Skip to main content
SpringerLink
Log in
Book cover

International Conference on Artificial Intelligence and Soft Computing

ICAISC 2015: Artificial Intelligence and Soft Computing pp 448–468Cite as

A New Interpretability Criteria for Neuro-Fuzzy Systems for Nonlinear Classification

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9119))

Abstract

In this paper a new approach for construction of neuro-fuzzy systems for nonlinear classification is introduced. In particular, we concentrate on the flexible neuro-fuzzy systems which allow us to extend notation of rules with weights of fuzzy sets. The proposed approach uses possibilities of hybrid evolutionary algorithm and interpretability criteria of expert knowledge. These criteria include not only complexity of the system, but also semantics of the rules. The approach presented in our paper was tested on typical nonlinear classification simulation problems.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alonso, J.M.: Embedding HILK in a three-objective evolutionary algorithm with the aim of modeling highly interpretable fuzzy rule-based classifiers, pp. 15–20. European Centre for Soft Computing (2010)

    Google Scholar 

  2. Alonso, J.M., Cordon, O., Quirin, A., Magdalena, L.: Analyzing interpretability of fuzzy rule-based systems by means of fuzzy inference-grams. In: 1st World Conference on Soft Computing, pp. 181.1–181.8 (2011)

    Google Scholar 

  3. Alonso, J.M., Magdalena, L., Guillaume, S.: HILK: A new methodology for designing highly interpretable linguistic knowledge bases using the fuzzy logic formalism. International Journal of Intelligent Systems 23(7), 761–794 (2008)

    Google Scholar 

  4. Aziz, D., Ali, M.A.M., Gan, K.B., Saiboon, I.: Initialization of Adaptive Neuro-Fuzzy Inference System Using Fuzzy Clustering in Predicting Primary Triage Category. In: 2012 4th International Conference on Intelligent and Advanced Systems (ICIAS), pp. 170–174. Dept. of Electr., Electron. & Syst. Eng., Univ. Kebangsaan (2012)

    Google Scholar 

  5. Bartczuk, Ł., Dziwiński, P., Starczewski, J.T.: New method for generation type-2 fuzzy partition for FDT. In: Rutkowski, L., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2010, Part I. LNCS (LNAI), vol. 6113, pp. 275–280. Springer, Heidelberg (2010)

    Google Scholar 

  6. Bartczuk, Ł., Dziwiński, P., Starczewski, J.T.: A new method for dealing with unbalanced linguistic term set. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2012, Part I. LNCS, vol. 7267, pp. 207–212. Springer, Heidelberg (2012)

    Google Scholar 

  7. Bilski, J.: Momentum modification of the RLS algorithms. In: Rutkowski, L., Siekmann, J.H., Tadeusiewicz, R., Zadeh, L.A. (eds.) ICAISC 2004. LNCS (LNAI), vol. 3070, pp. 151–157. Springer, Heidelberg (2004)

    Google Scholar 

  8. Bilski, J., Rutkowski, L.: Numerically robust learning algorithms for feed forward neural networks. Advances in Soft Computing, pp. 149–154 (2003)

    Google Scholar 

  9. Bilski, J., Smoląg, J.: Parallel realisation of the recurrent RTRN neural network learning. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2008. LNCS (LNAI), vol. 5097, pp. 11–16. Springer, Heidelberg (2008)

    Google Scholar 

  10. Bilski, J., Smoląg, J.: Parallel Realisation of the Recurrent Elman Neural Network Learning. In: Rutkowski, L., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2010, Part II. LNCS (LNAI), vol. 6114, pp. 19–25. Springer, Heidelberg (2010)

    Google Scholar 

  11. Bilski, J., Smoląg, J.: Parallel Realisation of the Recurrent Multi Layer Perceptron Learning. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2012, Part I. LNCS (LNAI), vol. 7267, pp. 12–20. Springer, Heidelberg (2012)

    Google Scholar 

  12. Bilski, J., Smoląg, J.: Parallel approach to learning of the recurrent jordan neural network. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2013, Part I. LNCS (LNAI), vol. 7894, pp. 32–40. Springer, Heidelberg (2013)

