Skip to main content
SpringerLink
Log in

Optimal parameters of an ELM-based interval type 2 fuzzy logic system: a hybrid learning algorithm

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

An optimized design of a fuzzy logic system can be regarded as setting of different parameters of the system automatically. For a single parameter, there may exist multiple feasible values. Consequently, with the increase in number of parameters, the complexity of a system increases. Type 2 fuzzy logic system has more parameters than the type 1 fuzzy logic system and is therefore much more complex than its counterpart. This paper proposes optimal parameters for an extreme learning machine-based interval type 2 fuzzy logic system to learn its best configuration. Extreme learning machine (ELM) is utilized to tune the consequent parameters of the interval type 2 fuzzy logic system (IT2FLS). A disadvantage of ELM is the random generation of its hidden neuron that causes additional uncertainty, in both approximation and learning. In order to overcome this limitation in an ELM-based IT2FLS, artificial bee colony optimization algorithm is utilized to obtain its antecedent parts parameters. The simulation results verified better performance of the proposed IT2FLS over other models with the benchmark data sets.

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.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Abbreviations

ABC:

Artificial bee colony

ANFIS:

Adaptive neuro-fuzzy inference system

ELM:

Extreme learning machine

FLS:

Fuzzy logic system

IT2FLS:

Interval type 2 fuzzy logic system

IT2FELM:

IT2FLS trained using extreme learning machine

IT2FKF:

IT2FLS trained using KF method

KF:

Kalman filter

NN:

Neural network

MF:

Membership function

MSE:

Mean square error

SLFN:

Single-hidden layer feedforward neural networks

T1:

Type 1

T1FLS:

Type 1 fuzzy logic system

T2:

Type 2

T2FLS:

Type 2 fuzzy logic system

References

  1. Abraham A (2005) Adaptation of fuzzy inference system using neural learning. In: Nedjah N, Macedo Mourelle LD (eds) Fuzzy systems engineering. Studies in fuzziness and soft computing, vol 181. Springer, Berlin, pp 53–83

    Google Scholar 

  2. Alcala R, Ducange P, Herrera F, Lazzerini B, Marcelloni F (2009) A multiobjective evolutionary approach to concurrently learn rule and data bases of linguistic fuzzy-rule-based systems. IEEE Trans Fuzzy Syst 17(5):1106–1122

    Article  Google Scholar 

  3. Almaraashi M (2012) Learning of type-2 fuzzy logic systems using simulated annealing. Ph.D. thesis. Department of Informatics DE MONTFORT UNIVERSITY

  4. Cao J, Lin Z, Huang G-B (2012) Self-adaptive evolutionary extreme learning machine. Neural Process Lett 36(3):285–305

    Article  Google Scholar 

  5. Castillo O, Melin P (2012a) Ant colony optimization algorithms for the design of type-2 fuzzy systems. In: Recent advances in interval type-2 fuzzy systems. Springer briefs in applied sciences and technology, vol 1. Springer, Berlin, pp 33–35

  6. Castillo O, Melin P (2012b) Optimization of type-2 fuzzy systems based on bio-inspired methods: a concise review. Inf Sci 205:1–19

    Article  Google Scholar 

  7. Cho JH, Chun MG Lee DJ (2007) Parameter optimization of extreme learning machine using bacterial foraging algorithm. In: SIS 2007 Proceedings of the 8th symposium on advanced intelligent systems, pp 742–747

  8. Cordon O, Herrera F, Sanchez L (1999) Solving electrical distribution problems using hybrid evolutionary data analysis techniques. Appl Intell 10(1):5–24. doi:10.1023/A:1008384630089

    Article  Google Scholar 

  9. Cordon O, Herrera F, Villar P (2001a) Generating the knowledge base of a fuzzy rule-based system by the genetic learning of the data base. IEEE Trans Fuzzy Syst 9(4):667–674

    Article  MATH  Google Scholar 

  10. Cordon O, Herrera F, Hoffmann F, Magdalena L (2001b) Genetic fuzzy systems: evolutionary tuning and learning of fuzzy knowledge bases. Advances in fuzzy systems applications and theory, vol 19, 1st edn. World Scientific, Singapore

  11. Cordon O, Herrera F, Magdalena L, Villar P (2001c) A genetic learning process for the scaling factors, granularity and contexts of the fuzzy rule-based system data base. Inf Sci 136(14):85–107. Recent advances in genetic fuzzy systems. doi:10.1016/S0020-0255(01)00143-8. http://www.sciencedirect.com/science/article/pii/S0020025501001438

