A general method for constructing left-continuous t-norms

被引：27
|
作者：
Jenei, S
Montagna, F
机构：
[1] Univ Pecs, Inst Math & Informat, H-7624 Pecs, Hungary
[2] Univ Siena, Dept Math, I-53100 Siena, Italy
来源：
FUZZY SETS AND SYSTEMS | 2003年 / 136卷 / 03期
关键词：
residuated lattice; conjunction for non-classical logics; T-norm;
D O I：
10.1016/S0165-0114(02)00275-0
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
A new method for constructing (left-continuous) t-norms is introduced and analyzed in this paper. We shall construct via embedding a left-continuous t-norm from any countable residuated totally and densely ordered commutative integral monoid. Moreover, we can construct a left-continuous t-norm from any countable, totally ordered, commutative integral monoid which is not necessarily densely ordered and residuated. A special case, the embedding of such monoids on lexicographic product spaces is investigated in detail, and several examples are demonstrated. The results shed some light to Chang's MV-algebra, to a recently proposed 'extraordinary' t-norm, and to the standard semantics of the recently introduced logic H-MTL of HJjek. (C) 2002 Elsevier Science B.V. All rights reserved.
引用
收藏
页码：263 / 282
页数：20
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