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Benchmarking over Distributive Lattices

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Book cover Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2016)

Abstract

We provides an axiomatic characterization of preorders in lattices that are representable as benchmarking procedure. We show that the key axioms are related to compatibility with lattice operations.

This paper propose also a characterization and a generalization of Sugeno integral in a ordinal framework.

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Notes

  1. 1.

    I would like to thank Esteban Indurain for pointing out this problem.

References

  1. Birkhoff, G.: Lattice Theory, Colloquium Pub, vol. 25. American Mathematical Society, Providence, R.I. (1967)

    Google Scholar 

  2. Couceiro, M., Marichal, J.-L.: Polynomial functions over bounded distributive lattices. J. Mul-Valued Log S 18, 247–256 (2012)

    MathSciNet  MATH  Google Scholar 

  3. Couceiro, M., Marichal, J.L.: Characterizations of discrete Sugeno integrals as lattice polynomial functions. In: Proceedings of the 30th Linz Seminar on Fuzzy Set Theory (LINZ2009), pp. 17–20 (2009)

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  5. Chambers, C.P., Miller, A.D.: Scholarly influence. J. Econ. Theory 151(1), 571–583 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  6. Chambers, C.P., Miller, A.D.: Benchmarking, working paper (2015)

    Google Scholar 

  7. Caspard, N., Leclerc, B., Monjardet, B.: Finite Ordered Sets. Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge (2012)

    MATH  Google Scholar 

  8. Davey, B.A., Priestley, H.A.: Introduction to Lattices and Order. Cambridge University Press, New York (2002)

    Book  MATH  Google Scholar 

  9. Fishburn, P.C.: Signed order and power set extensions. J. Econ. Theory 56, 1–19 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  10. Grabisch, M., Marichal, J.L., Mesiar, R., Pap, E.: Aggregation Functions. Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge (2009)

    Book  MATH  Google Scholar 

  11. Grätzer, G.: General Lattice Theory. Birkhäuser Verlag, Berlin (2003)

    MATH  Google Scholar 

  12. Halas̆ R., Mesiar, R., Pócs, J.: A new characterization of the discrete Sugeno integral. Inform. Fusion 29, 84–86 (2016)

    Google Scholar 

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Correspondence to Marta Cardin .

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© 2016 Springer International Publishing Switzerland

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Cardin, M. (2016). Benchmarking over Distributive Lattices. In: Carvalho, J., Lesot, MJ., Kaymak, U., Vieira, S., Bouchon-Meunier, B., Yager, R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2016. Communications in Computer and Information Science, vol 610. Springer, Cham. https://doi.org/10.1007/978-3-319-40596-4_11

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  • DOI: https://doi.org/10.1007/978-3-319-40596-4_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40595-7

  • Online ISBN: 978-3-319-40596-4

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