  12. Deng J, Li K, Irwin GW (2011) Fast automatic two-stage nonlinear model identification based on the extreme learning machine. Neurocomputing 74(16):2422–2429

    Article  Google Scholar 

  13. Deng Z, Choi K-S, Cao L, Wang S (2014) 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 

  14. Hayashi Y, Buckley JJ (1994) Approximations between fuzzy expert systems and neural networks. Int J Approx Reason 10(1):63–73

    Article  MATH  Google Scholar 

  15. He Y-L, Geng Z-Q, Zhu Q-X (2015) Data driven soft sensor development for complex chemical processes using extreme learning machine. Chem Eng Res Des 102:1–11

    Article  Google Scholar 

  16. Herrera F, Casillas J, Cordon O (2002) COR: a methodology to improve ad hoc data-driven linguistic rule learning methods by inducing cooperation among rules. IEEE Trans Syst Man Cybern B Cybern 32(4):526–537

    Google Scholar 

  17. Hosseini R, Qanadli SD, Barman S, Mazinani M, Ellis T, Dehmeshki J (2012) An automatic approach for learning and tuning gaussian interval type-2 fuzzy membership functions applied to lung CAD classification system. IEEE Trans Fuzzy Syst 20(2):224–234

    Article  Google Scholar 

  18. Huang G-B, Chen L, Siew C-K (2006a) Universal approximation using incremental constructive feedforward networks with random hidden nodes. IEEE Trans Neural Netw 17(4):879–892

    Article  Google Scholar 

  19. Huang G-B, Zhu Q-Y, Siew C-K (2006b) Extreme learning machine: theory and applications. Neurocomputing 70(1–3):489–501

    Article  Google Scholar 

  20. Huang G-B, Zhou H, Ding X, Zhang R (2012) Extreme learning machine for regression and multiclass classification. IEEE Trans Syst Man Cybern Part B Cybern 42(2):513–529

    Article  Google Scholar 

  21. Hyndman RJ, Koehler AB (2006) Another look at measures of forecast accuracy. Int J Forecast 22(4):679–688

    Article  Google Scholar 

  22. Jang J-SR, Sun C-T (1993) Functional equivalence between radial basis function networks and fuzzy inference systems. IEEE Trans Neural Netw 4(1):156–159

    Article  Google Scholar 

  23. Juang C-F, Tsao Y-W (2008) A self-evolving interval type-2 fuzzy neural network with online structure and parameter learning. IEEE Trans Fuzzy Syst 16(6):1411–1424

    Article  Google Scholar 

  24. Karaboga D (2005) An idea based on honey bee swarm for numerical optimization. Technical report TR06, Erciyes University, Engineering Faculty, Computer Engineering Department

  25. Karaboga D, Ozturk C (2009) Neural networks training by artificial bee colony algorithm on pattern classification. Neural Netw World 19:279–292

    Google Scholar 

  26. Kayacan E, Kayacan E, Khanesar MA (2015) Identification of nonlinear dynamic systems using type-2 fuzzy neural networks-a novel learning algorithm and a comparative study. IEEE Trans Industr Electron 62(3):1716–1724

    Article  MATH  Google Scholar 

  27. Khanesar MA, Kayacan E, Teshnehlab M, Kaynak O (2011) Levenberg marquardt algorithm for the training of type-2 fuzzy neuro systems with a novel type-2 fuzzy membership function. In: 2011 IEEE symposium on advances in type-2 fuzzy logic systems (T2FUZZ), pp 88–93

  28. Khanesar MA, Kayacan E, Teshnehlab M, Kaynak O (2012) Extended Kalman filter based learning algorithm for type-2 fuzzy logic systems and its experimental evaluation. IEEE Trans Ind Electron 59(11):4443–4455

    Article  Google Scholar 

  29. Liang Q, Mendel JM (2000) Interval type-2 fuzzy logic systems: theory and design. IEEE Trans Fuzzy Syst 8(5):535–550. doi:10.1109/91.873577

    Article  Google Scholar 

  30. Liang N-Y, Huang G-B, Saratchandran P, Sundararajan N (2006) A fast and accurate online sequential learning algorithm for feedforward networks. IEEE Trans Neural Netw 17(6):1411–1423

