  We consider the interval $]{-1},1[$ and intend to endow it with an algebraic
structure like a ring. The motivation lies in decision making, where scales
that are symmetric w.r.t. 0 are needed in order to represent a kind of symmetry
in the behaviour of the decision maker. A former proposal due to Grabisch was
based on maximum and minimum. In this paper, we propose to build our structure
on t-conorms and t-norms, and we relate this construction to uninorms. We show
that the only way to build a group is to use strict t-norms, and that there is
no way to build a ring. Lastly, we show that the main result of this paper is
connected to the theory of ordered Abelian groups.
