Electronic model of a dubois fuzzy integration neuron

 

J. L. Pérez S.*¹, A. Garcés M.², F. Cabiedes C.³, A. Miranda V.⁴

 

^1,2,3,4 Centro de Ciencias Aplicadas y Desarrollo Tecnológico Universidad Nacional Autónoma de México *E–mail:pepito@aleph.cinstrum.unam.mx

 

ABSTRACT

In this work, we present a fuzzy electronic neuron that has a Dubois fuzzy integration method, an activation function with a fuzzy threshold, and a fuzzy response. We generated a fuzzy sum of the input signals and a shooting threshold value defined by means of a triangular or sinusoidal membership function. We present the electronic circuits, the oscilograms of the neuron responses, the value of the fuzzy integral, and we compare their behavior with those of a conventional leaky integrator neuron.

Keywords: Biological based neuron models, artificial neuron models, Fuzzy neuron models.

 

RESUMEN

En este trabajo presentamos una neurona electrónica borrosa que contiene un integrador tipo Dubois, una función de activación con umbral borroso y respuesta borrosa. Generamos un sumador borroso de señales de entrada y un valor de disparo de umbral definido por medio de una función de membresía triangular o sinusoidal. Presentamos los circuitos electrónicos, los oscilogramas de la respuesta de la neurona, el valor de la integral borrosa, y comparamos estas características con una neurona integradora con fugas convencional.

 

DESCARGAR ARTÍCULO EN FORMATO PDF

 

References

[1] Mc Culloch W.S., Pitts W.A. "A logical calculus of the ideas imminent in nervous activity". Bull. Math. Biophys., 5 (1943).         [ Links ]

[2] Pozin N.V. Lyubinskii, I A, Neuron Model. Report Number FTD–HT–66–103 9 September 1966. 5 pages.         [ Links ]

[3] J.A. Deutsch. An electrophysiological stimulator with digital logic. J. exp. analysis Behav. 9 (1966). pp. 399–400.         [ Links ]

[4] Mitchell RA et al., J Appl Physiol 18. 523–533. (1963).         [ Links ]

[5] Hormann, "Gaku: An Artificial Student." Behavioral Science. vol. 10. No. 1 (January. 1965). pp. 88–107.         [ Links ]

[6] Frank Rosenblatt. The Perceptron: A Probabilistic Model for Information Storage and Organization in the Brain. Psychological Review. vol. 65. No. 6. pp. 386-408. November. (1958).         [ Links ]

[7] Caianiello, F.R. Outline of a theory of thought–processes and thinking machines J. Theoret. Binl. 1. 204–235 (1961).         [ Links ]

[8] B. Widrow and M.F. Hoff, Associative Storage and Retrieval of Digital Information in networks of Adaptive Neurons. Biological Prototypes and Synthetic Systems. 1:160. (1962).         [ Links ]

[9] Lewis F.R. Structural correlates of function in the anuran amphibian papilla. Scanning Flectron Microsc 2. pag 429–436. (1977).         [ Links ]

[10] French A.S., Stein R.B. "Flexible Neural Analog using integrated circuits". IEEE Trans. Binmed. Fng. 17. 248–253 (1970).         [ Links ]

[11] Mitchell. P. Molecule, group and electron translocation through natural membranes. Biochem Snc. Symp. 22 pag 142–168. (1981).         [ Links ]

[12] Vittoz. F.A. "Analog VLSI Signal Processing: Why. Where and How?" Journal of VLSI Signal Processing. 8 & Analog Integrated Circuits and Signal Processing. 2744. (1994).         [ Links ]

[13] Alexandre R.S. Romariz, Kelvin Wagner Optoelectronic Implementation of a FitzHugh–Nagumo Neural Model. IEEE Journal of Solid–State Circuits. 26 (7): 956–965. (1991).         [ Links ]

[14] R.D. Pinto, P. Varona, A.R. Volkovskii. A. Szucs, H.D. Abarbanel, and M.I. Rabinovich. Synchronous behavior of two coupled electronic neurons. Phys Rev F. vol. 62. pp. 2644–56. (2000).         [ Links ]

[15] Y.J. Lee, Lee, J., Kim, Y.B., Ayers J., Volkovskii. A., Selverston. A., Abarbanel, H., Rabinovich. M., "Low Power Real Time Flectronic Neuron VLSI Design Using Subthreshnld Techniques. IEEE Circuits and Systems. vol. 4. pp. 744–747. (2004).         [ Links ]

