A counter-example of Gottwald's theorem
type: Item
instance of: scholarly article
title: A counter-example of Gottwald's theorem
zbMATH Open document ID: 0635.03051
DOI: 10.1016/0165-0114(87)90053-4
published in: Fuzzy Sets and Systems
publication date: 1987-01-01T00:00:00Z
review text: The author claims to give a counter-example of one of the reviewer's results [Fuzzy Sets Syst. 17, 285-296 (1985; Zbl 0607.03015)]; but (un- ?)fortunately the criticism does not work: (i) as one of the basic ingredients, a binary operation * in the universe of discourse has to be given - the author never explains it and hence it is impossible to see how he gets some of the fuzzy sets he uses; (ii) the author (correctly) remarks that \(\vDash p\to_ 2q\wedge_ 2r\) cannot be inferred from \(\vDash p\to_ 2q\) and \(\vDash p\to_ 2r\)- but, again, the paper criticized uses this inference only in the case \(q=1\) which allows it.
Mathematics Subject Classification ID: 03E72
Mathematics Subject Classification ID: 03B50
zbMATH DE Number: 4033737
zbMATH Keywords: fuzzy sets
zbMATH Keywords: fuzzy relation equations
author: Mingsheng Ying
reviewed by: Siegfried J. Gottwald
MaRDI profile type: Publication
full work available at URL: 0165-0114(87)90053-4
OpenAlex ID: W2086255879
cites work: Generalized solvability criteria for fuzzy equations
cites work: Solution of fuzzy equations with extended operations
description: scientific article; zbMATH DE number 4033737