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Characterizations of idempotent discrete uninorms

Miguel Couceiro 1 Jimmy Devillet 2 Jean-Luc Marichal 2 
1 ORPAILLEUR - Knowledge representation, reasonning
Inria Nancy - Grand Est, LORIA - NLPKD - Department of Natural Language Processing & Knowledge Discovery
Abstract : In this paper we provide an axiomatic characterization of the idempotent discrete uninorms by means of three conditions only: conservativeness, symmetry, and nondecreasing monotonicity. We also provide an alternative characterization involving the bisymmetry property. Finally, we provide a graphical characterization of these operations in terms of their contour plots, and we mention a few open questions for further research.
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Submitted on : Monday, January 30, 2017 - 1:48:32 PM
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Miguel Couceiro, Jimmy Devillet, Jean-Luc Marichal. Characterizations of idempotent discrete uninorms. Fuzzy Sets and Systems, 2018, 334, pp.60-72. ⟨10.1016/j.fss.2017.06.013⟩. ⟨hal-01447513⟩



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