Abstract
In this paper we describe the class of idempotent n-ary uninorms on a given chain. When the chain is finite, we axiomatize the latter class by means of the following conditions: associativity, quasitriviality, symmetry, and nondecreasing monotonicity. Also, we show that associativity can be replaced with bisymmetry in this new axiomatization.
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Notes
- 1.
This paper is also an extended version of [7].
- 2.
When \(X=X_k\) for some integer \(k\ge 1\), the graphical representation of \(f_{\preceq }\) is then obtained by joining the points \((1,1),\ldots ,(k,k)\) by line segments.
- 3.
To simplify the representation of the connected components, we omit edges that can be obtained by transitivity.
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Acknowledgments
The first author is supported by the Luxembourg National Research Fund under the project PRIDE 15/10949314/GSM. The second author is also supported by the Hungarian National Foundation for Scientific Research, Grant No. K124749.
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Devillet, J., Kiss, G., Marichal, JL. (2019). On Idempotent n-ary Uninorms. In: Torra, V., Narukawa, Y., Pasi, G., Viviani, M. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2019. Lecture Notes in Computer Science(), vol 11676. Springer, Cham. https://doi.org/10.1007/978-3-030-26773-5_9
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DOI: https://doi.org/10.1007/978-3-030-26773-5_9
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