Stable embedding of ill-posed linear equality and inequality systems into fuzzified systems
type: Item
instance of: scholarly article
title: Stable embedding of ill-posed linear equality and inequality systems into fuzzified systems
zbMATH Open document ID: 0762.93056
DOI: 10.1016/0165-0114(92)90148-W
published in: Fuzzy Sets and Systems
publication date: 1992-09-27T00:00:00Z
review text: The classical linear problem of the form \[ \sum^ n_{j=1}\alpha_{ij}x_ j=\alpha_{i0},\quad i=1,2,\dots,m,\qquad\sum^ n_{j=1}\alpha_{ij}x_ j\leq\alpha_{i0},\quad i=m,2,\dots,s \] with the real parameters \(\alpha_{ij}\in{\mathbf R}\) is generalized by treating these parameters as fuzzy numbers. The paper shows that this generalization provides regularization capabilities to otherwise ill-posed problem. It is also shown that a suitable selection of the parameters and \(t\)-norms guarantees the well-posedness of the linear system generalized in this manner.
reviewed by: Witold Pedrycz
Mathematics Subject Classification ID: 93C42
Mathematics Subject Classification ID: 94D05
zbMATH DE Number: 58417
zbMATH Keywords: fuzzy numbers
zbMATH Keywords: regularization
zbMATH Keywords: ill-posed problem
author: Margit Kovács
MaRDI profile type: Publication
cites work: On stability in fuzzy linear programming problems
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description: scientific article; zbMATH DE number 58417