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A Historical Review of Mamdani-Type Genetic Fuzzy Systems

  • Oscar Cordón
Chapter
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 271)

Abstract

The need for trading off interpretability and accuracy is intrinsic to the use of fuzzy systems. The fuzzy modeling scientific community has proposed many different design techniques dealing with the interpretability-accuracy tradeoff. In particular, the use of genetic fuzzy systems has been widely extended thanks to their inherent flexibility and their capability to jointly consider different optimization criteria. The current contribution constitutes a brief review on some of the existing genetic fuzzy system approaches relying on Mamdani-type fuzzy rule-based systems to obtain interpretable linguistic fuzzy models with a good accuracy.

Keywords

Membership Function Fuzzy System Fuzzy Rule Fuzzy Logic Controller Fuzzy Partition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Alcalá, R., Alcalá- Fdez, J., Casillas, J., Cordón, O., Herrera, F.: Hybrid learning models to get the interpretability-accuracy trade-off in fuzzy modelling. Soft Computing 10(9), 717–734 (2006)CrossRefGoogle Scholar
  2. 2.
    Alcalá, R., Alcalá-Fdez, J., Gacto, M.J., Herrera, F.: Rule base reduction and genetic tuning of fuzzy systems based on the linguistic 3-tuples representation. Soft Computing 11(5), 401–419 (2007)CrossRefGoogle Scholar
  3. 3.
    Alcalá, R., Alcalá-Fdez, J., Herrera, F.: A proposal for the genetic lateral tuning of linguistic fuzzy systems and its interaction with rule selection. IEEE Transactions on Fuzzy Systems 15(4), 616–635 (2007)CrossRefGoogle Scholar
  4. 4.
    Alcalá, R., Alcalá-Fdez, J., Herrera, F., Otero, J.: Genetic learning of accurate and compact fuzzy rule based systems based on the 2-tuples linguistic representation. International Journal of Approximate Reasoning 44(1), 45–64 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Alcalá, R., Cano, J.R., Cordón, O., Herrera, F., Villar, P.: Linguistic modeling with hierarchical systems of weighted linguistic rules. International Journal of Approximate Reasoning 32(2-3), 187–215 (2003)CrossRefzbMATHGoogle Scholar
  6. 6.
    Alcalá, R., Casillas, J., Cordón, O., González, A., Herrera, F.: A genetic rule weighting and selection process for fuzzy control of heating, ventilating and air conditioning systems. Engineering Applications of Artificial Intelligence 18(3), 279–296 (2005)CrossRefGoogle Scholar
  7. 7.
    Alcalá, R., Casillas, J., Cordón, O., Herrera, F.: Applying rule weight derivation to obtain cooperative rules. In: Benítez, J.M., Cordón, O., Hoffmann, F., Roy, R. (eds.) Advances in soft Computing. Engineering Design and Manufacturing, pp. 139–147. Springer, Heidelberg (2003)Google Scholar
  8. 8.
    Alcalá, R., Casillas, J., Cordón, O., Herrera, F.: Linguistic modeling with weighted double-consequent fuzzy rules based on cooperative coevolutionary learning. Integrated Computer Aided Engineering 10(4), 343–355 (2003)Google Scholar
  9. 9.
    Alcalá, R., Ducange, P., Herrera, F., Lazzerini, B., Marcelloni, F.: A multi-objective evolutionary approach to concurrently learn rule and data bases of linguistic fuzzy rule-based systems. IEEE Transactions on Fuzzy Systems 17(5), 1106–1122 (2009)CrossRefGoogle Scholar
  10. 10.
    Alcalá, R., Gacto, M.J., Herrera, F., Alcalá-Fdez, J.: A multi-objective genetic algorithm for tuning and rule selection to obtain accurate and compact linguistic fuzzy rule-based systems. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 15(5), 45–64 (2007)CrossRefGoogle Scholar
  11. 11.
