Generalizing the migrativity of continuous t-norms
type: Item
instance of: scholarly article
title: Generalizing the migrativity of continuous t-norms
zbMATH Open document ID: 1268.03028
author: Yao Ouyang
published in: Fuzzy Sets and Systems
publication date: 2012-12-04T00:00:00Z
review text: The paper studies the migrativity property for continuous t-norms. In Section 1, two definitions which establish when a binary operation \(T:[0, 1]^2 \rightarrow [0, 1]\) is \(\alpha\)-migrative and \(\alpha\)-migrative with respect to a fixed t-norm \(T_0\) are recalled. Section 2 briefly recalls the definition of a t-norm and its representation as an ordinal sum. In the next section, continuous t-norms \(T\) which satisfy the relation \(T(\lambda_1x, \lambda_2y)=\lambda_3T(x,y)\) for given \(\lambda_i \in (0, 1]\), \(i=1,2,3\), with \(\lambda_1\geq \lambda_2 >\lambda_3\), are defined. In Theorem 3.2, a necessary and sufficient condition to satisfy that relation is proved. Other conditions are given by Corollaries 3.1 and 3.2 for additional conditions imposed for \(\lambda_1\) and \(\lambda_2\). Section 4 studies other cases: \(\lambda_1>\lambda_2=\lambda_3\) and \(\lambda_1=\lambda_2=\lambda_3\). In further papers, the author aims to investigate other binary operations and to extend the product from the relation investigated in this paper to other continuous t-norms.
reviewed by: Ion Iancu
Mathematics Subject Classification ID: 03B52
Mathematics Subject Classification ID: 68T27
zbMATH DE Number: 6112225
zbMATH Keywords: migrativity
zbMATH Keywords: continuous t-norms
zbMATH Keywords: strict t-norms
zbMATH Keywords: additive generator
MaRDI profile type: Publication
full work available at URL: j.fss.2012.03.008
OpenAlex ID: W2047725642
DOI: 10.1016/J.FSS.2012.03.008
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description: scientific article; zbMATH DE number 6112225