On the fuzziness measure and negation in totally ordered lattices
type: Item
instance of: scholarly article
title: On the fuzziness measure and negation in totally ordered lattices
zbMATH Open document ID: 0609.94019
DOI: 10.1016/0022-247X(86)90073-9
published in: Journal of Mathematical Analysis and Applications
publication date: 1986-01-01T00:00:00Z
review text: \textit{R. R. Yager} [Inf. Control 44, 236--260 (1980; Zbl 0429.04008)] considered (a degree of) fuzziness to be defined in a lattice as a lack of distinction of an element and its ``negation''. The authors continue this approach. Starting from any chain \(L\) with an order-reversing involutionary unary operation they get a new chain \(L^{\wedge}\) with \(| L| =| L^{\wedge}|\) by introducing a suitable fuzziness ordering. By an order-reversing lattice morphism, \(L^{\wedge}\) can be embedded into the lattice of negate pairs. Finally, valuations on \(L\) lead to valuations on \(L^{\wedge}\), and for \(L={\mathcal F}(X)\) such valuations give measures of fuzziness for fuzzy subsets of \(X\).
Mathematics Subject Classification ID: 94D05
Mathematics Subject Classification ID: 06D99
zbMATH DE Number: 3987205
zbMATH Keywords: fuzziness degrees
zbMATH Keywords: fuzziness in lattices
zbMATH Keywords: fuzziness ordering
zbMATH Keywords: valuations
zbMATH Keywords: measures of fuzziness
author: Antonio Di Nola
author: Salvatore Sessa
reviewed by: Siegfried J. Gottwald
MaRDI profile type: Publication
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full work available at URL: 0022-247x(86)90073-9
OpenAlex ID: W2016498566
description: scientific article; zbMATH DE number 3987205