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Aggregation Functions Defined by t-Norms and t-Conorms

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Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 12))

Abstract

We introduce a class of aggregation functions by the help of continuous t-norms and t-conorms. The general functional forms of such aggregations is determined. Associativity and idempotency are also studied separately.

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References

  1. G. De Rham, Sur quelques courbes définies par des équations fonctionelles, Rend. Sem. Mat. Univ. Politec. Torino 16 (1956) 101–113.

    Google Scholar 

  2. J. Fodor and M. Roubens, Fuzzy Preference Modelling and Multicriteria Decision Support ( Kluwer, Dordrecht, 1994 ).

    Book  MATH  Google Scholar 

  3. J.C. Fodor, R.R. Yager and A. Rybalov, Structure of uni-norms, Inf. Sci. (to appear).

    Google Scholar 

  4. L.W. Fling and K.S. Pu, “An axiomatic approach to rational decision making in a fuzzy environment”, in: Fuzzy Sets and Their Applications to Cognitive and Decision Processes, eds. L.A. Zadeh et al. ( Academic Press, New York, 1975 ) pp. 227–256.

    Google Scholar 

  5. C.H. Ling, Representation of associative functions, Publ. Math. Debrecen 12 (1965) 182–212.

    Google Scholar 

  6. G. Mayor, On a family of quasi-arithmetic means, Aeq. Math 48 (1994) 137–142.

    Article  MathSciNet  MATH  Google Scholar 

  7. G. Mayor and E. Trillas, On the representation of some aggregation functions, Proc. ISMVL (1986) 110–114.

    Google Scholar 

  8. R.R. Yager and A. Rybalov, Uninorm aggregation operators, Fuzzy Sets and Systems 80 (1996) 111–120.

    Article  MathSciNet  MATH  Google Scholar 

  9. H.-J. Zimmermann and P. Zysno, Latent connectives in human decision making, Fuzzy Sets and Systems 4 (1980) 37–51.

    Article  MATH  Google Scholar 

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© 1998 Springer-Verlag Berlin Heidelberg

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Fodor, J., Calvo, T. (1998). Aggregation Functions Defined by t-Norms and t-Conorms. In: Bouchon-Meunier, B. (eds) Aggregation and Fusion of Imperfect Information. Studies in Fuzziness and Soft Computing, vol 12. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1889-5_3

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  • DOI: https://doi.org/10.1007/978-3-7908-1889-5_3

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-662-11073-7

  • Online ISBN: 978-3-7908-1889-5

  • eBook Packages: Springer Book Archive

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