Abstract
By analogy with the usual extension of the group operation from the positive cone of an ordered Abelian group into the whole group, a construction—called symmetrization—is defined and it is related to the rotation construction [Jenei, On the structure of rotation-invariant semigroups, Archive for Mathematical Logic 42 (2003) 489–514]. Symmetrization turns out to be a kind of dualized rotation. A characterization is given for the left-continuous t-conorms for which their symmetrization is a uninorm. As a by-product a new family of involutive uninorms is introduced.
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