    Alonso, J.M., Magdalena, L., González-Rodríguez, G.: Looking for a good fuzzy system interpretability index: An experimental approach. International Journal of Approximate Reasoning 51(1), 115–134 (2009)CrossRefMathSciNetGoogle Scholar
  12. 12.
    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)CrossRefzbMATHGoogle Scholar
  13. 13.
    Antonelli, M., Ducange, P., Lazzerini, B., Marcelloni, F.: Learning concurrently partition granularities and rule bases of Mamdani fuzzy systems in a multi-objective evolutionary framework. International Journal of Approximate Reasoning 50(7), 1066–1080 (2009)CrossRefGoogle Scholar
  14. 14.
    Bardossy, A., Duckstein, L.: Fuzzy Rule-Based Modeling with Application to Geophysical, Biological and Engineering Systems. CRC Press (1995)Google Scholar
  15. 15.
    Bastian, A.: How to handle the flexibility of linguistic variables with applications. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 3(4), 463–484 (1994)CrossRefMathSciNetGoogle Scholar
  16. 16.
    Berlanga, F.J., Rivera, A.J., del Jesus, M.J., Herrera, F.: GP-COACH: Genetic programming based learning of compact and accurate fuzzy rule based classification systems for high dimensional problems. Information Sciences 180(8), 1183–1200 (2010)CrossRefGoogle Scholar
  17. 17.
    Bonissone, P.P., Khedkar, P.S., Chen, Y.: Genetic algorithms for automated tuning of fuzzy controllers: A transportation application. In: Proc. Fifth IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 1996), New Orleans, USA, pp. 674–680 (1996)Google Scholar
  18. 18.
    Botta, A., Lazzerini, B., Marcelloni, F.: Context adaptation of Mamdani fuzzy rule based systems. International Journal of Intelligent Systems 23(4), 397–418 (2008)CrossRefzbMATHGoogle Scholar
  19. 19.
    Botta, A., Lazzerini, B., Marcelloni, F., Stefanescu, D.C.: Context adaptation of fuzzy systems through a multi-objective evolutionary approach based on a novel interpretability index. Soft Computing 13(5), 437–449 (2009)CrossRefGoogle Scholar
  20. 20.
    Casillas, J., Cordón, O., Herrera, F.: COR: a methodology to improve ad hoc data-driven linguistic rule learning methods by inducing cooperation among rules. IEEE Transactions on Systems, Man, and Cybernetics - Part B: Cybernetics 32(4), 526–537 (2002)CrossRefGoogle Scholar
  21. 21.
    Casillas, J., Cordón, O., Herrera, F., Magdalena, L. (eds.): Accuracy improvements in linguistic fuzzy modeling. Springer, Heidelberg (2003)zbMATHGoogle Scholar
  22. 22.
    Casillas, J., Cordón, O., Herrera, F., Magdalena, L.: Interpretability improvements to find the balance interpretability-accuracy in fuzzy modeling: an overview. In: Casillas, J., Cordón, O., Herrera, F., Magdalena, L. (eds.) Interpretability Issues in Fuzzy Modeling, pp. 3–22. Springer, Heidelberg (2003)Google Scholar
  23. 23.
    Casillas, J., Cordón, O., Herrera, F., Magdalena, L. (eds.): Interpretability issues in fuzzy modeling. Springer, Heidelberg (2003)zbMATHGoogle Scholar
  24. 24.
    Casillas, J., Cordón, O., del Jesus, M.J., Herrera, F.: Genetic tuning of fuzzy rule deep structures preserving interpretability for linguistic modeling. IEEE Transactions on Fuzzy Systems 13(1), 13–29 (2005)CrossRefGoogle Scholar
  25. 25.
    Cho, J.S., Park, D.J.: Novel fuzzy logic control based on weighting of partially inconsistent rules using neural network. International Journal of Intelligent and Fuzzy Systems 8(2), 99–110 (2000)Google Scholar
  26. 26.
    Cococcioni, M., Ducange, P., Lazzerini, B., Marcelloni, F.: A Pareto-based multi-objective evolutionary approach to the identification of Mamdani fuzzy systems. Soft Computing 11(11), 1013–1031 (2007)CrossRefGoogle Scholar
  27. 27.
