On the relationship between the rotation construction and ordered Abelian groups

Authors:
Sándor Jenei
Affiliations:
Institute for Discrete Mathematics and Geometry, Technical University of Vienna, Wiedner Hauptstrasse 8-10, A--1040 Vienna, Austria and Institute of Mathematics and Informatics, University of P ...
Venue:
Fuzzy Sets and Systems
Year:
2010

Citing 2
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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.