Characterizing when an ordinal sum of t-norms is a t-norm on bounded lattices
type: Item
instance of: scholarly article
title: Characterizing when an ordinal sum of t-norms is a t-norm on bounded lattices
zbMATH Open document ID: 1272.03112
published in: Fuzzy Sets and Systems
publication date: 2012-12-20T00:00:00Z
review text: Ordinal sums of triangular norms (t-norms) on bounded lattices are studied. Originally, t-norms were defined on the unit interval. Later, a generalization on a more general algebraic structure, namely bounded lattices, was proposed. It turned out that in this case, an ordinal sum in Clifford's sense of t-norms may not be a t-norm. Hence, it is important to state necessary and sufficient conditions for ensuring whether an ordinal sum of arbitrary t-norms on a bounded lattice is a t-norm, too. In this paper, several conditions are formulated in order to verify whether an ordinal sum of a particular family of t-norms is a t-norm. First, ordinal sums with one t-norm are studied. The general case of an ordinal sum of a family of t-norms on pairwise disjoint subintervals is also covered. Many examples of ordinal sums of t-norms on non-linearly ordered bounded lattices are provided.
Mathematics Subject Classification ID: 03B52
zbMATH DE Number: 6117649
zbMATH Keywords: triangular norm
zbMATH Keywords: ordinal sum
zbMATH Keywords: bounded lattice
author: Jesús Medina
reviewed by: Antonín Dvořák
MaRDI profile type: Publication
full work available at URL: j.fss.2012.03.002
OpenAlex ID: W2035295995
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DOI: 10.1016/J.FSS.2012.03.002
description: scientific article; zbMATH DE number 6117649