    Article  Google Scholar 

  31. Lu C-H (2011) Wavelet fuzzy neural networks for identification and predictive control of dynamic systems. IEEE Trans Ind Electron 58(7):3046–3058

    Article  Google Scholar 

  32. Luo X, Chang X, Ban X (2015) Extreme learning machine for regression and classification using L 1-morm and L 2-norm. In: Cao J, Mao K, Cambria E, Man Z, Toh K-A (eds) Proceedings of ELM-2014 volume 1. Proceedings in adaptation, learning and optimization, vol 3. Springer, Berlin, pp 293–300

  33. Mendel JM (2001) Uncertain rule-based fuzzy logic systems: introduction and new directions. Prentice-Hall PTR, London

    MATH  Google Scholar 

  34. Mendel JM (2004) Computing derivatives in interval type-2 fuzzy logic systems. IEEE Trans Fuzzy Syst 12(1):84–98

    Article  MathSciNet  Google Scholar 

  35. Olatunji SO, Selamat A, Abdulraheem A (2014) A hybrid model through the fusion of type-2 fuzzy logic systems and extreme learning machines for modelling permeability prediction. Inf Fusion 16(0):29–45 (Special Issue on Information Fusion in Hybrid Intelligent Fusion Systems)

  36. Olatunji SO, Selamat A, Raheem AAA (2014) Improved sensitivity based linear learning method for permeability prediction of carbonate reservoir using interval type-2 fuzzy logic system. Appl Soft Comput 14 Part B: 144–155. Evolving soft computing techniques and applications. doi:10.1016/j.asoc.2013.02.018. http://www.sciencedirect.com/science/article/pii/S1568494613000720

  37. Olatunji SO, Selamat A, Azeez ARA (2015) Modeling permeability and PVT properties of oil and gas reservoir using hybrid model based on type-2 fuzzy logic systems. Neurocomputing 157:125–142. doi:10.1016/j.neucom.2015.01.027

    Article  Google Scholar 

  38. Paplinski AP. Neuro-fuzzy computing. http://www.csse.monash.edu.au/courseware/cse5301/2006/04/Lnts/L01.pdf

  39. Petalas YG, Parsopoulos KE, Vrahatis MN (2009) Improving fuzzy cognitive maps learning through memetic particle swarm optimization. Soft Comput 13(1):77–94

    Article  Google Scholar 

  40. Qu Y, Shang C, Wei W, Shen Q (2011) Evolutionary fuzzy extreme learning machine for mammographic risk analysis. Int J Fuzzy Syst 13(4):282–291

    MathSciNet  Google Scholar 

  41. Rao CR, Mitra SK (1971) Generalized inverse of matrices and its applications. Wiley, New York

    MATH  Google Scholar 

  42. Rong H-J, Sundararajan N, Huang G-B, Saratchandran P (2006) Sequential adaptive fuzzy inference system (safis) for nonlinear system identification and prediction. Fuzzy Sets Syst 157(9):1260–1275

    Article  MathSciNet  MATH  Google Scholar 

  43. Rong H-J, Huang G-B, Sundararajan N, Saratchandran P (2009) Online sequential fuzzy extreme learning machine for function approximation and classification problems. IEEE Trans Syst Man Cybern Part B Cybern 39(4):1067–1072

    Article  Google Scholar 

  44. Serre D (2002) Matrices: theory and application. Springer, New York

    MATH  Google Scholar 

  45. Soria-Olivas E, Gomez-Sanchis J, Jarman IH, Vila-Frances J, Martinez M, Magdalena JR, Serrano AJ (2011) Belm: Bayesian extreme learning machine. IEEE Trans Neural Netw 22(3):505–509

    Article  Google Scholar 

  46. Sun Z-L, Au K-F, Choi T-M (2007) A neuro-fuzzy inference system through integration of fuzzy logic and extreme learning machines. IEEE Trans Syst Man Cybern Part B Cybern 37(5):1321–1331

    Article  Google Scholar 

  47. Tseng T-LB, Jiang F, Kwon YJ (2015) Hybrid type II fuzzy system and data mining approach for surface finish. J Computat Des Eng 2(3):137–147. doi:10.1016/j.jcde.2015.02.002

    Google Scholar 

  48. Wang C, Cheng C, Lee T (2004) Dynamical optimal training for interval type-2 fuzzy neural network (T2FNN). IEEE Trans Syst Man Cybern 12(4):524–539

