Prospects for Truth Valuation in Fuzzy Extended Logic

  • Vesa A. Niskanen
Part of the Studies in Computational Intelligence book series (SCI, volume 530)


Lotfi Zadeh’s fuzzy extended logic is applied to approximate linguistic reasoning. The prevailing fuzzy reasoning methods still seem to have some bivalent commitments in truth valuation and thus an alternative many-valued resolution is presented at meta-level.


Fuzzy extended logic Truth valuation 



I express my thanks to Professor Lotfi Zadeh for his valuable ideas and comments to my examination


  1. 1.
    Zadeh, L.: Toward extended fuzzy logic - a first step. Fuzzy Sets Syst. 160, 3175–3181 (2009)CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Zadeh, L.: From computing with numbers to computing with words - from manipulation of measurements to manipulation of perceptions. IEEE Trans. Circuits Syst. 45, 105–119 (1999)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Zadeh, L.: From search engines to question answering systems? the problems of world knowledge, relevance, deduction and precisiation. In: Sanchez, E. (ed.) Fuzzy Logic and the Semantic Web. Elsevier, Amsterdam (2006)Google Scholar
  4. 4.
    Zadeh, L.: Fuzzy Logic and Approximate Reasoning. Synthese 30, 407–428 (1975)CrossRefMATHGoogle Scholar
  5. 5.
    Zadeh, L.: Fuzzy logic = computing with words. IEEE Trans. Fuzzy Syst. 2, 103–111 (1996)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Zadeh, L.: Toward a perception-based theory of probabilistic reasoning with imprecise probabilities. J. Stat. Planning Infer. 105(2), 233–264 (2002)CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    Zadeh, L.: Toward a theory of fuzzy information granulation and Its centrality in human reasoning and Fuzzy logic. Fuzzy Sets Syst. 90(2), 111–127 (1997)CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Fetzer, J.: Philosophy of Science. Paragon House, New York (1993)Google Scholar
  9. 9.
    Hempel, C.: Philosophy of Natural Science. Prentice Hall, Englewood Cliffs (1966)Google Scholar
  10. 10.
    Nagel, E.: The Structure of Science. Routledge & Kegan Paul, London (1961)Google Scholar
  11. 11.
    Niskanen, V.A.: A Meta-level approach to approximate probability. In R. Setchi et al. (Eds.): Lecture Notes in Artificial Intelligence, Vol. 6279, pp. 116–123, Springer, Heidelberg (2010)Google Scholar
  12. 12.
    Niskanen, V.A.: Application of approximate reasoning to hypothesis verification. J. Intell. Fuzzy Syst. 21(5), 331–339 (2010)MATHMathSciNetGoogle Scholar
  13. 13.
    Niskanen, V.A.: Application of Zadeh’s impossibility principle to approximate explanation. Proceedings of the IFSA ’09 Conference, 352–360, Lisbon (2009)Google Scholar
  14. 14.
    Popper, K.: The Logic of Scientific Discovery. Hutchinson, London (1959)Google Scholar
  15. 15.
    Rescher, N.: Scientific Explanation. The Free Press, New York (1970)Google Scholar
  16. 16.
    Von Wright, G.H.: Explanation and Understanding. Cornell University Press, Cornell (1971)Google Scholar
  17. 17.
    Niskanen, V.A.: Metric truth as a basis for fuzzy linguistic reasoning. Fuzzy Sets Syst. 57(1), 1–25 (1993)CrossRefMathSciNetGoogle Scholar
  18. 18.
    Niskanen, V.A.: Soft computing methods in human sciences, studies in fuzziness and soft computing, vol. 134. Springer Verlag, Berlin (2004)Google Scholar
  19. 19.
    Gadamer, H.-G.: Truth and Method. Sheed & Ward, London (1975)Google Scholar
  20. 20.
    Haack, S.: Philosophy of Logics. Cambridge University Press, Cambridge (1978)Google Scholar
  21. 21.
    Kleene, S.: Mathematical Logic. Wiley, New York (1976)Google Scholar
  22. 22.
    Niiniluoto, I.: Truthlikeness. Reidel, Dordrecht (1987)Google Scholar
  23. 23.
    Niskanen, V.A.: Fuzzy systems and scientific method - meta-level reflections and prospects. In R. Seising (Ed.) Fuzzy Set Theory - Philosophy, Logics, and Criticism, Springer, pp. 51–82 (2009)Google Scholar
  24. 24.
    Bandemer, H., Näther. Kluwer, W.: Fuzzy Data Analysis (1992)Google Scholar
  25. 25.
    Dubois, D., Prade, H.: Fuzzy sets in approximate reasoning, Part 1: inference with possibility distributions. Fuzzy Sets Syst. 40, 143–202 (1991)CrossRefMATHMathSciNetGoogle Scholar
  26. 26.
    Approaches, Logical: Dubois, D., et al.: Fuzzy sets in approximate reasoning, Part 2. Fuzzy Sets Syst. 40, 203–244 (1991)Google Scholar
  27. 27.
    Grzegorzewski, P., et al. (Eds.).: Soft Methods in Probability, Statistics and Data Analysis. Physica Verlag, Heidelberg (2002)Google Scholar

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© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of Economics and ManagementUniversity of HelsinkiHelsinkiFinland

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