    Google Scholar 

  13. Bilski, J., Smoląg, J.: Parallel architectures for learning the RTRN and Elman dynamic neural networks. IEEE Trans. Parallel and Distributed Systems PP(99) (2014)

    Google Scholar 

  14. Bilski, J., Smoląg, J., Galushkin, A.I.: The Parallel Approach to the Conjugate Gradient Learning Algorithm for the Feedforward Neural Networks. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2014, Part I. LNCS (LNAI), vol. 8467, pp. 12–21. Springer, Heidelberg (2014)

    Google Scholar 

  15. Bilski, J., Litwiński, S., Smoląg, J.: Parallel realisation of QR algorithm for neural networks learning. In: Rutkowski, L., Siekmann, J.H., Tadeusiewicz, R., Zadeh, L.A. (eds.) ICAISC 2004. LNCS (LNAI), vol. 3070, pp. 158–165. Springer, Heidelberg (2004)

    Google Scholar 

  16. Bartczuk, Ł., Przybył, A., Koprinkova-Hristova, P.: New method for nonlinear fuzzy correction modelling of dynamic objects. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2014, Part I. LNCS (LNAI), vol. 8467, pp. 169–180. Springer, Heidelberg (2014)

    Google Scholar 

  17. Bostanci, B., Bostanci, E.: An Evaluation of Classification Algorithms Using Mc Nemar’s Test. In: Bansal, J.C., Singh, P.K., Deep, K., Pant, M., Nagar, A.K. (eds.) Proceedings of Seventh International Conference on Bio-Inspired Computing: Theories and Applications (BIC-TA 2012). AISC, vol. 201, pp. 15–26. Springer, India (2013)

    Google Scholar 

  18. Chen, J.L., Hou, Y.L., Xing, Z.Y., Jia, L.M., Tong, Z.Z.: A Multi-objective Genetic-based Method for Design Fuzzy Classification Systems. IJCSNS International Journal of Computer Science and Network Security 6(8), 110–117 (2006)

    Google Scholar 

  19. Cpałka, K., Łapa, K., Przybył, A., Zalasiński, M., Rutkowski, L.: A new method for designing neuro-fuzzy systems for nonlinear modelling with interpretability aspects. Neurocomputing 135, 203–217 (2014)

    Google Scholar 

  20. Cpałka, K.: A New Method for Design and Reduction of Neuro-Fuzzy Classification Systems. IEEE Transactions on Neural Networks 20, 701–714 (2009)

    Google Scholar 

  21. Cpałka, K.: On evolutionary designing and learning of flexible neuro-fuzzy structures for nonlinear classification. Nonlinear Analysis Series A: Theory, Methods and Applications 71, 1659–1672 (2009)

    Google Scholar 

  22. Cpałka, K., Zalasiński, M.: On-line signature verification using vertical signature partitioning. Expert Systems with Applications 41, 4170–4180 (2014)

    Google Scholar 

  23. Cpałka, K., Zalasiński, M., Rutkowski, L.: New method for the on-line signature verification based on horizontal partitioning. Pattern Recognition 47, 2652–2661 (2014)

    Google Scholar 

  24. Dziwiński, P., Bartczuk, Ł., Starczewski, J.T.: Fully controllable ant colony system for text data clustering. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) SIDE 2012 and EC 2012. LNCS, vol. 7269, pp. 199–205. Springer, Heidelberg (2012)

    Google Scholar 

  25. Dziwiński, P., Starczewski, J.T., Bartczuk, Ł.: New linguistic hedges in construction of interval type-2 FLS. In: Rutkowski, L., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2010, Part II. LNCS (LNAI), vol. 6114, pp. 445–450. Springer, Heidelberg (2010)

    Google Scholar 

  26. Dziwiński, P., Bartczuk, Ł., Przybył, A., Avedyan, E.D.: A New Algorithm for Identification of Significant Operating Points Using Swarm Intelligence. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2014, Part II. LNCS (LNAI), vol. 8468, pp. 349–362. Springer, Heidelberg (2014)

