Gao H, Xia Q, Qi N (2016) Feature combination and the kNN framework in object classification. IEEE Trans Neural Netw Learn Syst 27(6):1368–1378

    Article  Google Scholar 

  17. Hu Q, Zhang L, Chen D, Pedrycz W, Yu D (2010) Gaussian kernel based fuzzy rough sets: model, uncertainty measures and applications. Int J Approx Reason 51(4):453–471

    Article  MATH  Google Scholar 

  18. Huang CC, Tseng TL, Jiang F, Fan YN, Hsu CH (2014) Rough set theory: a novel approach for extraction of robust decision rules based on incremental attributes. Ann Oper Res 216(1):163–189

    Article  MathSciNet  MATH  Google Scholar 

  19. Janssen J, Laatz W (2017) Naive Bayes. Springer, Berlin

    Book  Google Scholar 

  20. Kang X, Miao D (2016) A rough set model based on formal concept analysis in complex information systems. In: International conference on fuzzy systems and knowledge discovery, pp 206–214

  21. Kaytoue M, Codocedo V, Buzmakov A, Baixeries J, Kuznetsov SO, Napoli A (2015) Pattern structures and concept lattices for data mining and knowledge processing. Springer, Berlin

    Book  Google Scholar 

  22. Li H, Wu C, Wu L, Lam HK, Gao Y (2017) Filtering of interval type-2 fuzzy systems with intermittent measurements. IEEE Trans Cybern 46(3):668–678

    Article  Google Scholar 

  23. Li J, Huang C, Mei C, Yin Y (2016) An intensive study on rule acquisition in formal decision contexts based on minimal closed label concept lattices. Intelligent automation and soft computing, pp 1–15

  24. Lingras P, Haider F, Triff M (2016) Granular meta-clustering based on hierarchical, network, and temporal connections. Granul Comput 1(1):71–92

    Article  Google Scholar 

  25. Liu H, Cocea M (2016) Granular computing-based approach for classification towards reduction of bias in ensemble learning. Granul Comput 2(3):131–139

    Article  Google Scholar 

  26. Liu H, Cocea M (2017) Fuzzy information granulation towards interpretable sentiment analysis. Granul Comput 2(4):289–302

    Article  Google Scholar 

  27. Liu H, Cocea M (2017) Semi-random partitioning of data into training and test sets in granular computing context. Granul Comput 2(4):357–387

    Article  Google Scholar 

  28. Liu H, Gegov A, Cocea M (2016) Rule-based systems: a granular computing perspective. Granul Comput 1(4):259–274

    Article  Google Scholar 

  29. Livi L, Sadeghian A (2016) Granular computing, computational intelligence, and the analysis of non-geometric input spaces. Granul Comput 1(1):13–20

    Article  Google Scholar 

  30. Martinez-Ballesteros M, Troncoso A, Martinez-Alvarez F, Riquelme JC (2016) Improving a multi-objective evolutionary algorithm to discover quantitative association rules. Knowl Inf Syst 49(2):481–509

    Article  Google Scholar 

  31. Mondal KC, Pasquier N, Maulik U, Maulik U, Bandhopadyay S (2016) A new approach for association rule mining and bi-clustering using formal concept analysis. In: International conference on machine learning and data mining in pattern recognition, pp 86–101

  32. Parthal M, In N, Jensen R (2013) Unsupervised fuzzy-rough set-based dimensionality reduction. Inf Sci 229(6):106–121

    Article  MathSciNet  Google Scholar 

  33. Paul A (2016) Positive and negative association rule mining using correlation threshold and dual confidence approach. Springer India, New Delhi

    Book  Google Scholar 

  34. Peters G, Weber R (2016) DCC: a framework for dynamic granular clustering. Granul Comput 1(1):1–11

    Article  Google Scholar 

  35. Ren R, Wei L (2016) The attribute reductions of three-way concept lattices. Knowl Based Syst 99(C):92–102

    Article  Google Scholar 

  36. Robniksikonja M, Kononenko I (2003) Theoretical and empirical analysis of relieff and rrelieff. Mach Learn 53(1):23–69

    Article  MATH  Google Scholar 

  37. Sahoo J, Das AK, Goswami A (2015) An effective association rule mining scheme using a new generic basis. Knowl Inf Syst 43(1):127–156

    Article  Google Scholar 

  38. Sathyadevan S, Nair RR (2015) Comparative analysis of decision tree algorithms: id3, c4.5 and random forest. Springer India, New Delhi

    Google Scholar 

  39. Shawe-Taylor J, Cristianini N (2004) Kernel methods for pattern analysis. J Am Stat Assoc 101(476):1730–1730

    Google Scholar 

  40. Sheikhpour R, Sarram MA, Chahooki MAZ, Sheikhpour R (2017) A kernelized non-parametric classifier based on feature ranking in anisotropic Gaussian kernel. Neurocomputing 267:545–555

    Article  Google Scholar 

  41. Singh PK, Kumar CA (2017) Concept lattice reduction using different subset of attributes as information granules. Granul Comput 2(3):159–173

    Article  Google Scholar 

  42. Singh PK, Kumar CA, Li J (2016) Knowledge representation using interval-valued fuzzy formal concept lattice. Soft Comput 20(4):1485–1502

