Evolving Systems

, Volume 8, Issue 1, pp 35–47 | Cite as

Intuitionistic neuro-fuzzy network with evolutionary adaptation

Original Paper

Abstract

Intuitionistic fuzzy inference systems (IFISs) incorporate imprecision in the construction of membership functions present in fuzzy inference systems. In this paper we design intuitionistic neuro-fuzzy networks to adapt the antecedent and consequent parameters of IFISs. We also propose a mean of maximum defuzzification method for a class of Takagi–Sugeno IFISs and this method is compared with the basic defuzzification distribution operator. On both real-life credit scoring data and seven benchmark regression datasets we show that the intuitionistic neuro-fuzzy network trained with particle swarm optimization outperforms traditional ANFIS methods (hybrid and backpropagation) and ANFIS trained with evolutionary algorithms (genetic algorithm and particle swarm optimization), respectively. A set of nonparametric tests for multiple datasets is performed to demonstrate statistical differences between the algorithms. In the task of adapting the intuitionistic neuro-fuzzy network, we show that particle swarm optimization provides a higher prediction accuracy compared with traditional algorithms based on gradient descent or least-squares estimation.

Keywords

ANFIS Intuitionistic fuzzy sets Intuitionistic fuzzy inference systems of Takagi–Sugeno type Intuitionistic neuro-fuzzy network Defuzzification method Particle swarm optimization 

