Geodesic
On the structure of continuous uninorms
Kybernetika, Tome 43 (2007) no. 2, pp. 183-196.

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Uninorms were introduced by Yager and Rybalov [13] as a generalization of triangular norms and conorms. We ask about properties of increasing, associative, continuous binary operation $U$ in the unit interval with the neutral element $e\in [0,1]$. If operation $U$ is continuous, then $e=0$ or $e=1$. So, we consider operations which are continuous in the open unit square. As a result every associative, increasing binary operation with the neutral element $e\in (0,1)$, which is continuous in the open unit square may be given in $[0,1)^2$ or $(0,1]^2$ as an ordinal sum of a semigroup and a group. This group is isomorphic to the positive real numbers with multiplication. As a corollary we obtain the results of Hu, Li [7].
Classification : 03B52, 03E72, 06F05
Keywords: uninorms; continuity; $t$-norms; $t$-conorms; ordinal sum of semigroups 
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Drygaś, Paweł. On the structure of continuous uninorms. Kybernetika, Tome 43 (2007) no. 2, pp. 183-196. http://geodesic.mathdoc.fr/item/KYB_2007__43_2_a5/