    Google Scholar 

  27. El-Abd, M.: On the hybridization on the artificial bee colony and particle swarm optimization algorithms. Journal of Artificial Intelligence and Soft Computing Research 2(2), 147–155 (2012)

    MathSciNet  Google Scholar 

  28. Fazzolari, M., Alcalá, R., Herrera, F.: A multi-objective evolutionary method for learning granularities based on fuzzy discretization to improve the accuracy-complexity trade-off of fuzzy rule-based classification systems: D-MOFARC algorithm. Applied Soft Computing 24, 470–481 (2014)

    Google Scholar 

  29. Gabryel, M., Cpałka, K., Rutkowski, L.: Evolutionary strategies for learning of neuro-fuzzy systems. In: Proceedings of the I Workshop on Genetic Fuzzy Systems, Granada, pp. 119–123 (2005)

    Google Scholar 

  30. Gacto, M.J., Alcalá, R., Herrera, F.: Interpretability of linguistic fuzzy rule-based systems: An overview of interpretability measures. Information Sciences 181, 4340–4360 (2011)

    Google Scholar 

  31. Gacto, M.J., Alcalá, R., Herrera, F.: A Multiobjective Evolutionary Algorithm for Tuning Fuzzy Rule Based Systems with Measures for Preserving Interpretability. In: Proc. of the Joint International Fuzzy Systems Association World Congress and the European Society for Fuzzy Logic and Technology Conference (IFSA/EUSFLAT 2009) (2009)

    Google Scholar 

  32. Gałkowski, T.: Kernel estimation of regression functions in the boundary regions. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2013, Part II. LNCS (LNAI), vol. 7895, pp. 158–166. Springer, Heidelberg (2013)

    Google Scholar 

  33. Galkowski, T., Pawlak, M.: Nonparametric function fitting in the presence of nonstationary noise. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2014, Part I. LNCS (LNAI), vol. 8467, pp. 531–538. Springer, Heidelberg (2014)

    Google Scholar 

  34. Galkowski, T., Rutkowski, L.: Nonparametric fitting of multivariate functions. IEEE Trans. Automatic Control AC-31(8), 785–787 (1986)

    Google Scholar 

  35. Gao, M., Hong, X., Harris, C.J.: Construction of Neurofuzzy Models For Imbalanced Data Classification. IEEE Transactions on Fuzzy Systems 22(6), 1472–1488 (2014)

    Google Scholar 

  36. Ghandar, A., Michalewicz, Z.: An experimental study of Multi-Objective Evolutionary Algorithms for balancing interpretability and accuracy in fuzzy rule base classifiers for financial prediction. In: 2011 IEEE Symposium on Computational Intelligence for Financial Engineering and Economics, pp. 1–6 (2011)

    Google Scholar 

  37. Gorzałczany, M.B., Rudziński, F.: Accuracy vs. interpretability of fuzzy rule-based classifiers: An evolutionary approach. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) EC 2012 and SIDE 2012. LNCS, vol. 7269, pp. 222–230. Springer, Heidelberg (2012)

    Google Scholar 

  38. Grycuk, R., Gabryel, M., Korytkowski, M., Scherer, R., Voloshynovskiy, S.: From single image to list of objects based on edge and blob detection. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2014, Part II. LNCS (LNAI), vol. 8468, pp. 605–615. Springer, Heidelberg (2014)

    Google Scholar 

  39. Guillaume, S., Charnomordic, B.: Generating an Interpretable Family of Fuzzy Partitions From Data. IEEE Transactions on Fuzzy Systems 12(3), 324–335 (2004)

    Google Scholar 

  40. Hossen, J., Sayeed, S., Yusof, I., Kalaiarasi, S.M.A.: A Framework of Modified Adaptive Fuzzy Inference Engine (MAFIE) and Its Application. International Journal of Computer Information Systems and Industrial Management Applications 5, 662–670 (2013)