References

  1. Akram MS, Habib S, Javed I (2014) Intuitionistic fuzzy logic control for washing machines. Indian J Sci Technol 7(5):654–661Google Scholar
  2. Alcalá-Fdez J, Fernández A, Luengo J, Derrac J, García S, Sánchez L, Herrera F (2011) KEEL data-mining software tool: data set repository, integration of algorithms and experimental analysis framework. J Multiple-Valued Logic Soft Comput 17(2–3):255–287Google Scholar
  3. Angelov P (1995) Crispification: defuzzification over intuitionistic fuzzy sets. BUSEFAL 64:51–55Google Scholar
  4. Angelov P (2001) Multi-objective optimisation in air-conditioning systems: comfort/discomfort definition by IF sets. Notes Intuit Fuzzy Sets 7(1):10–23MathSciNetMATHGoogle Scholar
  5. Angelov P (2012) Evolving fuzzy systems. Computational complexity: theory, techniques, and applications. Springer-Verlag, Berlin, pp 1053–1065CrossRefGoogle Scholar
  6. Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Set Syst 20:87–96MathSciNetCrossRefMATHGoogle Scholar
  7. Atanassov KT (1999) Intuitionistic fuzzy sets. Physica-Verlag, HeidelbergCrossRefMATHGoogle Scholar
  8. Barrenechea E (2009) Generalized Atanassov’s intuitionistic fuzzy index. Construction method. IFSA-EUSFLAT, Lisbon, pp 478–482Google Scholar
  9. Bernardo D, Hagras H, Tsang E (2013) A genetic type-2 fuzzy logic based system for the generation of summarised linguistic predictive models for financial applications. Soft Comput 17(12):2185–2201CrossRefGoogle Scholar
  10. Castillo O, Melin P (2012) Optimization of type-2 fuzzy systems based on bio-inspired methods: a concise review. Inf Sci 205:1–19CrossRefGoogle Scholar
  11. Castillo O, Alanis A, Garcia M, Arias H (2007) An intuitionistic fuzzy system for time series analysis in plant monitoring and diagnosis. Appl Soft Comput 7(4):1227–1233CrossRefGoogle Scholar
  12. Castillo O, Martínez-Marroquín R, Melin P, Valdez F, Soria J (2012) Comparative study of bio-inspired algorithms applied to the optimization of type-1 and type-2 fuzzy controllers for an autonomous mobile robot. Inf Sci 192:19–38CrossRefGoogle Scholar
  13. Chakravarty S, Dash PK (2012) A PSO based integrated functional link net and interval type-2 fuzzy logic system for predicting stock market indices. Appl Soft Comput 12(2):931–941CrossRefGoogle Scholar
  14. Chen LH, Tu CC (2015) Time-validating-based Atanassov’s intuitionistic fuzzy decision-making. IEEE Trans Fuzzy Syst 23(4):743–756MathSciNetCrossRefGoogle Scholar
  15. Chen S, Montgomer J, Bolufé-Röhler A (2015) Measuring the curse of dimensionality and its effects on particle swarm optimization and differential evolution. Appl Intell 42(3):514–526CrossRefGoogle Scholar
  16. Chiu S (1994) Fuzzy model identification based on cluster estimation. J Intell Fuzzy Syst 2:267–278CrossRefGoogle Scholar
  17. Demertzis K, Iliadis L, Avramidis S, El-Kassaby YA (2016) Machine learning use in predicting interior spruce wood density utilizing progeny test information. Neural Comput Appl. doi:10.1007/s00521-015-2075-9 Google Scholar
  18. Deschrijver G, Cornelis C, Kerre E (2004) On the representation of intuitionistic fuzzy t-norm and t-conorm. IEEE T Fuzzy Syst 12:45–61CrossRefGoogle Scholar
  19. Dubois D, Prade H (2005) Interval-valued fuzzy set, possibility theory and imprecise probability. European Society for Fuzzy Logic and Technology, EUSFLAT/LFA, Barcelona, pp 314–319Google Scholar
  20. García S, Fernández A, Luengo J, Herrera F (2010) Advanced nonparametric tests for multiple comparisons in the design of experiments in computational intelligence and data mining: experimental analysis of power. Inf Sci 180(10):2044–2064CrossRefGoogle Scholar
  21. Hagras H, Wagner Ch (2012) Towards the widespread use of type-2 fuzzy logic systems in real world applications. IEEE Comput Intell Mag 7(3):4–24CrossRefGoogle Scholar
  22. Hájek P (2012) Credit rating analysis using adaptive fuzzy rule-based systems: an industry specific approach. Cent Eur J Oper Res 20(3):421–434CrossRefMATHGoogle Scholar
  23. Hájek P, Olej V (2012) Adaptive intuitionistic fuzzy inference systems of Takagi-Sugeno type for regression problems. In: Iliadis LS, Maglogianis I, Papadopoulos H (eds) Artificial intelligence applications and innovations. IFIP advances in information and communication technology, vol 381. Springer, Heidelberg, pp 206–216Google Scholar
  24. Hájek P, Olej V (2013) Evaluating sentiment in annual reports for financial distress prediction using neural networks and support vector machines. In: Iliadis L, Papadopoulos H, Jayne C (eds) Engineering applications of neural networks. Communications in computer and information science, vol 384. Springer, Heidelberg, pp 1–10Google Scholar