[16] Shin'Ichiro Kanoh. Makoto Imai. Nozomu Hoshimiy. Analog LSI Neuron Model inspired by biological excitable membrane. Systems and Computers in Japan, Volume 36 Issue 6. Pages 84 – 91. (2005).         [ Links ]

[17] A.van Schaik, Building blocks for electronic spiking neural networks. Volume 14. Issues 6–7, Pages 617–6289 (2001).         [ Links ]

[18] Szlavik Robert B.; Bhuiyan Abuhanif K.; Carver Anthony; Jenkins Frank. Neural–electronic inhibition simulated with a Neuron Model implemented in SPICE. IEEE Engineering in Medicine and Biology. vol. 14. n 1. pp. 109–115. (2006).         [ Links ]

[19] A. Volkovskii, S. Bruginni, R. Levi, M. Rabinovich, A. Selverston and H.D.I. Abarbanel. Analog electronic Model of the lobster pyloric central pattern generator. Journal of Physics: Conference Series 23 47–57 (2005).         [ Links ]

[20] Wu J, DiCecco J, Sun Y, Hill R. An analog Neuron emulator for education and testing of neurophysiological instruments. Society for Neuroscience 34th Annual Meeting. San Diego. CA. October 23–27. (2004).         [ Links ]

[21] Breau F. Main–Cannon S. Davis R. Wu J. DiCecco J. Sun Y. The Neuron emulator: an undergraduate biomedical engineering design project. 31 Northeast Bioengineering Conference. Hoboken. NJ. April 2–3. (2005).         [ Links ]

[22] Allen I. Selverston, Mikhail I. Rabinovich, Henry D. Abarbanel, Robert Elson, Attila Szucs, Reynaldo D. Pinto, Ramon Huerta, Pablo Varona. Reliable circuits from irregular Neurons: A dynamical approach to understanding central pattern generators. Journal of Physiology–Paris. vol. 94. No. 5–6., pp. 357–374 (2000).         [ Links ]

[23] Maeda Ynshinnbu Satn. Shunsuke Makinn Hiden. Bifurcation Structure of an Electronic Circuit Model for Neuronal Firings. Transactions of the Institute of Electrical Engineers of Japan. C. ISSN:0385–4221, Vol. 121–C; No.7; 1153–1159 (2001).         [ Links ]

[24] Shinya Suenaga. Yoshihiro Hayakawa and Koji Nakajima. Design of a Neural network Chip for the Burst ID Model with Ability of Burst Firing. IEICE Transactions on Fundamentals of Electronics. Communications and Computer Sciences F90–A(4):715–723 (2007)        [ Links ]

[25] Perez S. J.L., Calva G.: Modelo electrónico de un sistema Neuronal. Memorias del IV Simposio Nacional de Instrumentación. México. 1987.         [ Links ]

[26] Perez S. J.L.: Diseño de un modelo de Neurona analógico. Reporte técnico. Centro de Instrumentos UNAM. (1974). Mexico. 10 pag.         [ Links ]

[27] Zadeh L.A.: Fuzzy sets. Inform Control. (1965). 338–353.         [ Links ]

[28] Wee W.C., Fu K.S. "A formulation of Fuzzy Automata and its applications as a Model of Learning system". IEEE Trans. Syst. Sci. Cybernetics. (1969). SSC–5.         [ Links ]

[29] Lee., F.T. Lee. Fuzzy sets and neural networks. J. Cybernetics. (1974). 4. 83–103.         [ Links ]

[30] Keller., D. Hunt. Incorporating fuzzy membership functions into the perceptron algorithm. IEEE Trans. Pattern Anal. Machine Intelligence. (1985). 7. 693–699.         [ Links ]

[31] Yamakawa y S. Tnmnda. A fuzzy Neuron and its application to pattern recognition. Proc. Third IFSA Congr., Seattle. August 6–11. 30–38, 1989.         [ Links ]

[32] Requema y M. Delgado. "A Model of fuzzy Neuron". Proc. 2nd. Int. Cnnf. Fuzzy logic Neural networks. (IIZUKA'90). Iizuka. Japón. July 20–24. 13–26 (1990).         [ Links ]

[33] Kandel A. Fuzzy Switching and automata. Crane, Russak & Company. New York. (1979).         [ Links ]

[34] Dubnis D. Towars Fuzzy Differential Calculus. Fuzzy Sets and Systems., 8. 1–17 (1982).         [ Links ]