Comparison of Two Interval Models for Fuzzy-Valued Genetic Algorithm

Part of the Mathematics for Industry book series (MFI, volume 9)


Genetic algorithm (GA) employs real numbers (or bit strings) as genotype values for solving real-valued optimization problems. The author previously proposed an extension of GA. The proposed method extends the processes of GA to handle fuzzy numbers as genotype values so that GA can be applied to fuzzy-valued optimization problems. The author has applied the FGA to the evolution of fuzzy-valued neural networks (FNN) and showed that FGA could evolve FNNs, which model fuzzy functions well, despite that the training (evolution) of the FNNs was not supervised. In the previous paper, fuzzy numbers as the genotype values were symmetric triangular ones. Each symmetric triangular fuzzy number can be specified by its lower and upper limit values or its center and width values, and thus the FGA can employ either of two models, the lower and upper (LU) model or the center and width (CW) model for specifying genotype values. Ability of the FGA in searching solutions may depend on the model, because the crossover and the mutation operations for the fuzzy genotypes with the LU model are slightly different from those operations with the CW model. In this paper, the author compares the two models to investigate which model contributes better for the FGA to find better solutions. Application of the FGA is evolutionary training of the FNNs. An experimental result shows that the CW model contributed slightly better than the LU model in evolving FNNs which model fuzzy functions.


Evolutionary algorithm Genetic algorithm Neural network Neuroevolution Fuzzy number 



This research was supported by Kyoto Sangyo University Research Grant.


  1. 1.
    Goldberg, D.E.: Genetic Algorithms in Search Optimization and Machine Learning. Kluwer Academic Publishers, Norwell (1989)Google Scholar
  2. 2.
    Back, T.: Evolutionary Algorithms in Theory and Practice: Evolution Strategies, Evolutionary Programming, Genetic Algorithms. Oxford Univ Press, Oxford (1996)Google Scholar
  3. 3.
    Okada, H., Matsuse, T., Wada, T.: GA with fuzzy-valued genotypes and its application to neuroevolution. In: Proceedings of Asia Pacific Symposium of Intelligent and Evolutionary Systems (IES) 2012, pp. 15–18 (2012)Google Scholar
  4. 4.
    Ishibuchi, H., Tanaka, H., Okada, H.: Fuzzy neural networks with fuzzy weights and fuzzy biases. In: Proceedings of IEEE International Conferences on Neural Networks, pp. 1650–1655 (1993)Google Scholar
  5. 5.
    Yao, X.: Evolving artificial neural networks. In: Proceedings of the IEEE, vol. 87, no. 9, pp. 1423–1447 (1999)Google Scholar
  6. 6.
    Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning—I, II, and III. In: Information Science, vol. 8, pp. 199–249, pp. 301–357 and vol. 9, pp. 43–80 (1975)Google Scholar
  7. 7.
    Alefeld, G., Herzberger, J.: Introduction to Interval Computation Academic Press, New York (1983)Google Scholar
  8. 8.
    Eshelman, L.J., Schaffer, J.D.: Real-coded genetic algorithms and interval-schemata. In: Whitley, D.L. (ed.) Foundation of Genetic Algorithms 2, pp. 187–202 (1993)Google Scholar

Copyright information

© Springer Japan 2015

Authors and Affiliations

  1. 1.Faculty of Computer Science and EngineeringKyoto Sangyo UniversityKyotoJapan

Personalised recommendations