  25. Hájek P, Olej V (2014) Defuzzification methods in intuitionistic fuzzy inference systems of Takagi-Sugeno type. The case of corporate bankruptcy prediction. Fuzzy Systems and Knowledge Discovery (FSKD’14), Xiamen, China, pp 240–244Google Scholar
  26. Hall MA (1999) Correlation-based feature selection for machine learning. Dissertation, The University of WaikatoGoogle Scholar
  27. Henzgen S, Strickert M, Hüllermeier E (2014) Visualization of evolving fuzzy rule-based systems. Evol Syst 5(3):175–191CrossRefGoogle Scholar
  28. Huarng K, Yu HK (2005) A type-2 fuzzy time series model for stock index forecasting. Stat Mech Appl 353:445–462CrossRefGoogle Scholar
  29. Jang JSR (1991) Fuzzy modeling using generalized neural networks Kalman filter algorithm. In: Artificial intelligence (AAAI-91), Anaheim, California, pp 762–767Google Scholar
  30. Jang JSR (1993) ANFIS: adaptive-network-based fuzzy inference systems. IEEE Trans Syst Man Cybern 23(3):665–685CrossRefGoogle Scholar
  31. Kaczmarz S (1993) Approximate solution of systems of linear equations. Int J Control 53:1269–1271MathSciNetCrossRefMATHGoogle Scholar
  32. Kasabov N (2015) Evolving connectionist systems: from neuro-fuzzy-, to spiking- and neuro-genetic. Springer handbook of computational intelligence. Springer-Verlag, Heidelberg, pp 771–782CrossRefGoogle Scholar
  33. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: IEEE International Conference on Neural Networks, pp 1942–1948. doi:10.1109/ICNN.1995.488968
  34. Klement EP, Mesiar R, Pap E (2004) Triangular norms. Position paper I: basic analytical and algebraic properties. Fuzzy Set Syst 143:5–26MathSciNetCrossRefMATHGoogle Scholar
  35. Liang Q, Mendel JM (2000) Interval type-2 fuzzy logic systems: theory and design. IEEE Trans Fuzzy Syst 8(5):535–550CrossRefGoogle Scholar
  36. Loganathan C, Girija KV (2013) Hybrid learning for adaptive neuro fuzzy inference system. Int J Eng Sci 2(11):6–13Google Scholar
  37. Loughran T, McDonald B (2011) When is a liability not a liability? Textual analysis, dictionaries, and 10-Ks. J Financ 66(1):35–65CrossRefGoogle Scholar
  38. Maciel L, Lemos A, Gomide F, Ballini R (2012) Evolving fuzzy systems for pricing fixed income options. Evol Syst 3(1):5–18CrossRefGoogle Scholar
  39. Mendel JM (2006) Interval type-2 fuzzy logic systems made simple. IEEE Trans Fuzzy Syst 14(6):808–821CrossRefGoogle Scholar
  40. Olej V, Hájek P (2010) IF-inference systems design for prediction of ozone time series: the case of Pardubice micro-region. In: Diamantaras K, Duch W, Iliadis LS (eds) Artificial neural networks – ICANN 2010. Lecture Notes in Computer Science, vol 6352. Springer, Heidelberg, pp 1–11Google Scholar
  41. Olej V, Hájek P (2011) Comparison of fuzzy operators for IF-inference systems of Takagi-Sugeno type in ozone prediction. In: Iliadis LS, Maglogianis I, Papadopoulos H (eds) Artificial intelligence applications and innovations. IFIP advances in information and communication technology, vol 364. Springer, Heidelberg, pp 92–97Google Scholar
  42. Ramaswamy P, Riese M, Edwards RM, Lee KY (1993) Two approaches for automating the tuning process of fuzzy logic controllers. In: IEEE Conference on Decision and Control, San Antonio, TX, pp 1753–1758Google Scholar
  43. Shi Y, Eberhart RC (1998) A modified particle swarm optimizer. In: IEEE International Conference on Evolutionary Computation, pp 69–73Google Scholar
  44. Simon D (2002) Training fuzzy systems with the extended Kalman filter. Fuzzy Set Syst 132(2):189–199MathSciNetCrossRefMATHGoogle Scholar
  45. Strohmer T, Vershynin R (2007) A randomized Kaczmarz algorithm with exponential convergence. J Fourier Anal Appl 15(2):262–278MathSciNetCrossRefMATHGoogle Scholar
  46. Wang J, Wang D (2008) Particle swarm optimization with a leader and followers. Progress Nat Sci 18(11):1437–1443CrossRefGoogle Scholar
  47. Wang L, Ye J (1998) Extracting fuzzy rules for system modeling using a hybrid of genetic algorithms and Kalman filter. Fuzzy Set Syst 101:353–362MathSciNetCrossRefGoogle Scholar
  48. Zarandi F, Rezaee B, Turksen IB, Neshat E (2009) A type-2 fuzzy rules-based expert system model for stock price analysis. Expert Syst Appl 36:139–154CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Faculty of Economics and Administration, Institute of System Engineering and InformaticsUniversity of PardubicePardubiceCzech Republic

Personalised recommendations