Interpolation and extrapolation of fuzzy quantities -- the multiple-dimensional case
type: Item
instance of: scholarly article
title: Interpolation and extrapolation of fuzzy quantities -- the multiple-dimensional case
zbMATH Open document ID: 1026.93030
author: Sándor Jenei
author: Erich Peter Klement
author: R. Konzel
published in: Soft Computing
publication date: 2003-03-18T00:00:00Z
review text: The objective of this study is to deliver a comprehensive methodology for interpolation and extrapolation in multivariable rule-based systems. Proceeding with the standard format of multiple input rule-based systems of the form ``if condition\(_1\) is \(A_i\) and condition\(_2\) is \(B_i\dots\) then conclusion is \(Z_i\)'' involving fuzzy sets defined in the corresponding spaces \((A_i,B_i, \dots,Z_i)\) and a collection of formal interpolation requirements (such as compatibility with the rule base, monotonicity, continuity, linearity, etc.), techniques are discussed for constructing fuzzy sets that interpolate and extrapolate in fuzzy rule bases. This process is discussed at the level of computing realized for antecedents and conclusions of the rules. Furthermore the properties of the resulting interpolation/extrapolation mapping are studied.
reviewed by: Witold Pedrycz
Mathematics Subject Classification ID: 93C42
Mathematics Subject Classification ID: 93C35
zbMATH DE Number: 1883908
zbMATH Keywords: fuzzy interpolation
zbMATH Keywords: sparse rule base
zbMATH Keywords: approximate reasoning
zbMATH Keywords: multivariable fuzzy systems
zbMATH Keywords: multiple input rule-based systems
zbMATH Keywords: compatibility
zbMATH Keywords: monotonicity
zbMATH Keywords: continuity
zbMATH Keywords: linearity
MaRDI profile type: Publication
full work available at URL: s005000100152
OpenAlex ID: W2049305902
DOI: 10.1007/S005000100152
description: scientific article; zbMATH DE number 1883908