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Associative and preassociative functions

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Abstract

We investigate the associativity property for functions of multiple arities and introduce and discuss the more general property of preassociativity, a generalization of associativity which does not involve any composition of functions.

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References

  1. Beliakov, G., Pradera, A., Calvo, T.: Aggregation Functions: A Guide for Practitioners. Studies in Fuziness and Soft Computing, vol. 221. Springer, Berlin (2007)

    Google Scholar 

  2. Calvo, T., Kolesárová, A., Komorníková, M., Mesiar, R.: Aggregation operators: properties, classes and construction methods. In: Aggregation Operators. New Trends and Applications. Stud. Fuzziness Soft Comput., vol. 97, pp. 3–104. Physica-Verlag, Heidelberg (2002)

    Chapter  Google Scholar 

  3. Couceiro, M., Marichal, J.-L.: Associative polynomial functions over bounded distributive lattices. Order 28, 1–8 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  4. Couceiro, M., Marichal, J.-L.: Aczélian n-ary semigroups. Semigroup Forum 85, 81–90 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  5. Grabisch, M., Marichal, J.-L., Mesiar, R., Pap, E.: Aggregation Functions. Encyclopedia of Mathematics and Its Applications, vol. 127. Cambridge University Press, Cambridge (2009)

    Book  MATH  Google Scholar 

  6. Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms. Trends in Logic—Studia Logica Library, vol. 8. Kluwer Academic, Dordrecht (2000)

    MATH  Google Scholar 

  7. Marichal, J.-L.: Aggregation operators for multicriteria decision aid. Ph.D. Thesis, Department of Mathematics, University of Liège, Liège, Belgium (1998)

  8. Schweizer, B., Sklar, A.: Probabilistic Metric Spaces. North-Holland Series in Probability and Applied Mathematics. North-Holland, Amsterdam (1983). New edition in: Dover, New York (2005)

    MATH  Google Scholar 

  9. Yager, R.R.: Quasi-associative operations in the combination of evidence. Kybernetes 16, 37–41 (1987)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

The authors would like to thank the anonymous reviewer for timely and helpful suggestions for improving the organization of this paper. They are also grateful to Henri Prade for calling their attention to reference [9]. This research is supported by the internal research project F1R-MTH-PUL-12RDO2 of the University of Luxembourg.

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Authors and Affiliations

  1. Mathematics Research Unit, FSTC, University of Luxembourg, 6, rue Coudenhove-Kalergi, 1359, Luxembourg, Luxembourg

    Jean-Luc Marichal & Bruno Teheux

Authors
  1. Jean-Luc Marichal
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  2. Bruno Teheux
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Correspondence to Jean-Luc Marichal.

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Communicated by Mikhail Volkov.

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Marichal, JL., Teheux, B. Associative and preassociative functions. Semigroup Forum 89, 431–442 (2014). https://doi.org/10.1007/s00233-014-9580-5

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  • DOI: https://doi.org/10.1007/s00233-014-9580-5

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