Abstract
A family of S-functions is introduced and characterized. S-functions may be used as activation functions in neural networks and allow the interpretation of the activity of the artificial neurons as fuzzy if-then rules, where the degree of satisfaction of the premises for a given input is calculated by means of the symmetric summation. These rules are appropriate to model compensating systems.
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
Alsina C., Trillas E., Valverde L. (1983): On some logical connectives for fuzzy sets theory. Jr. of Mathematical Analysis and Applications 93, 15–26
Amari S. (1968): Geometrical Theory of Information. Kyoritsu-Shuppan, Tokyo
Benitez J.M., Castro J.L., Requena I. (1997): Are neural networks black boxes? IEEE Trans. on Neural Networks 8, 1156–1163
Dombi J. (1982): Basic concepts for a theory of evaluation: The aggregative operator. European Jr. Operation Research 10, 282–293
Dubois D., Prade H. (1985): A review of fuzzy set aggregation connectives. Information Sciences 36, 85–121
Funahashi K.I. (1989): On the approximate realization of continuous mappings by neural networks. Neural Networks 2, 183–192
Georgiou G.M. (1992): Parallel distributed processing in the complex domain. Ph.D. Thesis, Dept. C. Sc., Tulane University, New Orleans, Lousiana
Glorennec P.Y., Barret C., Brunet M. (1992): Application of Neuro—Fuzzy Networks to identification and control of nonlinear dynamic systems. Proc. Int. Conference on Information Processing and Management of Uncertainty in Knowledge—based Systems (IPMU), 507–510, Palma de Mallorca
Han J., Moraga C. (1996): Parametric Feedforward Network based Adaptive Fuzzy Modeling. Proc. Int. Symp. Intelligent Industrial Automation and Soft Computing, B-159–165, Reading UK, ICSC Academic Press
Horikawa S.I., Furuhashi T., Uchikawa Y. (1992): A new type of Fuzzy Neural Network for Linguistic Fuzzy Modeling. Proc. 2nd. Int. Conference on Fuzzy Logic and Neural Networks. 1053–1056, Iizuka, Japan
Hornik K., Stinchcombe M., White H. (1989): Multilayer Feedforward Networks are universal approximators. Neural Networks 2, 359–366
Jang J.S.R. (1993): ANFIS: Adaptive Network based Fuzzy Inference System. IEEE Trans. on Systems, Man and Cybernetics 23, (3), 665–685
Jang J.S.R., Sun C.T. (1995): Neuro—fuzzy Modeling and Control. Proceedings IEEE 83, (3), 378–406
Klement, P.; Mesiar, R.; Pap, E. (1996): On the relationship of associative compensatory operators to triangular norms and conorms, Intl Jr. of Uncertainty, Fuzziness and Knowledge-based Systems 4 (2) 129–144
Kosko B. (1994): Fuzzy systems as universal approximators. IEEE Trans. Computers 43, (11), 1324–1333
Keller J.M., Tager R.R., Tahani H. (1992): Neural Network implementation of fuzzy logic. Fuzzy Sets and Systems 45, (1), 1–12
Moraga C. (1997): Properties of Parametric Feedforward Networks. Proceedings XXIII Conferencia Latinoamericana de Informatica, 861–870, Valparaiso, Chile
Silvert W. (1979): Symmetric summation: A class of operations on fuzzy sets. IEEE Trans. on Systems, Man and Cybernetics 9, 659–667
Takagi H., Hayashi I. (1991): NN-driven fuzzy reasoning. Int. Journal of Approximate Reasoning 5, (3), 191–212
Takagi H., Sugeno M. (1985): Fuzzy identification of systems and its application to modeling and control. IEEE Trans. on Systems, Man and Cybernetics 15, (1), 116–132
Temme K.-H., Heider R., Moraga C. (1999): Generalized neural networks for fuzzy modeling. Proc., Int’l Conference of the European Society of Fuzzy Logic and Technology, EUSFLAT’99, 469–472, Palma de Mallorca, Spain
Takagi H., Susuki N., Koda T., Kojima Y. (1992): Neural Networks designed on approximate reasoning architecture and their applications. IEEE Trans. Neural Networks 3, (5), 752–760
Yi H.J., Oh K.W. (1992): Neural Network based Fuzzy Production Rule Generation and its application to an Approximate Reasoning Approach. Proceedings 2nd. Int. Conference on Fuzzy Logic and Neural Networks. 333–336, lizuka, Japan
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Moraga, C., Temme, KH. (2002). Functional Equivalence between S-neural Networks and Fuzzy Models. In: Bouchon-Meunier, B., Gutiérrez-RÃos, J., Magdalena, L., Yager, R.R. (eds) Technologies for Constructing Intelligent Systems 2. Studies in Fuzziness and Soft Computing, vol 90. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1796-6_28
Download citation
DOI: https://doi.org/10.1007/978-3-7908-1796-6_28
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-7908-2504-6
Online ISBN: 978-3-7908-1796-6
eBook Packages: Springer Book Archive