Advertisement

Hierarchical fuzzy design by a multi-objective evolutionary hybrid approach

  • Yosra JarrayaEmail author
  • Souhir Bouaziz
  • Adel M. Alimi
  • Ajith Abraham
Methodologies and Application

Abstract

This paper presents a new tree hierarchical representation of type-2 fuzzy systems. The proposed system is called the type-2 hierarchical flexible beta fuzzy system (T2HFBFS) and is trained based on two-phase optimization mechanism. The first optimization step is a multi-objective structural learning phase. This phase is based on the multi-objective extended immune programming algorithm and aims to obtain an improved T2HFBFS structure with good interpretability-accuracy trade-off. The second optimization step is a parameter tuning phase. Using a hybrid evolutionary algorithm, this phase allows the adjustment of antecedent and consequent membership function parameters of the obtained T2HFBFS. By interleaving the two learning steps, an optimal and accurate hierarchical type-2 fuzzy system is derived with the least number of possible rules. The performance of the system is evaluated by conducting case studies for time series prediction problems and high-dimensional classification problems. Results prove that the T2HFBFS could attain superior performance than other existing approaches in terms of achieving high accuracy with a significant rule reduction.

Keywords

Hierarchical design Type-2 fuzzy systems Beta basis function Structure learning Multi-objective optimization Parameter tuning 

