Skip to main content

Functional Equivalence between S-neural Networks and Fuzzy Models

  • Chapter
Technologies for Constructing Intelligent Systems 2

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 90))

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

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

    Article  MathSciNet  MATH  Google Scholar 

  • Amari S. (1968): Geometrical Theory of Information. Kyoritsu-Shuppan, Tokyo

    Google Scholar 

  • Benitez J.M., Castro J.L., Requena I. (1997): Are neural networks black boxes? IEEE Trans. on Neural Networks 8, 1156–1163

    Article  Google Scholar 

  • Dombi J. (1982): Basic concepts for a theory of evaluation: The aggregative operator. European Jr. Operation Research 10, 282–293

    Article  MathSciNet  MATH  Google Scholar 

  • Dubois D., Prade H. (1985): A review of fuzzy set aggregation connectives. Information Sciences 36, 85–121

    Article  MathSciNet  MATH  Google Scholar 

  • Funahashi K.I. (1989): On the approximate realization of continuous mappings by neural networks. Neural Networks 2, 183–192

    Article  Google Scholar 

  • Georgiou G.M. (1992): Parallel distributed processing in the complex domain. Ph.D. Thesis, Dept. C. Sc., Tulane University, New Orleans, Lousiana

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Hornik K., Stinchcombe M., White H. (1989): Multilayer Feedforward Networks are universal approximators. Neural Networks 2, 359–366

    Article  Google Scholar 

  • Jang J.S.R. (1993): ANFIS: Adaptive Network based Fuzzy Inference System. IEEE Trans. on Systems, Man and Cybernetics 23, (3), 665–685

    Article  Google Scholar 

  • Jang J.S.R., Sun C.T. (1995): Neuro—fuzzy Modeling and Control. Proceedings IEEE 83, (3), 378–406

    Article  Google Scholar 

  • 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

    Article  MathSciNet  MATH  Google Scholar 

  • Kosko B. (1994): Fuzzy systems as universal approximators. IEEE Trans. Computers 43, (11), 1324–1333

    Article  Google Scholar 

  • Keller J.M., Tager R.R., Tahani H. (1992): Neural Network implementation of fuzzy logic. Fuzzy Sets and Systems 45, (1), 1–12

    Article  MathSciNet  MATH  Google Scholar 

  • Moraga C. (1997): Properties of Parametric Feedforward Networks. Proceedings XXIII Conferencia Latinoamericana de Informatica, 861–870, Valparaiso, Chile

    Google Scholar 

  • Silvert W. (1979): Symmetric summation: A class of operations on fuzzy sets. IEEE Trans. on Systems, Man and Cybernetics 9, 659–667

    MathSciNet  Google Scholar 

  • Takagi H., Hayashi I. (1991): NN-driven fuzzy reasoning. Int. Journal of Approximate Reasoning 5, (3), 191–212

    Article  MATH  Google Scholar 

  • 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

    Article  MATH  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints 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-Ríos, 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

Publish with us

Policies and ethics