NMŁ, a schematic extension of F. Esteva and L. Godo's logic MTL
type: Item
instance of: scholarly article
title: NMŁ, a schematic extension of F. Esteva and L. Godo's logic MTL
zbMATH Open document ID: 1060.03044
author: Bao-Shu Wang
author: Fang Ren
author: Sanmin Wang
published in: Fuzzy Sets and Systems
publication date: 2005-01-11T00:00:00Z
review text: The authors study an extension of the MTL logic of \textit{F. Esteva} and \textit{L. Godo} [ibid. 124, 271--288 (2001; Zbl 0994.03017)] by defining the new fuzzy logic NMŁ. The corresponding standard algebra is \(([0,1], *_J, \rightarrow_J, \max, \min, 0,1)\), where \(*_J : [0,1]^2\to[0,1]\) is defined as \((a*_J b) = 0\) if \(a + b \leq 1\), \((a*_J b) = (a + b - 2/3)\) if \(1/3 < 1 - a< b < 2/3\), \((a*_J b) = \min(a,b)\) otherwise for all \(a,b\in [0,1]\), and \(\rightarrow_ J : [0,1]^2\to[0,1]\) is defined as \((a\rightarrow_ J b) = 1\) if \(a\leq b\), \((a\rightarrow_ J b) = 2/3 -a +b\) if \(1/3 < b < a < 2/3\), \((a\rightarrow_ J b) = \max(1 - a,b)\) otherwise for all \(a,b\in [0,1]\). Note that \(*_J\) stands for the t-norm due to \textit{S. Jenei} [ibid. 110, 157--174 (2000; Zbl 0941.03059)]. As \textit{S. Jenei} and \textit{F. Montagna} [Stud. Log. 70, 183--192 (2002; Zbl 0997.03027)] have proved a completeness theorem for the MTL logic, here the authors prove an analogous result for the NMŁ logic.
reviewed by: Salvatore Sessa
Mathematics Subject Classification ID: 03B52
zbMATH DE Number: 2126004
zbMATH Keywords: left continuous t-norm
zbMATH Keywords: extension of MTL logic
zbMATH Keywords: fuzzy logic
Wikidata QID: Q59306584
MaRDI profile type: Publication
full work available at URL: j.fss.2003.12.005
OpenAlex ID: W2091855908
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DBLP publication ID: journals/fss/WangWR05
DOI: 10.1016/J.FSS.2003.12.005
description: scientific article; zbMATH DE number 2126004