    Google Scholar 

  41. Icke, I., Rosenberg, A.: Multi-objective Genetic Programming for Visual Analytics. In: Silva, S., Foster, J.A., Nicolau, M., Machado, P., Giacobini, M. (eds.) EuroGP 2011. LNCS, vol. 6621, pp. 322–334. Springer, Heidelberg (2011)

    Google Scholar 

  42. Ishibuchi, H., Nakashima, T.: Effect of the rule weights in fuzzy rule-based classification systems. IEEE Trans. Fuzzy Syst. 9, 506–515 (2001)

    Google Scholar 

  43. Jensen, R., Cornelis, C.: Fuzzy-Rough Nearest Neighbour Classification. In: Peters, J.F., Skowron, A., Chan, C.-C., Grzymala-Busse, J.W., Ziarko, W.P. (eds.) Transactions on Rough Sets XIII. LNCS, vol. 6499, pp. 56–72. Springer, Heidelberg (2011)

    Google Scholar 

  44. Kalaiselvi, C., Nasira, G.M.: A Novel Approach for the Diagnosis of Diabetes and Liver Cancer using ANFIS and Improved KNN. Research Journal of Applied Sciences, Engineering and Technology 8(2), 243–250 (2014)

    Google Scholar 

  45. Kaur, G.: Similarity measure of different types of fuzzy sets. School of Mathematics and Computer Applications, Tharpar University (2010)

    Google Scholar 

  46. Kenesei, T., Abonyi, J.: Interpetable Support Vector Machines in Regression and Classification - Application In Process Engineering. Hungarian Journal of Industrial Chemistry, Veszprém 35, 101–108 (2007)

    Google Scholar 

  47. Korytkowski, M., Nowicki, R., Rutkowski, L., Scherer, R.: AdaBoost Ensemble of DCOG Rough–Neuro–Fuzzy Systems. In: Jędrzejowicz, P., Nguyen, N.T., Hoang, K. (eds.) ICCCI 2011, Part I. LNCS, vol. 6922, pp. 62–71. Springer, Heidelberg (2011)

    Google Scholar 

  48. Korytkowski, M., Nowicki, R., Scherer, R.: Neuro-fuzzy rough classifier ensemble. In: Alippi, C., Polycarpou, M., Panayiotou, C., Ellinas, G. (eds.) ICANN 2009, Part I. LNCS, vol. 5768, pp. 817–823. Springer, Heidelberg (2009)

    Google Scholar 

  49. Kumar, G., Rani, P., Devaraj, C., Victoire, D.: Hybrid Ant Bee Algorithm for Fuzzy Expert System Based Sample Classification. IEEE/ACM Transactions on Computational Biology and Bioinformatics 11(2), 347–360 (2014)

    Google Scholar 

  50. Laskowski, Ł., Laskowska, M.: Functionalization of SBA-15 mesoporous silica by Cu-phosphonate units: Probing of synthesis route. Journal of Solid State Chemistry 220, 221–226 (2014)

    Google Scholar 

  51. Laskowski, Ł., Laskowska, M., Jelonkiewicz, J., Boullanger, A.: Spin-glass implementation of a Hopfield neural structure. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2014, Part I. LNCS (LNAI), vol. 8467, pp. 89–96. Springer, Heidelberg (2014)

    Google Scholar 

  52. Łapa, K., Zalasiński, M., Cpałka, K.: A new method for designing and complexity reduction of neuro-fuzzy systems for nonlinear modelling. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2013, Part I. LNCS (LNAI), vol. 7894, pp. 329–344. Springer, Heidelberg (2013)

    Google Scholar 

  53. Lobato, F.S., Steffen Jr., V.: A new multi-objective optimization algorithm based on differential evolution and neighborhood exploring evolution strategy. Journal of Artificial Intelligence and Soft Computing Research 1(4), 259–267 (2011)

    Google Scholar 

  54. Lobato, F.S., Steffen Jr., V., Silva Neto, A.J.: Solution of singular optimal control problems using the improved differential evolution algorithm. Journal of Artificial Intelligence and Soft Computing Research 1(3), 195–206 (2011)