    Coello, C.C., Lamont, G.B., Van Veldhuizen, D.A.: Evolutionary Algorithms for Solving Multi-objective Problems, 2nd edn. Springer, Heidelberg (2007)zbMATHGoogle Scholar
  28. 28.
    Cordón, O., Herrera, F.: A three-stage evolutionary process for learning descriptive and approximate fuzzy logic controller knowledge bases from examples. International Journal of Approximate Reasoning 17(4), 369–407 (1997)CrossRefzbMATHGoogle Scholar
  29. 29.
    Cordón, O., Herrera, F.: A proposal for improving the accuracy of linguistic modeling. IEEE Transactions on Fuzzy Systems 8(3), 335–344 (2000)CrossRefGoogle Scholar
  30. 30.
    Cordón, O., Herrera, F., Magdalena, L., Villar, P.: A genetic learning process for the scaling factors, granularity and contexts of the fuzzy rule-based system data base. Information Sciences 136(1-4), 85–107 (2001)CrossRefzbMATHGoogle Scholar
  31. 31.
    Cordón, O., Herrera, F., Villar, P.: Generating the knowledge base of a fuzzy rule-based system by the genetic learning of the data base. IEEE Transactions on Fuzzy Systems 9(4), 667–674 (2001)CrossRefGoogle Scholar
  32. 32.
    Cordón, O., del Jesus, M.J., Herrera, F.: Genetic learning of fuzzy rule-based classification systems cooperating with fuzzy reasoning methods. International Journal of Intelligent Systems 13(10-11), 1025–1053 (1998)CrossRefGoogle Scholar
  33. 33.
    Cordón, O., del Jesús, M.J., Herrera, F., Lozano, M.: MOGUL: A methodology to obtain genetic fuzzy rule-based systems under the iterative rule learning approach. International Journal of Intelligent Systems 14(11), 1123–1153 (1999)CrossRefzbMATHGoogle Scholar
  34. 34.
    Cordón, O., del Jesus, M.J., Herrera, F., Villar, P.: A multiobjective genetic algorithm for feature selection and granularity learning in fuzzy-rule based classification systems. In: Proc. Joint 9th IFSA World Congress and 20th NAFIPS International Conference (IFSA-NAFIPS 2001), Vancouver, Canada, vol. 3, pp. 1253–1258 (2001)Google Scholar
  35. 35.
    Cordón, O., del Jesus, M.J., Herrera, F., Villar, P.: A multiobjective genetic learning process for joint feature selection and granularity and contexts learning in fuzzy rule-based classification systems. In: Casillas, J., Cordón, O., Herrera, F., Magdalena, L. (eds.) Interpretability Issues in Fuzzy Modeling, pp. 79–99. Springer, Heidelberg (2003)Google Scholar
  36. 36.
    Cordón, O., Gomide, F., Herrera, F., Hoffmann, F., Magdalena, L.: Ten years of genetic fuzzy systems: current framework and new trends. Fuzzy Sets and Systems 141(1), 5–31 (2004)CrossRefzbMATHMathSciNetGoogle Scholar
  37. 37.
    Cordón, O., Herrera, F., Hoffmann, F., Magdalena, L.: Genetic Fuzzy Systems. In: Evolutionary Tuning and Learning of Fuzzy Knowledge Bases. World Scientific (2001)Google Scholar
  38. 38.
    Cordón, O., Herrera, F., Zwir, I.: Linguistic modeling by hierarchical systems of linguistic rules. IEEE Transactions on Fuzzy Systems 10(1), 2–20 (2002)CrossRefGoogle Scholar
  39. 39.
    Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6(2), 182–197 (2002)CrossRefGoogle Scholar
  40. 40.
    Driankov, D., Hellendoorn, H. (eds.): Fuzzy Model Identification. Selected Approaches. Springer, Heidelberg (1997)zbMATHGoogle Scholar
  41. 41.
