On the relationship between the rotation construction and ordered Abelian groups

Sandor Jenei

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On the relationship between the rotation construction and ordered Abelian groups

机译：关于自转构造与有序阿贝尔群之间的关系

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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.

机译：与通常将组运算从有序Abelian组的正锥扩展到整个组类似，定义了一种称为对称化的结构，它与旋转结构有关[Jenei，关于旋转不变的结构Semigroups，Archive for Mathematical Logic 42（2003）489-514]，对称化是一种双重旋转。给出了左连续t型锥的对称性的特征。作为副产品，引入了新的对合单体。

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来源
《Fuzzy sets and systems》 |2010年第2期|277-284|共8页
作者
Sandor Jenei;
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作者单位

Institute for Discrete Mathematics and Geometry, Technical University of Vienna, Wiedner Hauptstrasse 8-10, A-1040 Vienna, Austria Institute of Mathematics and Informatics, University of Pics, Ifjusag u. 6, H-7624 Pecs, Hungary;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
rotation construction; symmetrization; associativity; uninorm;

机译：旋转结构;对称化关联性统一;

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On the relationship between the rotation construction and ordered Abelian groups

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