    Article  MATH  Google Scholar 

  43. Skowron A, Jankowski A, Dutta S (2016) Interactive granular computing. Granul Comput 1(2):95–113

    Article  MathSciNet  MATH  Google Scholar 

  44. Smatana M, Butka P, Covekova L (2017) Tree based reduction of concept lattices based on conceptual indexes. Springer, Berlin

    Book  Google Scholar 

  45. Sola HB, Fernandez J, Hagras H, Herrera F, Pagola M, Barrenechea E (2015) Interval type-2 fuzzy sets are generalization of interval-valued fuzzy sets: toward a wider view on their relationship. IEEE Trans Fuzzy Syst 23(5):1876–1882

    Article  Google Scholar 

  46. Song M, Wang Y (2016) A study of granular computing in the agenda of growth of artificial neural networks. Granul Comput 1(4):247–257

    Article  Google Scholar 

  47. Tahayori H, Antoni GD (2008) Operations on concavoconvex type-2 fuzzy sets. Int J Fuzzy Syst 10(4):276–286

    MathSciNet  Google Scholar 

  48. Tripathy BK, Sooraj TR, Mohanty RK (2017) A new approach to interval-valued fuzzy soft sets and its application in decision-making. Springer, Singapore

    Book  Google Scholar 

  49. Tsai PW, Pan JS, Chen SM, Liao BY (2012) Enhanced parallel cat swarm optimization based on the Taguchi method. Expert Syst Appl 39(7):6309–6319

    Article  Google Scholar 

  50. Vluymans S, Fernández A, Saeys Y, Cornelis C, Herrera F (2017) Dynamic affinity-based classification of multi-class imbalanced data with one-versus-one decomposition: a fuzzy rough set approach. Knowl Inf Syst 2017(1):1–30

    Google Scholar 

  51. Wang C, Qi Y, Shao M, Hu Q, Chen D, Qian Y, Lin Y (2017) A fitting model for feature selection with fuzzy rough sets. IEEE Trans Fuzzy Syst 25(4):741–753

    Article  Google Scholar 

  52. Wang G (2017) DGCC: data-driven granular cognitive computing. Granul Comput 2(4):343–355

    Article  Google Scholar 

  53. William-West TO, Singh D (2018) Information granulation for rough fuzzy hypergraphs. Granul Comput 3(1):75–92

    Article  Google Scholar 

  54. Xie WX, Zhang QY, Sun ZM, Zhang F (2015) A clustering routing protocol for WSN based on type-2 fuzzy logic and ant colony optimization. Wirel Pers Commun 84(2):1165–1196

    Article  Google Scholar 

  55. Xu W, Li W, Zhang X (2017) Generalized multigranulation rough sets and optimal granularity selection. Granul Comput 2(4):271–288

    Article  Google Scholar 

  56. Xu WH, Zhang XY, Zhong JM, Zhang WX (2010) Attribute reduction in ordered information systems based on evidence theory. Knowl Inf Syst 25(1):169–184

    Article  Google Scholar 

  57. Yang C, Liu H, McLoone S, Chen CLP, Wu X (2018) A novel variable precision reduction approach to comprehensive knowledge systems. IEEE Trans Cybern 48(2):661–674

    Article  Google Scholar 

  58. Yang C, Liu H, Sun Y, Abraham A (2013) Multi-knowledge extraction from violent crime datasets using swarm rough algorithm. In: International conference on hybrid intelligent systems, pp 560–565

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

    Article  MathSciNet  MATH  Google Scholar 

  60. Yao Y (2016) A triarchic theory of granular computing. Granul Comput 1(2):145–157

    Article  Google Scholar 

  61. Yu Q, Liu Z, Lin W, Shi B, Li Y (2005) Research on fuzzy concept lattice in knowledge discovery and a construction algorithm. Acta Electron Sin 33(2):350–353

    Google Scholar 

  62. Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning. Inf Sci 8(3):199–249

    Article  MathSciNet  MATH  Google Scholar 

  63. Zhao T, Xiao J (2013) Interval type-2 fuzzy rough sets based on inclusion measures. Acta Autom Sin 39(10):1714–1721

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The authors would like to thank Zongmei Wang and Chao Yang for their scientific collaboration in this research. This work is partly supported by the Program for New Century Excellent Talents in University (NCET-11-0861) and the National Natural Science Foundation of China (Grant Nos. 61472058, 61602086, 61702291 and 61772102).

Author information

Authors and Affiliations

  1. School of Information Science and Technology, Dalian Maritime University, Dalian, 116026, China

    Guangyao Dai, Yu Yang, Nanxun Zhang & Hongbo Liu

  2. Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA, 30460, USA

    Yi Hu

  3. Machine Intelligence Research Labs, Scientific Network for Innovation and Research Excellence, Auburn, WA, 98071, USA

    Ajith Abraham

Authors
  1. Guangyao Dai
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yi Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yu Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Nanxun Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Ajith Abraham
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Hongbo Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hongbo Liu.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (zip 1125 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dai, G., Hu, Y., Yang, Y. et al. A novel fuzzy rule extraction approach using Gaussian kernel-based granular computing. Knowl Inf Syst 61, 821–846 (2019). https://doi.org/10.1007/s10115-018-1318-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10115-018-1318-3

Keywords

Search

Navigation