Abstract
Several applications need a guaranty of the precision of their numerical data. Important tools which allow control of the numerical errors are dealing these data as intervals. This work presents a new approach to use with Interval Computing in Neural Networks, studying the particular case of one layer interval neural networks, which extend Punctual One Layer Neural Networks, and try to be a solution for the problems in calculus precision error and treatment of interval data without modify it. Beyond it, seemly, interval connections between neurons permit the number of the epochs needed to converge to be lower than the needed in punctual networks without loss efficiency.
The interval computing in a one layer neural network with supervised training was tested and compared with the traditional one. Experiences show that the behavior of the interval neural network is better than the traditional one beyond of include the guarantee about the computational errors.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alefeld, G., Herzberger, J.: Introduction to interval computations. Academic Press, New York (1983)
Alefeld, G., Mayer, G.: Interval analysis – theory and applications. Journal of Computational and Applied Mathematics 121, 421–464 (2000)
Baker, M.R., Patil, R.B.: Universal approximation theorem for interval neural networks. Reliable Computing 4, 235–239 (1998)
Barboza, L.V., Dimuro, G.P., Reiser, R.H.S.: Power Flow with load Uncertainty. TEMA-Tendências em Matemática Aplicada e Computacional 5(-1), 27–36 (2004)
Beheshti, M., Berrached, A., Korvin, A.D., Hu, C., Sirisaengtaksin, O.: On Interval Weighted Three-Layer Neural Networks. In: The 31st Annual Simulation Symposium, pp. 188–195 (1998)
Bock, H.H., Diday, E.: Analysis of Simbolic Data. In: Exploratory methods for extracting statistical information from complex data. Springer, Heidelberg (2000)
Hayes, B.: A lucid Interval. American Science 91(-6), 484–488 (2003)
Ishibuchi., H., Nii, M.: Interval-Arithmetic-Based Neural Networks. In: Bunke, H., Kande, A. (eds.) Hybrid Methods in Pattern Recognition. Series in Machine Perception and Artificial Intelligence, vol. 47 (2001)
Kearfott, R.B., Kreinovich, V.: Applications of Interval Computations. Kluwer Academic Publishers, Dordrecht (1996)
Kohout, L.J., Kim, E.: Characterization of Interval Fuzzy Logic Systems of Connectives by Group Transformation. Reliable Computing 10, 299–334 (2004)
Kreinovich, V., Scott, F., Ginzburg, L., Schulte, H., Barry, M.R., Nguyen, H.T.: From Interval Methods of Representing Uncertainty to a General Description of Uncertainty. In: Mohanty, H., Baral, C. (eds.) Trends in Information Technology. Proceedings of the International Conference on Information Technology CIT 1999, Bhubaneswar, India, pp. 161–166. Tata McGraw-Hill, New Delhi (2000)
McCulloch, W.S., Pitts, W.: A logical calculus of the ideas immanent in nervous activity. Bulletin of Mathematical Biophysics 5, 115–133 (1943)
Moore, R.E.: Automatic error analysis. in digital computation, Technical Report LMSD-48421, Lockheed Aircraft Corporation, Missiles and Space Division, Sunnyvale-CA (January 1959)
Moore, R.E.: Interval Arithmetic and Automatic Error Analysis in Digital Computing. Ph.D. Thesis, Stanford University, Stanford-CA (1962)
Moore, R.E.: Interval Analysis. Prentice Hall, New Jersey (1966)
Moore, R.E.: Methods and Applications of Interval Analysis. SIAM, Philadelphia (1979)
Rossi, F., Conan-Guez, B.: Multilayer Perceptron on Interval Data. In: Classification, Clustering, and Data Analysis (IFCS 2002), pp. 427–434. Springer, Poland (2002) (Cracow. Abstracts) http://apiacoa.org/publications/2002/ifcs02.pdf
Silveira, M.M.M.T., Bedregal, B.R.C.: A Method of Inference and Defuzzification Fuzzy Interval. In: The 2001 Artificial Intelligence and Application. Marbella- Spanish (September 2001)
Sunaga, T.: Theory of an Interval Algebra and its Applications to Numerical Analysis. RAAG Memoirs 2, 29–46 (1958)
Turksen, I.B.: Interval value fuzzy sets based on normal form. Fuzzy Sets and Systems 20, 191–210 (1986)
Voschinin, A.P., Dyvak, N.P., Simoff, S.J.: Interval Methods: Theory and Application in the Design of Experiments, Data Analysis and Fittin. In: Letzky, E.K. (ed.) Design of Experiments and Data Analysis: New Trends and Results. Antal Publishing Co., Moscow (1993)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Patiño-Escarcina, R.E., Callejas Bedregal, B.R., Lyra, A. (2004). Interval Computing in Neural Networks: One Layer Interval Neural Networks. In: Das, G., Gulati, V.P. (eds) Intelligent Information Technology. CIT 2004. Lecture Notes in Computer Science, vol 3356. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30561-3_8
Download citation
DOI: https://doi.org/10.1007/978-3-540-30561-3_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24126-3
Online ISBN: 978-3-540-30561-3
eBook Packages: Computer ScienceComputer Science (R0)