Skip to main content
Log in

Fuzzy Logic Programming and Fuzzy Control

  • Published:
Studia Logica Aims and scope Submit manuscript

Abstract

We show that it is possible to base fuzzy control on fuzzy logic programming. Indeed, we observe that the class of fuzzy Herbrand interpretations gives a semantics for fuzzy programs and we show that the fuzzy function associated with a fuzzy system of IF-THEN rules is the fuzzy Herbrand interpretation associated with a suitable fuzzy program.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Biacino, L., and G. Gerla, ‘Recursively enumerable L-sets’, Zeitschr. f. math. Logik und Grundlagen d. Math., 33:107–113, 1987.

    Google Scholar 

  2. Damásio, C.V., and L. M. Pereira, ‘Hybrid probabilistic logic programs as residuated logic programs’, in G. Brewka and L. M. Pereira, (eds.), Logic in A.I., Proceedings of JELIA’00 LNAI 1919, Springer-Verlag, 2000, pp. 57–72.

  3. Dubois, D., and H. Prade, ‘What are fuzzy rules and how to use them’, Fuzzy Sets and Systems, 84:169–185, 1996.

    Article  Google Scholar 

  4. Fitting, M., ‘Bilattices and the semantics of logic programming’, Journal of Logic Programming, 11:91–116, 1991.

    Article  Google Scholar 

  5. Fontana, A., F. Formato, and G. Gerla, Logic Programming and Soft Computing, chapter Fuzzy unification as a foundation of fuzzy logic programming, Research Studies Press, 1998, pp. 51–68.

  6. Gerla, G., ‘Decidability, partial decidability and sharpness relation for L-subsets’, Studia Logica, 46:227–238, 1987.

    Article  Google Scholar 

  7. Gerla, G., Fuzzy logic: Mathematical Tools for Approximate Reasoning. Kluwer Academic Publishers, Dordrecht, The Netherlands, 2000.

    Google Scholar 

  8. Gerla, G., ‘Fuzzy control as a fuzzy deduction system’, Fuzzy Sets and Systems, 121:409–425, 2001.

    Article  MathSciNet  Google Scholar 

  9. Goguen, J.A., ‘The logic of inexact concepts’, in D. Dubois, H. Prade, and R.R. Yager, (eds.), eadings in Fuzzy Sets for Intelligent Systems, Kaufmann, San Mateo, CA, 1993, pp. 417–441.

  10. Hájek, P., Metamathematics of Fuzzy Logic, volume 4 of Trends in Logic, Kluwer Academic Publishers, Dordrecht, August 1998.

    Google Scholar 

  11. Klir, G. J., and B. Yuan, Fuzzy sets and fuzzy logic: theory and applications, Prentice-Hall, Inc., 1995.

  12. Mamdani, E., ‘Application of fuzzy logic to approximate reasoning using linguistic systems’, Fuzzy Sets and Systems, 26:1182–1191, 1977.

    Google Scholar 

  13. Medina, J., M. Ojeda-Aciego, and P. Vojtáš, ‘Multi-adjoint logic programming with continuous semantics’, in Lecture Notes in Computer Science, volume 2173, 2001, pp. 351–364.

  14. Pavelka, J., ‘On fuzzy logic I: Many-valued rules of inference’, Zeitschr. f. math.Logik und Grundlagen d. Math., 25:45–52, 1979.

    Google Scholar 

  15. Pavelka, J., ‘On fuzzy logic II: Enriched residuated lattices and semantics of propositional calculi’, eitschr. f. math. Logik und Grundlagen d. Math., 25:119–134, 1979.

    Google Scholar 

  16. Pavelka, J., ‘On fuzzy logic III: Semantical completeness of some many-valued propositional calculi’, Zeitschr. f. math. Logik und Grundlagen d. Math., 25:447–464, 1979.

    Google Scholar 

  17. Vojtáš, P., ‘Many valued logic programming handling uncertainty in A.I.’, in Proceedings of LACS, Warsawa, 1966.

  18. Vojtáš, P., ‘Fuzzy logic programming’, Fuzzy Sets and Systems, 124:361–370, 2001.

    Article  Google Scholar 

  19. Zadeh, L. A., ‘Fuzzy logic and approximate reasoning’, Synthese, 30:407–428, 1965.

    Article  Google Scholar 

  20. Zadeh, L. A., ‘Fuzzy Sets’, Information and Control, 3:338–353, 1965.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Giangiacomo Gerla.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gerla, G. Fuzzy Logic Programming and Fuzzy Control. Stud Logica 79, 231–254 (2005). https://doi.org/10.1007/s11225-005-2977-0

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11225-005-2977-0

Keywords

Navigation