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.
I would like to thank Esteban Indurain for pointing out this problem.
References
Birkhoff, G.: Lattice Theory, Colloquium Pub, vol. 25. American Mathematical Society, Providence, R.I. (1967)
Couceiro, M., Marichal, J.-L.: Polynomial functions over bounded distributive lattices. J. Mul-Valued Log S 18, 247–256 (2012)
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)
Couceiro, M., Marichal, J.L.: Characterizations of discrete Sugeno integrals as polynomial functions over distributive lattices. Fuzzy Set Syst. 161, 694–707 (2010)
Chambers, C.P., Miller, A.D.: Scholarly influence. J. Econ. Theory 151(1), 571–583 (2014)
Chambers, C.P., Miller, A.D.: Benchmarking, working paper (2015)
Caspard, N., Leclerc, B., Monjardet, B.: Finite Ordered Sets. Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge (2012)
Davey, B.A., Priestley, H.A.: Introduction to Lattices and Order. Cambridge University Press, New York (2002)
Fishburn, P.C.: Signed order and power set extensions. J. Econ. Theory 56, 1–19 (1992)
Grabisch, M., Marichal, J.L., Mesiar, R., Pap, E.: Aggregation Functions. Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge (2009)
Grätzer, G.: General Lattice Theory. Birkhäuser Verlag, Berlin (2003)
Halas̆ R., Mesiar, R., Pócs, J.: A new characterization of the discrete Sugeno integral. Inform. Fusion 29, 84–86 (2016)
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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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