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55 th International Symposium on Functional Equations

Hongwa Hotel, Chengdu, China, June 1118, 2017

On conservative and associative operations on nite chains

Jimmy Devillet

University of Luxembourg

(joint work with Miguel Couceiro and Jean-Luc Marichal)

We provide a full description of the class of conservative, associative, and symmet- ric operations F: X2 → X, where X is an arbitrary nite chain. Here, an operation F: X2 → X is conservative if F(x, y) ∈ {x, y} for all x, y ∈ X. We put a particular emphasis on the graphical properties of these operations by looking into their contour plots. We also investigate and describe the subclass of operations that are nonde- creasing in each variable and we show how this description is related to the so-called single-peaked permutations.

References

1. M. Couceiro, J. Devillet, and J.-L. Marichal. Characterizations of idempotent discrete uninorms. Fuzzy Sets and Systems. Submitted for revision. arXiv:1701.07253

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