Notes

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

References

  1. Aliev RA, Guirimov BG, Aliev RR (2009) Evolutionary algorithm-based learning of fuzzy neural networks, part 2: recurrent fuzzy neural networks. Fuzzy Set Syst 160(17):2553–2566MathSciNetzbMATHGoogle Scholar
  2. Alimi AM (1997) Beta fuzzy basis functions for the design of universal robust neuro-fuzzy controllers. In: Proceeding of Séminaire sur la Commande Robuste ses Applications: SCRA’97, Nabeul, Tunisia, pp C1–C5Google Scholar
  3. Alimi AM (2000) The beta system: toward a change in our use of neuro-fuzzy systems. Int J Manag 15–19Google Scholar
  4. Alimi AM (2003) Beta neuro-fuzzy systems. TASK Q J Spec Issue Neural Netw 7(1):23–41Google Scholar
  5. Almaraashi M, John R (2011) Tuning of type-2 fuzzy systems by simulated annealing to predict time series. In: Proceedings of the world congress on engineering, London, UK, vol 2, pp 976–980Google Scholar
  6. Almaraashi M, John R, Hopgood A, Ahmadi S (2016) Learning of interval and general type-2 fuzzy logic systems using simulated annealing: theory and practice. Inf Sci 360:21–42Google Scholar
  7. Ammar M, Bouaziz S, Alimi AM, Abraham A (2013) Hybrid harmony search algorithm for global optimization. In: Fifth world congress on nature and biologically inspired computing, pp 69–75, Fargo, USAGoogle Scholar
  8. Ayat S, Rahi M (2014) Application of ant colony algorithm and principal components analysis in the diagnosis of lung cancer. J Math Comput Sci (JMCS) 13:343–352Google Scholar
  9. Balazs K, Botzheim J, Koczy LT (2010) Hierarchical fuzzy system modeling by genetic and bacterial programming approaches. In: International conference on fuzzy systems, pp 1–6. IEEEGoogle Scholar
  10. Benítez AD, Casillas J (2013) Multi-objective genetic learning of serial hierarchical fuzzy systems for large-scale problems. Soft Comput 17(1):165–194Google Scholar
  11. Bouaziz S, Alimi AM, Abraham A (2013) Evolving flexible beta basis function neural tree for nonlinear systems. In: The 2013 international joint conference on neural networks (IJCNN), pp 1–8, Dallas, TexasGoogle Scholar
  12. Bouaziz S, Dhahri H, Alimi AM, Abraham A (2016) Evolving flexible beta basis function neural tree using extended genetic programming & hybrid Artificial Bee Colony. Appl Soft Comput 47:653–668Google Scholar
  13. Boutleux E, Dubuisson B (1996) Fuzzy pattern recognition to characterize evolutionary complex systems. Application to the French telephone network. In: The fifth IEEE international conference on fuzzy systems fuzz-IEEE ‘96, vol 2, pp 780–785Google Scholar
  14. Box GEP, Jenkins GM (1976) Time series analysis forecasting and control. Holden Day, San FranciscozbMATHGoogle Scholar
  15. Chellapilla K (1998) Evolving computer programs without subtree crossover. IEEE Trans Evol Comput 1(3):209–216Google Scholar
  16. Chen Y, Dong J, Yang B (2004) Automatic design of hierarchical TS–FS model using ant programming and PSO algorithm. In: International conference on artificial intelligence: methodology, systems, and applications, pp 285–294. SpringerGoogle Scholar
  17. Chen Y, Yang B, Dong J, Abraham A (2005) Time-series forecasting using flexible neural tree model. Inf Sci 174:219–235MathSciNetGoogle Scholar
  18. Chen Y, Yang B, Dong J (2006) Time-series prediction using a local linear wavelet neural network. Neurocomputing 69(4–6):449–456Google Scholar
  19. Chen Y, Yang B, Abraham A, Peng L (2007) Automatic design of hierarchical Takagi-Sugeno type fuzzy systems using evolutionary algorithms. IEEE Trans Fuzzy Syst 15(3):385–397Google Scholar
  20. Chen YW, Yang JB, Xu DL, Yang SL (2013) On the inference and approximation properties of belief rule based systems. Inf Sci 234:121–135MathSciNetzbMATHGoogle Scholar
  21. Cheong F, Lai R (2007) Designing a hierarchical fuzzy logic controller using the differential evolution approach. Appl Soft Comput 7(2):481–491Google Scholar
  22. Chiu S (1994) Fuzzy model identification based on cluster estimation. J Intell Fuzzy Syst 2(3):267–278Google Scholar
  23. da Silva CG (2008) Time series forecasting with a non-linear model and the scatter search meta-heuristic. Inf Sci 178(16):3288–3299 (Including Special Issue: Recent advances in granular computing) MathSciNetzbMATHGoogle Scholar
  24. Deb K, Agrawal S, Pratap A, Meyarivan T (2002) A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. IEEE Trans Evol Comput 6(2):182–197Google Scholar
  25. Dhahri H, Alimi AM, Abraham A (2012) Designing beta basis function neural network for optimization using Artificial Bee Colony (ABC). In: WCCI 2012 IEEE world congress on computational intelligence, pp. 1–7, Brisbane, AustraliaGoogle Scholar
  26. Dhahri H, Alimi AM, Abraham A (2013) Hierarchical particle swarm optimization for the design of beta basis function neural network. In: Abraham A, Thampi S (eds) Intelligent informatics. Springer, Berlin, pp 193–205Google Scholar
  27. Di Martino F, Loia V, Sessa S (2011) Fuzy transforms method in prediction data analysis. Fuzzy Sets Syst 180(1):146–163zbMATHGoogle Scholar
  28. Eyoh I, John R, De Maere G, Kayacan E (2018) Hybrid learning for interval type-2 intuitionistic fuzzy logic systems as applied to identification and prediction problems. IEEE Trans Fuzzy Syst 26(5):2672–2685Google Scholar
  29. Fernández A, del Jesus MJ, Herrera F (2009) Hierarchical fuzzy rule based classification systems with genetic rule selection for imbalanced data-sets. Int J Approx Reason 50(3):561–577zbMATHGoogle Scholar
  30. Geem ZW, Kim JH, Loganathan GV (2001) A new heuristic optimization algorithm: harmony search. Simulation 76(2):60–68Google Scholar
  31. Hagras H (2004) Hierarchical type-2 fuzzy logic control architecture for autonomous mobile robots. IEEE Trans Fuzzy Syst 12(4):524–539Google Scholar
  32. Huerta EB, Duval B, Hao JK (2008) Gene selection for microarray data by a LDA-based genetic algorithm. In: IAPR international conference on pattern recognition in bioinformatics, pp 250–261, SpringerGoogle Scholar
  33. Hüllermeier E (2005) Fuzzy methods in machine learning and data mining: status and prospects. Fuzzy Set Syst 156(3):387–406MathSciNetGoogle Scholar