    Google Scholar 

  55. Luukka, P.: A New Nonlinear Fuzzy Robust PCA Algorithm and Similarity Classifier in Classification of Medical Data Sets. International Journal of Fuzzy Systems 13(3), 153–163 (2011)

    Google Scholar 

  56. Machine Learning Repository [Online], https://archive.ics.uci.edu/ml/datasets.html (accessed: December 16, 2014)

  57. Marquez, A.A., Marquez, F.A., Peregrin, A.: A multi-objective evolutionary algorithm with an interpretability improvement mechanism for linguistic fuzzy systems with adaptive defuzzification. In: 2010 IEEE International Conference on Fuzzy Systems (FUZZ), pp. 1–7 (2010)

    Google Scholar 

  58. Michalewicz, Z.: Genetic Algorithms + Data Structures = Evolution Programs. Springer (1999)

    Google Scholar 

  59. Nauck, D., Kruse, R.: How the Learning of the RuleWeight Affects the Interpretability of the Fuzzy Systems. In: Proceedings of 1998 IEEE International Conference on Fuzzy Systems, vol. 2, pp. 1235–1240 (1998)

    Google Scholar 

  60. Nouri, J.D., Abadeh, S.M., Mohammadi, G.F.: HYEI: A New Hybrid Evolutionary Imperialist Competitive Algorithm for Fuzzy Knowledge Discovery. Advances in Fuzzy Systems 2014, 1–9 (2014)

    Google Scholar 

  61. Nowicki, R., Rutkowski, L., Scherer, R.: A method for learning of hierarchical fuzzy systems. In: Intelligent Technologies - Theory and Applications, pp. 124–129 (2002)

    Google Scholar 

  62. Pławiak, P., Tadeusiewicz, R.: Approximation of phenol concentration using novel hybrid computational intelligence methods. Applied Mathematics and Computer Science 24(1) (2014)

    Google Scholar 

  63. Paiva, R.P., Dourado, A.: Interpretability and learning in neuro-fuzzy systems. Fuzzy Sets and Systems 147, 17–38 (2004)

    MathSciNet  Google Scholar 

  64. Pham, D.T., Ghanbarzadeh, A., Koc, E., Otri, S., Rahim, S., Zaidi, M.: The Bees Algorithm, A Novel Tool for Complex Optimisation Problems. In: Proceedings of the 2nd International Virtual Conference on Intelligent Production Machines and Systems, pp. 454–459 (2006)

    Google Scholar 

  65. Pouyan, B.M., Yousefi, R., Ostadabbas, S., Nourani, M.: A Hybrid Fuzzy-Firefly Approach for Rule-Based Classification. In: The Twenty-Seventh International Flairs Conference (2014)

    Google Scholar 

  66. Prampero, P.S., Attux, R.: Magnetic particle swarm optimization. Journal of Artificial Intelligence and Soft Computing Research 2(1), 59–72 (2012)

    Google Scholar 

  67. Przybył, A., Er, M.J.: The idea for the integration of neuro-fuzzy hardware emulators with real-time network. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2014, Part I. LNCS (LNAI), vol. 8467, pp. 279–294. Springer, Heidelberg (2014)

    Google Scholar 

  68. Przybył, A., Jelonkiewicz, J.: Genetic algorithm for observer parameters tuning in sensorless induction motor drive. In: Neural Networks and Soft Computing, pp. 376–381 (2003)

    Google Scholar 

  69. Przybył, A., Smoląg, J., Kimla, P.: Distributed control system based on real time ethernet for computer numerical controlled machine tool (in Polish). Przegląd Elektrotechniczny 86(2), 342–346 (2010)

    Google Scholar 

  70. Qu, Y., Shang, C., Shen, Q., Parthalain, M., Wei, W.N.: Kernel-based fuzzy-rough nearest neighbour classification. In: 2011 IEEE International Conference on Fuzzy Systems (FUZZ), pp. 1523–1529 (2011)