    Google Scholar 

  49. Wu D (2013) Approaches for reducing the computational cost of interval type-2 fuzzy logic systems: overview and comparisons. IEEE Trans Fuzzy Syst 21(1):80–99

    Article  Google Scholar 

  50. Xiang J, Westerlund M, Sovilj D, Pulkkis G (2014) Using extreme learning machine for intrusion detection in a big data environment. In: Proceedings of the 2014 workshop on artificial intelligent and security workshop. ACM, pp 73–82

  51. Xin J, Wang Z, Qu L, Wang G (2015) Elastic extreme learning machine for big data classification. Neurocomputing 149:464–471

    Article  Google Scholar 

  52. Xu Y, Shu Y (2006) Evolutionary extreme learning machine—based on particle swarm optimization. In: Advances in neural networks—ISNN 2006. In: Wang J, Yi Z, Zurada J, Lu B-L, Yin H (eds) Lecture notes in computer science, vol 3971. Springer, Berlin, pp 644–652. 978-3-540-34439-1

  53. Yin S, Kaynak O (2015) Big data for modern industry: challenges and trends [point of view]. Proc IEEE 103(2):143–146

    Article  Google Scholar 

  54. Yin S, Wang G, Gao H (2015a) Data-driven process monitoring based on modified orthogonal projections to latent structures. IEEE Trans Control Syst Technol 99:1–8

    Google Scholar 

  55. Yin S, Zhu X, Kaynak O (2015b) Improved pls focused on key-performance-indicator-related fault diagnosis. IEEE Trans Industr Electron 62(3):1651–1658

    Article  Google Scholar 

  56. Yong Z, Joo EM, Sundaram S (2014) Meta-cognitive fuzzy extreme learning machine. In: 2014 13th international conference on control automation robotics vision (ICARCV), pp 613–618

  57. Zhang WB, Ji HB (2013) Fuzzy extreme learning machine for classification. Electron Lett 49(7):448–450

    Article  Google Scholar 

  58. Zhang R, Lan Y, Huang G-B, Xu Z-B (2012) Universal approximation of extreme learning machine with adaptive growth of hidden nodes. IEEE Trans Neural Netw Learn Syst 23(2):365–371

    Article  Google Scholar 

  59. Zhang Y, Cai Z, Gong W, Wang X (2015) Self-adaptive differential evolution extreme learning machine and its application in water quality eva. Comput Inf Syst 11(4):1443–1451

    Google Scholar 

  60. Zhao L (2011) Adaptive interval type-2 fuzzy control based on gradient descent algorithm. In: 2011 2nd international conference on Intelligent control and information processing (ICICIP), vol 2, pp 899–904

  61. Zheng E, Liu J, Lu H, Wang L, Chen L (2013) A new fuzzy extreme learning machine for regression problems with outliers or noises. In: Motoda H, Wu Z, Cao L, Zaiane O, Yao M, Wang W (eds) Advanced data mining and applications. Lecture notes in computer science, vol 8347. Springer, Berlin, pp 524–534

  62. Zhou P, Yuan M, Wang H (2015) ELM based dynamic modeling for online prediction of molten iron silicon content in blast furnace. In: Proceedings of ELM-2014, vol 2. Springer, Berlin, pp 267–277

  63. Zhu Q-Y, Qin AK, Suganthan PN, Huang G-B (2005) Evolutionary extreme learning machine. Pattern Recogn 38(10):1759–1763

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Universiti Teknologi PETRONAS, Seri Iskandar, Malaysia

    Saima Hassan & Jafreezal Jaafar

  2. Kohat University of Science and Technology, Kohat, Pakistan

    Saima Hassan

  3. Faculty of Electrical and Computer Engineering, Semnan University, Semnan, Iran

    Mojtaba Ahmadieh Khanesar

  4. Centre for Intelligent Systems Research, Deakin University, Waurn Ponds Campus, Geelong, Australia

    Abbas Khosravi

Authors
  1. Saima Hassan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mojtaba Ahmadieh Khanesar
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jafreezal Jaafar
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Abbas Khosravi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Saima Hassan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hassan, S., Khanesar, M.A., Jaafar, J. et al. Optimal parameters of an ELM-based interval type 2 fuzzy logic system: a hybrid learning algorithm. Neural Comput & Applic 29, 1001–1014 (2018). https://doi.org/10.1007/s00521-016-2503-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-016-2503-5

Keywords

Search

Navigation