  34. Hurrell JW, van Loon H (1997) Decadal variations in climate associated with the North Atlantic Oscillation. Clim Change 36:301–326Google Scholar
  35. Innocent N, Kurian M (2014) Cancer prediction based on gene expression data through association rule based classification and fuzzy rough set attribute reduction on information gain ratio. Int J Res Appl Sci Eng Technol 2(4):42–46Google Scholar
  36. Izeman AJ (1985) J. R. Wolf, the Zurich sunspot relative numbers. Math Intel 7(1):27–33zbMATHGoogle Scholar
  37. Jahromi MZ, Moosavi MR (2011) Designing cost-sensitive fuzzy classification systems using rule-weight. In: The first international conference on advances in information mining and management (IMMM 2011), pp 168–173Google Scholar
  38. Jarraya Y, Bouaziz S, Alimi AM, Abraham A (2013) Fuzzy modeling system based on hybrid evolutionary approach. In: 13th International conference on hybrid intelligent systems (HIS), Yassmine Hamammet, TunisiaGoogle Scholar
  39. Jarraya Y, Bouaziz S, Alimi AM, Abraham A (2014) Multi-agent evolutionary design of beta fuzzy systems. In: The 2014 IEEE international conference on fuzzy systems (FUZZ-IEEE 2014), Beijing, ChinaGoogle Scholar
  40. Jarraya Y, Bouaziz S, Alimi AM, Abraham A (2015) Evolutionary multi-objective optimization for evolving hierarchical fuzzy system. In: 2015 IEEE congress on evolutionary computation (CEC 2015), Sendai, JapanGoogle Scholar
  41. Leite D, Gomide F, Ballini R, Costa P (2011) Fuzzy granular evolving modeling for time series prediction. In: 2011 IEEE international conference on fuzzy systems, Taipei, TaiwanGoogle Scholar
  42. León IC, Taylor PC (2015) Memetic type-2 fuzzy system learning for load forecasting. In: 2015 Conference of the international fuzzy systems association and the European Society for Fuzzy Logic and Technology (IFSA-EUSFLAT-15), Gijon, SpainGoogle Scholar
  43. Liang Q, Mendel JM (1999) An introduction to type-2 TSK fuzzy logic systems. In: Proceedings IEEE international conference on fuzzy systems, vol 3, pp 1534–1539. Seoul, South KoreaGoogle Scholar
  44. Lin LC, Lee GY (1999) Hierarchical fuzzy control for C-axis of CNC tuning centers using genetic algorithms. J Intell Robot Syst 25(3):255–275zbMATHGoogle Scholar
  45. Mackey MC, Glass L (1977) Oscillation and chaos in physiological control systems. Science 197(4300):287–289zbMATHGoogle Scholar
  46. Mahdavi M, Fesanghary M, Damangir E (2007) An improved harmony search algorithm for solving optimization problems. Appl Math Comput 188(2):1567–1579MathSciNetzbMATHGoogle Scholar
  47. Mendel J, John R (2002) Type-2 fuzzy sets made simple. IEEE Trans Fuzzy Syst 10(2):117–127Google Scholar
  48. Musilek P, Lau A, Reformat M, Wyard-scot L (2006) Immune programming. Inf Sci 176(8):972–1002MathSciNetzbMATHGoogle Scholar
  49. Ojha V, Snasel V, Abraham A (2017) Multiobjective programming for type-2 hierarchical fuzzy inference trees. IEEE Trans Fuzzy Syst 26(2):915–936Google Scholar
  50. Pang S, Havukkala I, Hu Y, Kasabov N (2007) Classification consistency analysis for bootstrapping gene selection. Neural Comput Appl 16:527–539Google Scholar
  51. Paul S, Kumar S (2002) Subsethood-product fuzzy neural inference system (SuPFuNIS). IEEE Trans Neural Netw 13(3):578–599Google Scholar
  52. Pohjalainen J, Räsänen O, Kadioglu S (2015) Feature selection methods and their combinations in high-dimensional classification of speaker likability, intelligibility and personality traits. Comput Speech Lang 29:145–171Google Scholar
  53. Raju GVS, Zhou J (1993) Adaptive hierarchical fuzzy controller. IEEE Trans Syst Man Cybern 23(4):973–980Google Scholar
  54. Salgado P (2008) Rule generation for hierarchical collaborative fuzzy system. Appl Math Model 32:1159–1178MathSciNetzbMATHGoogle Scholar
  55. Samanta B (2011) Prediction of chaotic time series using computational intelligence. Expert Syst Appl 38:11406–11411Google Scholar
  56. Shimojima K, Fukuda T, Hasegawa Y (1995) Self-tuning fuzzy modeling with adaptive membership function, rules, and hierarchical structure based on genetic algorithm. Fuzzy Sets Syst 71(3):295–309Google Scholar
  57. Singhala P, Shah DN, Patel B (2014) Temperature control using fuzzy logic. Int J Instrum Control Syst (IJICS) 4(1)Google Scholar
  58. Tanaka K, Sano M (1994) A robust stabilization problem of fuzzy control systems and its application to backing up control of a truck-trailer. IEEE Trans Fuzzy Syst 2:119–134Google Scholar
  59. Tang Y, Zhang YQ, Huang Z, Hu X (2005) Granular SVM-RFE gene selection algorithm for reliable prostate cancer classification on microarray expression data. In: Proceedings of the 5th IEEE symposium on bioinformatics and bioengineering (BIBE’05), pp 290–293Google Scholar
  60. Uslan V, Seker H, John R (2014) A support vector-based interval type-2 fuzzy system. In: IEEE international conference on fuzzy systems, pp 2396–2401, Beijing, ChinaGoogle Scholar
  61. Wadhawan S, Goel G, Kaushik S (2013) Data driven fuzzy modeling for Sugeno and Mamdani type fuzzy model using memetic algorithm. Int J Inf Technol Comput Sci 5(8):24–37Google Scholar
  62. Wang LX, Mendel JM (1992) Generating fuzzy rules by learning from examples. IEEE Trans Syst Man Cybern 22(6):1414–1427MathSciNetGoogle Scholar
  63. Wang Z, Palade V (2011) Building interpretable fuzzy models for high dimensional data analysis in cancer diagnosis. In: BMC genomics, vol 12, no 2, p S5, BioMed CentralGoogle Scholar
  64. Yilmaz S, Oysal Y (2010) Fuzzy wavelet neural network models for prediction and identification of dynamical systems. IEEE Trans Neural Netw 21:1599–1609Google Scholar
  65. Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning. Inf Sci 8(3):199–249MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Research Groups in Intelligent Machines (REGIM-Lab), National School of Engineers (ENIS)University of SfaxSfaxTunisia
  2. 2.Machine Intelligence Research Labs (MIR Labs)AuburnUSA
  3. 3.IT4InnovationsVSB-Technical University of OstravaOstravaCzech Republic

Personalised recommendations