On the direct decomposability of strong negations and S-implication operators on product lattices

被引：50
作者：
Karacal, Funda [1 ]
机构：
[1] Karadeniz Tech Univ, Dept Math, TR-61080 Trabzon, Turkey
来源：
INFORMATION SCIENCES | 2006年 / 176卷 / 20期
关键词：
strong negation; product lattice; t-norm; S-implication operator;
D O I：
10.1016/j.ins.2005.12.010
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In this paper, we discuss the direct product of strong negations. We characterize strong negations on product lattices that are direct products of strong negations. Furthermore, we present a method for constructing t-norms on product lattices which are not direct products. This method is quite general and useful to generate a wide class of such t-norms and solves an open problem posed in 2003 by Jenei and De Baets. Finally, we study direct decompositions of S-implication operators on product lattices. (C) 2005 Elsevier Inc. All rights reserved.
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收藏
页码：3011 / 3025
页数：15
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