A comment on fuzzy linear systems.
type: Item
instance of: scholarly article
title: A comment on fuzzy linear systems.
zbMATH Open document ID: 1050.15003
DOI: 10.1016/S0165-0114(03)00139-8
author: Tofigh Allahviranloo
published in: Fuzzy Sets and Systems
publication date: 2004-05-27T00:00:00Z
review text: Two recent papers of \textit{M. Friedman}, \textit{M. Ma} and \textit{A. Kandel} [Fuzzy Sets Syst. 96, No. 2, 201--209 (1998; Zbl 0929.15004); comment and reply ibid. 140, 559--561 (2003); ibid. 109, 55--58 (2000; Zbl 0945.15002)] deal with systems of linear equations with fuzzy right-hand side. In formulation of Theorem 3 (or Lemma 2 in the latter paper), instead of the quantifier `for every \(Y\)', the phrase `for arbitrary \(Y\)' was used. If we neglect the proof, then we can suppose that \(Y\) is arbitrarily fixed, and therefore, the theorem appears to be false. This note indicates that Example 3 in the former paper contradicts Theorem 3 (for arbitrarily fixed \(Y\)). However, in \textit{M. Friedman}, \textit{M. Ma} and \textit{A. Kandel}'s reply [loc. cit.], the part of the proof of the theorem is repeated with an explanation of the used quantifier. Another discussion of the mentioned theorem was presented by \textit{R. Tyrala} [Linear systems with fuzzy solutions, to appear in: Proc. Warsaw Internat. Seminar Soft Comp., Warsaw, Poland, November 2003], where we can find the next opinion that the formulation of the theorem is misleading.
reviewed by: Józef Drewniak
Mathematics Subject Classification ID: 15A06
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 08A72
Mathematics Subject Classification ID: 15B33
zbMATH DE Number: 2066693
zbMATH Keywords: linear equation
zbMATH Keywords: fuzzy number
zbMATH Keywords: fuzzy solution
MaRDI profile type: Publication
full work available at URL: s0165-0114(03)00139-8
OpenAlex ID: W2083301174
description: scientific article; zbMATH DE number 2066693