    Google Scholar 

  71. Rey, M.I., Galende, M., Sainz, G.I., Fuente, M.J.: Checking orthogonal transformations and genetic algorithms for selection of fuzzy rules based on interpretability-accuracy concepts. In: 2011 IEEE International Conference on Fuzzy Systems, pp. 1271–1278 (2011)

    Google Scholar 

  72. Riid, A., Rustern, E.: Interpretability improvement of fuzzy systems: Reducing the number of unique singletons in zeroth order Takagi-Sugeno systems. In: 2010 IEEE International Conference on Fuzzy Systems (FUZZ), pp. 1–6 (2010)

    Google Scholar 

  73. Riid, A., Rüstern, E.: Interpretability, Interpolation and Rule Weights in Linguistic Fuzzy Modeling. In: Fanelli, A.M., Pedrycz, W., Petrosino, A. (eds.) WILF 2011. LNCS (LNAI), vol. 6857, pp. 91–98. Springer, Heidelberg (2011)

    Google Scholar 

  74. Rini, D.P., Shamsuddin, S.M., Yuhaniz, S.S.: Balanced the Trade-offs Problem of ANFIS using Particle Swarm Optimization. Telkomnika 11(3), 611–616 (2013)

    Google Scholar 

  75. Rutkowski, L.: On Bayes risk consistent pattern-recognition procedures in a quasi-stationary environment. IEEE Trans. Pattern Analysis and Machine Intelligence 4(1), 84–87 (1982)

    MathSciNet  Google Scholar 

  76. Rutkowski, L.: Online Identification of Time-Varying Systems by Nonparametric Techniques. IEEE Trans. Automatic Control 27(1), 228–230 (1982)

    MathSciNet  Google Scholar 

  77. Rutkowski, L.: On nonparametric identification with prediction of time-varying systems. IEEE Trans. Automatic Control 29(1), 58–60 (1984)

    MathSciNet  Google Scholar 

  78. Rutkowski, L.: Computational Intelligence. Springer (2008)

    Google Scholar 

  79. Rutkowski, L., Cpałka, K.: Flexible structures of neuro-fuzzy systems. In: Sincak, P., Vascak, J. (eds.) Quo Vadis Computational Intelligence. STUDFUZZ, vol. 54, pp. 479–484. Springer, Heidelberg (2000)

    Google Scholar 

  80. Rutkowski, L., Cpałka, K.: Compromise approach to neuro-fuzzy systems. In: Sincak, P., Vascak, J., Kvasnicka, V., Pospichal, J. (eds.) Intelligent Technologies - Theory and Applications, vol. 76, pp. 85–90. IOS Press (2002)

    Google Scholar 

  81. Rutkowski, L., Jaworski, M., Pietruczuk, L., Duda, P.: Decision Trees for Mining Data Streams Based on the Gaussian Approximation. IEEE Transactions on Knowledge and Data Engineering 26, 108–119 (2014)

    Google Scholar 

  82. Rutkowski, L., Jaworski, M., Pietruczuk, L., Duda, P.: The CART decision tree for mining data streams. Information Sciences 266, 1–15 (2014)

    Google Scholar 

  83. Rutkowski, L., Przybył, A., Cpałka, K., Er, M.J.: Online speed profile generation for industrial machine tool based on neuro-fuzzy approach. In: Rutkowski, L., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2010, Part II. LNCS (LNAI), vol. 6114, pp. 645–650. Springer, Heidelberg (2010)

    Google Scholar 

  84. Rutkowski, L., Rafajłowicz, E.: On optimal global rate of convergence of some nonparametric identification procedures. IEEE Trans. Automatic Control 34(10), 1089–1091 (1989)

    Google Scholar 

  85. Sánchez, G., Jiménez, F., Sánchez, J.F., Alcaraz, J.M.: A Multi-objective Neuro-evolutionary Algorithm to Obtain Interpretable Fuzzy Models. In: Meseguer, P., Mandow, L., Gasca, R.M. (eds.) CAEPIA 2009. LNCS, vol. 5988, pp. 51–60. Springer, Heidelberg (2010)

