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Non-conventional conjunctions and implications in fuzzy logic

  • János C. Fodor
  • Tibor Keresztfalvi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 695)

Abstract

First, we make some remarks concerning the definition of connectives in fuzzy logic. We point out possible disadvantages of considering exclusively t-norms and t-conorms as proper models for the conjunction and disjunction. Coincidence of S- and R-implications is investigated by solving functional equations for conjunctions. Then, we suggest a constructive approach to axiomatics of the generalized modus ponens (GMP). Besides a special model, a particular class of conjunctions satisfying the axioms for GMP and based on the Hamacher family of t-norms is also characterized. On the other hand, the coincidence of R- and S-implications defined by the members of this class is verified.

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References

  1. 1.
    Weber, S.: A general concept of fuzzy connectives, negations and implications based on t-norms and t-conorms. Fuzzy Sets and Systems 11 (1983) 115–134Google Scholar
  2. 2.
    Dubois, D., and Prade, H.: Fuzzy sets in approximate reasoning, Part 1: Inference with possibility distributions. Fuzzy Sets and Systems 40 (1991) 143–202Google Scholar
  3. 3.
    Fodor, J. C.: On fuzzy implication operators. Fuzzy Sets and Systems 42 (1991) 293–300Google Scholar
  4. 4.
    Smets, P., and Magrez, P.: Implications in fuzzy logic. Int. J. Approximate Reasoning 1 (1987) 327–347Google Scholar
  5. 5.
    Magrez, P., and Smets, P.: Fuzzy modus ponens: a new model suitable for applications in knowledge-based systems. Internat. J. Intelligent Systems 4 (1989) 181–200Google Scholar
  6. 6.
    Hamacher, H.: Über logische Verknüpfungen unscharfer Aussagen und deren zugehörige Bewertungsfunktionen. Working Paper 75/14, RWTH Aachen, Aachen, Germany (1975)Google Scholar
  7. 7.
    Schweizer, B., and Sklar, A.: Probabilistic Metric Spaces. North-Holland, Amsterdam, 1983Google Scholar
  8. 8.
    Dubois, D., and Prade, H.: A theorem on implication functions defined from triangular norms. Stochastica VIII (1984) 267–279Google Scholar
  9. 9.
    Fodor, J. C.: A new look at fuzzy connectives. Technical Report TR 91/1, Computer Center, Eötvös L. University, Budapest, Hungary, 1991.Google Scholar
  10. 10.
    Trillas, E., and Valverde, L.: On mode and implication in approximate reasoning. In: M. M. Gupta, A. Kandel, W. Bandler, J. B. Kiszka (eds.): Approximate Reasoning in Expert Systems. North-Holland, Amsterdam, 1985, pp. 157–166Google Scholar
  11. 11.
    Fodor, J. C., and Keresztfalvi, T.: Non-standard connectives in fuzzy logic. Proc. of 2nd IEEE Int. Conf. on Fuzzy Systems, San Francisco, March 28–April 1, 1993Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • János C. Fodor
    • 1
  • Tibor Keresztfalvi
    • 1
  1. 1.Eötvös Loránd UniversityBudapest 112Hungary

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