    Driankov, D., Hellendoorn, H., Reinfrank, M.: An Introduction to Fuzzy Control. Springer, Heidelberg (1993)zbMATHGoogle Scholar
  42. 42.
    Ducange, P., Lazzerini, B., Marcelloni, F.: Multi-objective genetic fuzzy classifiers for imbalanced and cost-sensitive datasets. Soft Computing 14(7), 713–728 (2010)CrossRefGoogle Scholar
  43. 43.
    Eiben, A.E., Smith, J.E.: Introduction to Evolutionary Computing. Springer, Heidelberg (2003)zbMATHGoogle Scholar
  44. 44.
    Fernández, A., Gacto, M.J., Herrera, F.: Hierarchical fuzzy rule based classification systems with genetic rule selection for imbalanced data-sets. International Journal of Approximate Reasoning 50(3), 561–577 (2009)CrossRefzbMATHGoogle Scholar
  45. 45.
    Fernández, A., Herrera, F.: Linguistic Fuzzy Rules in Data Mining: Follow-up Mamdani Fuzzy Modeling Principle. In: Trillas, E., Bonissone, P.P., Magdalena, L., Kacprycz, J. (eds.) Combining Experimentation and Theory. A Hommage to Abe Mamdani. Springer, Heidelberg (2011) (in press)Google Scholar
  46. 46.
    Fonseca, C.M., Fleming, P.J.: Genetic algorithms for multiobjective optimization: Formulation, discussion and generalization. In: Proc. Fifth International Conference on Genetic Algorithms (ICGA 1993), Urbana-Champaign, IL, USA, pp. 416–423 (1993)Google Scholar
  47. 47.
    Gacto, M.J., Alcalá, R., Herrera, F.: Adaptation and application of multi-objective evolutionary algorithms for rule reduction and parameter tuning of fuzzy rule-based systems. Soft Computing 13(5), 419–436 (2009)CrossRefGoogle Scholar
  48. 48.
    Gacto, M.J., Alcalá, R., Herrera, F.: Integration of an index to preserve the semantic interpretability in the multi-objective evolutionary rule selection and tuning of linguistic fuzzy systems. IEEE Transactions on Fuzzy Systems 18(3), 515–531 (2010)CrossRefGoogle Scholar
  49. 49.
    Gacto, M.J., Alcalá, R., Herrera, F.: Interpretability of linguistic fuzzy rule-based systems: An overview of interpretability measures. Information Sciences (2011) (in press), doi:10.1016/j.ins.2011.02.021Google Scholar
  50. 50.
    González, A., Pérez, R.: SLAVE: a genetic learning system based on an iterative approach. IEEE Transactions on Fuzzy Systems 7(2), 176–191 (1999)CrossRefGoogle Scholar
  51. 51.
    González, A., Pérez, R.: A study about the inclusion of linguistic hedges in a fuzzy rule learning algorithm. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 7(3), 257–266 (1999)CrossRefGoogle Scholar
  52. 52.
    Gudwin, R., Gomide, F., Pedrycz, W.: Context adaptation in fuzzy processing and genetic algorithms. International Journal of Intelligent Systems 13(10/11), 929–948 (1998)CrossRefGoogle Scholar
  53. 53.
    Guillaume, S.: Designing fuzzy inference systems from data: An interpretability-oriented review. IEEE Transactions on Fuzzy Systems 9(3), 426–443 (2001)CrossRefMathSciNetGoogle Scholar
  54. 54.
    Gurocak, H.B.: A genetic-algorithm-based method for tuning fuzzy logic controllers. Fuzzy Sets and Systems 108(1), 39–47 (1999)CrossRefGoogle Scholar
  55. 55.
    Ishibuchi, H.: Multiobjective genetic fuzzy systems: Review and future research directions. In: Proc. 2007 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2007), London, UK, pp. 1–6 (2007)Google Scholar
  56. 56.
    Ishibuchi, H., Murata, T.: A genetic-algorithm-based fuzzy partition method for pattern classification problems. In: Herrera, F., Verdegay, J.L. (eds.) Genetic Algorithms and Soft Computing, pp. 555–578. Physica-Verlag (1996)Google Scholar
  57. 57.
