Constructions of quotient algebras via triangular norms

被引：2

作者：

Han, Jeong Soon ^{[2
]}

Kim, Hee Sik ^{[1
]}

Neggers, J. ^{[3
]}

机构：

[1] Hanyang Univ, Dept Math, Seoul 133791, South Korea

[2] Hanyang Univ, Dept Appl Math, Ahnsan 426791, South Korea

[3] Univ Alabama, Dept Math, Tuscaloosa, AL 35487 USA

来源：

MATHEMATICA SLOVACA | 2010年 / 60卷 / 03期

关键词：

d-algebra; (fuzzy) triangular norm; (fuzzy) d*-ideal; magnitude;

D O I：

10.2478/s12175-010-0012-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, properties of certain real-valued mappings Delta on binary systems X which satisfy versions of the triangle inequality are investigated. For example, via a quotient construction using Ker Delta = {x: Delta(x) = 0} it is shown that X/Ker Delta is a d-algebra if X is a d-algebra. In addition fuzzy versions of these triangular norms and their properties are considered as well. Finally boundedness conditions on Delta and a concept of magnitude are both introduced and some consequences are derived.

引用

页码：279 / 288

页数：10

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