When \((S,N)\)-implications are \((T,T _{1})\)-conditional functions?
type: Item
instance of: scholarly article
title: When \((S,N)\)-implications are \((T,T _{1})\)-conditional functions?
zbMATH Open document ID: 1014.03026
DOI: 10.1016/S0165-0114(02)00178-1
author: Claudi Alsina
author: Enric Trillas
published in: Fuzzy Sets and Systems
publication date: 2003-04-02T00:00:00Z
review text: One of the key issues in the formalization of approximate reasoning is the so-called compositional rule of inference, also called the generalized modus ponens, i.e., from an imprecise fact \(P\) and an imprecise rule \(P\Rightarrow Q\) can we deduce the imprecise conclusion \(Q\)? The answer heavily depends on the implication used to model the rule and on the triangular norm used to model the confluence between the given fact and the given rule. In mathematical terms, the following problem arises. Starting from a non-strict Archimedean t-norm \(T\), a continuous Archimedean t-conorm \(S\), and a strong negation induced by \(T\), under which conditions is the \([0,1]^2-[0,1]\) mapping \(T_1\), defined by \(T_1(x,y)=T(x,S(N(x),y))\), a triangular norm? This paper gives three characterizations.
reviewed by: E. E. Kerre
Mathematics Subject Classification ID: 03B52
Mathematics Subject Classification ID: 68T37
zbMATH DE Number: 1891695
zbMATH Keywords: fuzzy implications
zbMATH Keywords: triangular norm
zbMATH Keywords: compositional rule of inference
zbMATH Keywords: generalized modus ponens
MaRDI profile type: Publication
cites work: On a family of connectives for fuzzy sets
cites work: Some remarks on approximate entailment
cites work: Q4315286
cites work: Valued preference structures
cites work: On the simultaneous associativity of F(x,y) and x+y-F(x,y)
cites work: Q3336431
cites work: ON LOGIC AND FUZZY LOGIC
cites work: Logic: Going farther from Tarski?
cites work: A general concept of fuzzy connectives, negations and implications based on t-norms and t-conorms
description: scientific article; zbMATH DE number 1891695