On the convex combination of left-continuous t-norms

被引：0
|
作者：
Jenei S. [1 ]
机构：
[1] Institute of Mathematics and Informatics, University of Pécs, H-7624 Pécs
来源：
aequationes mathematicae | 2006年 / 72卷 / 1-2期
关键词：
Arithmetic mean; Associative functions; Associativity equation; t-norms;
D O I：
10.1007/s00010-006-2840-z
中图分类号：
学科分类号：
摘要：
A conjecture of C. Alsina M. J. Frank and B. Schweizer concerning the convex combinations of t-norms [4] is proved for certain left-continuous t-norms. It is shown that a nontrivial convex combination of two left-continuous t-norms is never a t-norm (in fact the associativity property of t-norms is violated) provided that the two t-norms have the same involutive u-level set for some u [0 1[. The proof is motivated by a geometrical understanding of associativity. © Birkhäuser Verlag, Basel, 2006.
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页码：47 / 59
页数：12
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