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Aggregation via Clone Theory Approach

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New Trends in Aggregation Theory (AGOP 2019)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 981))

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Abstract

In our recent papers we have observed that the set of aggregation functions (on any bounded poset) contains all the projections and it is composition-closed. These classes of functions, called clones, are very intensively studied for decades in many different branches of mathematics.

The aim of our paper is to give an extended overview of results concerning certain important clones of aggregation functions on bounded lattices. In particular, we focus on the full clone of aggregation functions, the clone of idempotent aggregation functions, the clone of Sugeno integrals and the clone of polynomial functions.

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References

  1. Baker, K.A., Pixley, A.F.: Polynomial interpolation and the Chinese remainder theorem for algebraic systems. Math. Zeitschrift 143, 165–174 (1975)

    Article  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  3. Botur, M., Halaš, R., Mesiar, R., Pócs, J.: On generating of idempotent aggregation functions on finite lattices. Inf. Sci. 430–431, 39–45 (2018)

    Article  MathSciNet  Google Scholar 

  4. Calvo, T., Mayor, G., Mesiar, R. (eds.): Aggregation Operators. Physica Verlag, Heidelberg (2002)

    MATH  Google Scholar 

  5. Chajda, I.: Algebraic Theory of Tolerance Relations. Monograph Series. Palacký University Olomouc, Olomouc (1991)

    MATH  Google Scholar 

  6. Couceiro, M., Marichal, J.-L.: Characterizations of discrete Sugeno integrals as polynomial functions over distributive lattices. Fuzzy Sets Syst. 161, 694–707 (2010)

    Article  MathSciNet  Google Scholar 

  7. Goldstern, M., Shelah, S.: There are no infinite order polynomially complete lattices, after all. Algebra Universalis 42(1–2), 49–57 (1999)

    Article  MathSciNet  Google Scholar 

  8. Grabisch, M., Marichal, J.-L., Mesiar, R., Pap, E.: Aggregation Functions. Cambridge University Press, Cambridge (2009)

    Book  Google Scholar 

  9. Grätzer, G.: Lattice Theory: Foundation. Birkhäuser, Basel (2011)

    Book  Google Scholar 

  10. Halaš, R., Kurač, Z., Mesiar, R., Pócs, J.: Binary generating set of the clone of idempotent aggregation functions on bounded lattices. Inf. Sci. 462, 367–373 (2018)

    Article  MathSciNet  Google Scholar 

  11. Halaš, R., Mesiar, R., Pócs, J.: A new characterization of the discrete Sugeno integral. Inf. Fusion 29, 84–86 (2016)

    Article  Google Scholar 

  12. Halaš, R., Mesiar, R., Pócs, J.: Congruences and the discrete Sugeno integrals on bounded distributive lattices. Inf. Sci. 367–368, 443–448 (2016)

    Article  Google Scholar 

  13. Halaš, R., Mesiar, R., Pócs, J.: Generators of Aggregation Functions and Fuzzy Connectives. IEEE Trans. Fuzzy Syst. 24(6), 1690–1694 (2016)

    Article  Google Scholar 

  14. Halaš, R., Mesiar, R., Pócs, J.: On generating sets of the clone of aggregation functions on finite lattices. Inf. Sci. 476, 38–47 (2019)

    Article  MathSciNet  Google Scholar 

  15. Halaš, R., Mesiar, R., Pócs, J., Torra, V.: A note on some algebraic properties of discrete Sugeno integrals. Fuzzy Sets Syst. 355, 110–120 (2019)

    Article  MathSciNet  Google Scholar 

  16. Halaš, R., Pócs, J.: On lattices with a smallest set of aggregation functions. Inf. Sci. 325, 316–323 (2015)

    Article  MathSciNet  Google Scholar 

  17. Halaš, R., Pócs, J.: On the clone of aggregation functions on bounded lattices. Inf. Sci. 329, 381–389 (2016)

    Article  Google Scholar 

  18. Marichal, J.-L.: Weighted lattice polynomials. Discrete Math. 309(4), 814–820 (2009)

    Article  MathSciNet  Google Scholar 

  19. Mayor, G., Torrens, J.: Triangular norms on discrete settings. In: Klement, E.P., Mesiar, R. (eds.) Logical, Algebraic, Analytic and Probabilistic Aspects of Triangular Norms, pp. 189–230. Elsevier, Amsterdam (2005)

    Chapter  Google Scholar 

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Acknowledgments

The authors were supported by the project of Grant Agency of the Czech Republic (GAČR) no. 18-06915S. The second author was also supported by the Slovak Research and Development Agency under the contract No. APVV-16-0073.

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Authors and Affiliations

  1. Department of Algebra and Geometry, Faculty of Science, Palacký University Olomouc, 17. listopadu 12, 771 46, Olomouc, Czech Republic

    Radomír Halaš & Jozef Pócs

  2. Mathematical Institute, Slovak Academy of Sciences, Grešákova 6, 040 01, Košice, Slovakia

    Jozef Pócs

Authors
  1. Radomír Halaš
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  2. Jozef Pócs
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Correspondence to Radomír Halaš .

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Editors and Affiliations

  1. Faculty of Science, Palacký University, Olomouc, Czech Republic

    Radomír Halaš

  2. Systems Research Institute, Polish Academy of Science, Warsaw, Poland

    Marek Gagolewski

  3. Slovak University of Technology, Bratislava, Slovakia

    Radko Mesiar

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Halaš, R., Pócs, J. (2019). Aggregation via Clone Theory Approach. In: Halaš, R., Gagolewski, M., Mesiar, R. (eds) New Trends in Aggregation Theory. AGOP 2019. Advances in Intelligent Systems and Computing, vol 981. Springer, Cham. https://doi.org/10.1007/978-3-030-19494-9_23

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