    Google Scholar 

  86. Shukla, P.K., Tripathi, S.P.: A Review on the Interpretability-Accuracy Trade-Off in Evolutionary Multi-Objective Fuzzy Systems (EMOFS). Information 3, 256–277 (2012)

    Google Scholar 

  87. Shukla, P.K., Tripathi, S.P.: A new approach for tuning interval type-2 fuzzy knowledge bases using genetic algorithms. Journal of Uncertainty Analysis and Applications 2, 4 (2014)

    Google Scholar 

  88. Shukla, P.K., Tripathi, S.P.: Handling High Dimensionality and Interpretability-Accuracy Trade-Off Issues in Evolutionary Multiobjective Fuzzy Classifiers. International Journal of Scientific & Engineering Research 5(6) (2014)

    Google Scholar 

  89. Siminski, K.: Rule Weights in a Neuro-Fuzzy System with a Hierarchical Domain Partition. Int. J. Appl. Math. Comput. Sci. 20(2), 337–347 (2010)

    Google Scholar 

  90. Sood, A., Aggarwal, S.: Crossroads in Classification: Comparison and Analysis of Fuzzy and Neuro-Fuzzy Techniques. International Journal of Computer Applications (0975-8887) 24(2), 13–17 (2011)

    Google Scholar 

  91. Starczewski, J., Rutkowski, L.: Connectionist structures of type 2 Fuzzy Inference Systems. In: Wyrzykowski, R., Dongarra, J., Paprzycki, M., Waśniewski, J. (eds.) PPAM 2001. LNCS, vol. 2328, pp. 634–642. Springer, Heidelberg (2002)

    Google Scholar 

  92. Starczewski, J., Rutkowski, L.: Interval type 2 neuro-fuzzy systems based on interval consequents. Advances in Soft Computing, pp. 570–577 (2003)

    Google Scholar 

  93. Starczewski, J.T., Bartczuk, Ł., Dziwiński, P., Marvuglia, A.: Learning methods for type-2 FLS based on FCM. In: Rutkowski, L., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2010, Part I. LNCS (LNAI), vol. 6113, pp. 224–231. Springer, Heidelberg (2010)

    Google Scholar 

  94. Szarek, A., Korytkowski, M., Rutkowski, L., Scherer, R., Szyprowski, J.: Application of neural networks in assessing changes around implant after total hip arthroplasty. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2012, Part II. LNCS (LNAI), vol. 7268, pp. 335–340. Springer, Heidelberg (2012)

    Google Scholar 

  95. Szarek, A., Korytkowski, M., Rutkowski, L., Scherer, R., Szyprowski, J.: Forecasting wear of head and acetabulum in hip joint implant. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2012, Part II. LNCS (LNAI), vol. 7268, pp. 341–346. Springer, Heidelberg (2012)

    Google Scholar 

  96. Szczypta, J., Przybył, A., Cpałka, K.: Some aspects of evolutionary designing optimal controllers. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2013, Part II. LNCS (LNAI), vol. 7895, pp. 91–100. Springer, Heidelberg (2013)

    Google Scholar 

  97. Szczypta, J., Przybył, A., Wang, L.: Evolutionary approach with multiple quality criteria for controller design. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2014, Part I. LNCS (LNAI), vol. 8467, pp. 455–467. Springer, Heidelberg (2014)

    Google Scholar 

  98. Tadeusiewicz, R., Chaki, R., Chaki, N.: Exploring Neural Networks with C#. CRC Press, Taylor & Francis Group, Boca Raton (2014)

    Google Scholar 

  99. Troiano, L., Ranilla, J., Díaz, I.: Interpretability of Fuzzy Association Rules as means of Discovering Threaths to Privacy (CMMSE 2010). International Journal of Computer Mathematics, 325–333 (2011)

    Google Scholar 

  100. Wang, H., Kwong, S., Jin, Y., Wei, W., Man, K.F.: Multi-objective hierarchical genetic algorithm for interpretable fuzzy rule-based knowledge extraction. Fuzzy Sets and Systems 149(1), 149–186 (2005)

