Some results of weighted quasi-arithmetic mean of continuous triangular norms
type: Item
instance of: scholarly article
title: Some results of weighted quasi-arithmetic mean of continuous triangular norms
zbMATH Open document ID: 1158.03016
author: Yao Ouyang
author: Jin-Xuan Fang
published in: Information Sciences
publication date: 2008-11-19T00:00:00Z
review text: Let \(T_1\) and \(T_2\) be two continuous t-norms, \(f:[0,1]\to[-\infty,\infty]\) be strictly monotone. Then the function \(T(x,y)=f^{-1}(pf(T_1(x,y))+(1-p)f(T_2(x,y)))\), where \(p\in(0,1)\), is called the weighted quasi-arithmetic mean of \(T_1\) and \(T_2\) with respect to \(f\). This function satisfies all properties of t-norms except associativity. The authors investigate the associativity of the weighted quasi-arithmetic mean for several classes of continuous t-norms. Some results on convex combination of continuous t-norms are generalized. Several methods coming from functional equations are applied and various open problems are stated.
reviewed by: Michał Baczyński
Mathematics Subject Classification ID: 03B52
Mathematics Subject Classification ID: 39B22
zbMATH DE Number: 5368817
zbMATH Keywords: continuous triangular norm
zbMATH Keywords: weighted quasi-arithmetic mean
zbMATH Keywords: convex combination
MaRDI profile type: Publication
full work available at URL: j.ins.2008.07.007
OpenAlex ID: W2043196595
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DOI: 10.1016/J.INS.2008.07.007
description: scientific article; zbMATH DE number 5368817