    Ishibuchi, H., Murata, T., Türksen, I.B.: Single-objective and two-objective genetic algorithms for selecting linguistic rules for pattern classification problems. Fuzzy Sets and Systems 89(2), 135–150 (1997)CrossRefGoogle Scholar
  58. 58.
    Ishibuchi, H., Nakashima, T., Murata, T.: Performance evaluation of fuzzy classifier systems for multidimensional pattern classification problems. IEEE Transactions on Systems, Man and Cybernetics - Part B: Cybernetics 29(5), 601–618 (1999)CrossRefGoogle Scholar
  59. 59.
    Ishibuchi, H., Nakashima, T., Murata, T.: Three-objective genetics-based machine learning for linguistic rule extraction. Information Sciences 136(1-4), 109–133 (2001)CrossRefzbMATHGoogle Scholar
  60. 60.
    Ishibuchi, H., Nojima, Y.: Analysis of interpretability-accuracy tradeoff of fuzzy systems by multiobjective fuzzy genetics-based machine learning. International Journal of Approximate Reasoning 44(1), 4–31 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  61. 61.
    Ishibuchi, H., Nozaki, K., Yamamoto, N., Tanaka, H.: Selecting fuzzy if-then rules for classification problems using genetic algorithms. IEEE Transactions on Fuzzy Systems 3(3), 260–270 (1995)CrossRefGoogle Scholar
  62. 62.
    Ishibuchi, H., Yamamoto, T., Nakashima, T.: Hybridization of fuzzy GBML approaches for pattern classification problems. IEEE Transactions on Systems, Man, and Cybernetics - Part B: Cybernetics 35(2), 359–365 (2005)CrossRefGoogle Scholar
  63. 63.
    Karr, C.: Genetic algorithms for fuzzy controllers. AI Expert 6(2), 26–33 (1991)Google Scholar
  64. 64.
    Knowles, J.D., Corne, D.W.: Approximating the non dominated front using the Pareto archived evolution strategy. Evolutionary Computation 8(2), 149–172 (2000)CrossRefGoogle Scholar
  65. 65.
    Kuncheva, L.I.: Fuzzy Classifier Design. Studies in Fuzziness and Soft Computing, vol. 49. Physica-Verlag (2000)Google Scholar
  66. 66.
    Liu, B.D., Chen, C.Y., Tsao, J.Y.: Design of adaptive fuzzy logic controller based on linguistic-hedge concepts and genetic algorithms. IEEE Transactions on Systems, Man, and Cybernetics - Part B: Cybernetics 31(1), 32–53 (2001)CrossRefGoogle Scholar
  67. 67.
    Magdalena, L.: Adapting the gain of an FLC with genetic algorithms. International Journal of Approximate Reasoning 17(4), 327–349 (1997)CrossRefzbMATHGoogle Scholar
  68. 68.
    Magdalena, L., Monasterio, F.: A fuzzy logic controller with learning through the evolution of its knowledge base. International Journal of Approximate Reasoning 16(3/4), 335–358 (1997)CrossRefzbMATHGoogle Scholar
  69. 69.
    Mamdani, E.H.: Applications of fuzzy algorithm for control a simple dynamic plant. Proceedings of the IEEE 121(12), 1585–1588 (1974)Google Scholar
  70. 70.
    Miettinen, K.: Nonlinear Multiobjective Optimization. Kluwer Academic Publishers (1999)Google Scholar
  71. 71.
    Mikut, R., Jakel, J., Groll, L.: Interpretability issues in data-based learning of fuzzy systems. Fuzzy Sets and Systems 150, 179–197 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  72. 72.
    Muñoz-Salinas, R., Aguirre, E., Cordón, O., García-Silvente, M.: Automatic tuning of a fuzzy visual system using evolutionary algorithms: Single-objective vs. multiobjective approaches. IEEE Transactions on Fuzzy Systems 16(2), 485–501 (2008)CrossRefGoogle Scholar
  73. 73.