    MathSciNet  Google Scholar 

  101. Woźniak, M., Kempa, W.M., Gabryel, M., Nowicki, R.: A finite-buffer queue with single vacation policy-analytical study with evolutionary positioning. Int. Journal of Applied Mathematics and Computer Science 24, 887–900 (2014)

    Google Scholar 

  102. Yang, Z., Wang, Y., Ouyang, G.: Adaptive Neuro-Fuzzy Inference System for Classification of Background EEG Signals from ESES Patients and Controls. The Scientific World Journal 2014, 1–8 (2014)

    Google Scholar 

  103. Zalasiński, M., Cpałka, K.: A new method of on-line signature verification using a flexible fuzzy one-class classifier, pp. 38–53. Academic Publishing House EXIT (2011)

    Google Scholar 

  104. Zalasiński, M., Łapa, K., Cpałka, K.: New Algorithm for Evolutionary Selection of the Dynamic Signature Global Features. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2013, Part II. LNCS (LNAI), vol. 7895, pp. 113–121. Springer, Heidelberg (2013)

    Google Scholar 

  105. Zalasiński, M., Cpałka, K.: Novel algorithm for the on-line signature verification. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2012, Part II. LNCS (LNAI), vol. 7268, pp. 362–367. Springer, Heidelberg (2012)

    Google Scholar 

  106. Zalasiński, M., Cpałka, K.: New approach for the on-line signature verification based on method of horizontal partitioning. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2013, Part II. LNCS (LNAI), vol. 7895, pp. 342–350. Springer, Heidelberg (2013)

    Google Scholar 

  107. Zalasiński, M., Cpałka, K.: Novel Algorithm for the On-Line Signature Verification Using Selected Discretization Points Groups. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2013, Part I. LNCS (LNAI), vol. 7894, pp. 493–502. Springer, Heidelberg (2013)

    Google Scholar 

  108. Zalasiński, M., Cpałka, K., Er, M.J.: New Method for Dynamic Signature Verification Using Hybrid Partitioning. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2014, Part II. LNCS (LNAI), vol. 8468, pp. 216–230. Springer, Heidelberg (2014)

    Google Scholar 

  109. Zalasiński, M., Cpałka, K., Hayashi, Y.: New Method for Dynamic Signature Verification Based on Global Features. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2014, Part II. LNCS (LNAI), vol. 8468, pp. 231–245. Springer, Heidelberg (2014)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Computational Intelligence, Częstochowa University of Technology, Częstochowa, Poland

    Krystian Łapa & Krzysztof Cpałka

  2. Moscow Institute of Physics and Technology, Moscow Oblast, Russia

    Alexander I. Galushkin

Authors
  1. Krystian Łapa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Krzysztof Cpałka
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Alexander I. Galushkin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Krystian Łapa .

Editor information

Editors and Affiliations

  1. Częstochowa University of Technology, Częstochowa, Poland

    Leszek Rutkowski

  2. Częstochowa University of Technology, Częstochowa, Poland

    Marcin Korytkowski

  3. Częstochowa University of Technology, Częstochowa, Poland

    Rafal Scherer

  4. AGH University of Science and Technology, Krakow, Poland

    Ryszard Tadeusiewicz

  5. University of California, Berkeley, California, USA

    Lotfi A. Zadeh

  6. University of Louisville, Louisville, Kentucky, USA

    Jacek M. Zurada

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Łapa, K., Cpałka, K., Galushkin, A.I. (2015). A New Interpretability Criteria for Neuro-Fuzzy Systems for Nonlinear Classification. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L., Zurada, J. (eds) Artificial Intelligence and Soft Computing. ICAISC 2015. Lecture Notes in Computer Science(), vol 9119. Springer, Cham. https://doi.org/10.1007/978-3-319-19324-3_41

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-19324-3_41

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19323-6

  • Online ISBN: 978-3-319-19324-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation