Abstract
In this paper we provide two axiomatizations of the class of idempotent discrete uninorms as conservative binary operations, where an operation is conservative if it always outputs one of its input values. More precisely we first show that the idempotent discrete uninorms are exactly those operations that are conservative, symmetric, and nondecreasing in each variable. Then we show that, in this characterization, symmetry can be replaced with both bisymmetry and existence of a neutral element.
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Acknowledgements
The authors thank Gergely Kiss for fruitful discussion and valuable remarks. This research is partly supported by the internal research project R-AGR-0500-MRO3 of the University of Luxembourg.
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Couceiro, M., Devillet, J., Marichal, JL. (2018). On Idempotent Discrete Uninorms. In: Torra, V., Mesiar, R., Baets, B. (eds) Aggregation Functions in Theory and in Practice. AGOP 2017. Advances in Intelligent Systems and Computing, vol 581. Springer, Cham. https://doi.org/10.1007/978-3-319-59306-7_15
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DOI: https://doi.org/10.1007/978-3-319-59306-7_15
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