    Nauck, D.D., Kruse, R.: How the learning of rule weights affects the interpretability of fuzzy systems. In: Proc. 7th IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 1998), pp. 1235–1240. IEEE Press, Anchorage (1998)Google Scholar
  74. 74.
    Nojima, Y., Ishibuchi, H.: Incorporation of user preference into multi-objective genetic fuzzy rule selection for pattern classification problems. Artificial Life and Robotics 14(3), 418–421 (2009)CrossRefGoogle Scholar
  75. 75.
    Nozaki, K., Ishibuchi, H., Tanaka, H.: A simple but powerful heuristic method for generating fuzzy rules from numerical data. Fuzzy Sets and Systems 86, 251–270 (1997)CrossRefGoogle Scholar
  76. 76.
    Peña-Reyes, C.A., Sipper, M.: Fuzzy CoCo: A cooperative-coevolutionary approach to fuzzy modeling. IEEE Transactions on Fuzzy Systems 9(5), 727–737 (2001)CrossRefGoogle Scholar
  77. 77.
    Potter, M., Jong, K.D.: Cooperative coevolution: An architecture for evolving coadapted subcomponents. Evolutionary Computation 8(1), 1–29 (2000)CrossRefGoogle Scholar
  78. 78.
    Pulkkinen, P., Hytonen, J., Koivisto, H.: Developing a bioaerosol detector using hybrid genetic fuzzy systems. Engineering Applications of Artificial Intelligence 21(8), 1330–1346 (2008)CrossRefGoogle Scholar
  79. 79.
    Pulkkinen, P., Koivisto, H.: Fuzzy classifier identification using decision tree and multiobjective evolutionary algorithms. International Journal of Approximate Reasoning 48(2), 526–543 (2008)CrossRefGoogle Scholar
  80. 80.
    Ruspini, E.H.: A new approach to clustering. Information and Control 15(1), 22–32 (1969)CrossRefzbMATHGoogle Scholar
  81. 81.
    Setzkorn, C., Paton, R.C.: On the use of multi-objective evolutionary algorithms for the induction of fuzzy classification rule systems. BioSystems 81(2), 101–112 (2005)CrossRefGoogle Scholar
  82. 82.
    Söderström, T., Stoica, P.: System Identification. Prentice-Hall, Englewood Cliffs (1989)zbMATHGoogle Scholar
  83. 83.
    Valente de Oliveira, J.: Semantic constraints for membership functions optimization. IEEE Transactions on Systems, Man and Cybernetics-Part A: Systems and Humans 29, 128–138 (1999)CrossRefGoogle Scholar
  84. 84.
    Van Broekhoven, E., Adriaenssens, V., De Baets, B.: Interpretability-preserving genetic optimization of linguistic terms in fuzzy models for fuzzy ordered classification: An ecological case study. International Journal of Approximate Reasoning 44(1), 65–90 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  85. 85.
    Wang, H., Kwong, S., Jin, Y., Wei, W., Man, K.F.: Agent-based evolutionary approach for interpretable rule-based knowledge extraction. IEEE Transactions on Systems, Man, and Cybernetics - Part C 35(2), 143–155 (2005)CrossRefGoogle Scholar
  86. 86.
    Zadeh, L.A.: Outline of a new approach to the analysis of complex systems and decision processes. IEEE Transactions on Systems, Man, and Cybernetics 3, 28–44 (1973)CrossRefzbMATHMathSciNetGoogle Scholar
  87. 87.
    Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: improving the strength Pareto evolutionary algorithm. In: Proc. EUROGEN 2001 - Evolutionary Methods for Design, Optimisation and Control with Applications to Industrial Problems, pp. 19–26 (2001)Google Scholar
  88. 88.
    Zitzler, E., Thiele, L.: Multiobjective evolutionary algorithms: A comparative case study and the strength Pareto approach. IEEE Transactions on Evolutionary Computation 3(4), 257–271 (1999)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.European Centre for Soft ComputingEdificio Científico-TecnológicoMieresSpain

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