BZMV\(^{\text{dM}}\) algebras and Stonian MV-algebras (applications to fuzzy sets and rough approximations)
type: Item
instance of: scholarly article
title: BZMV\(^{\text{dM}}\) algebras and Stonian MV-algebras (applications to fuzzy sets and rough approximations)
zbMATH Open document ID: 0948.06008
DOI: 10.1016/S0165-0114(97)00328-X
author: G. Cattaneo
author: Roberto Giuntini
author: Ramani S. Pilla
published in: Fuzzy Sets and Systems
publication date: 2000-03-13T00:00:00Z
review text: This paper proposes, as the logic of fuzzy sets, de Morgan BZMV-algebras, which are both MV-algebras and distributive de Morgan BZ-lattices. The set of all closed elements with respect to the Brouwerian orthocomplementation in such a logic is shown to be a Boolean algebra. Two modal operators representing sharp approximations from the top and the bottom can be introduced by means of Kleene and Brouwerian orthocomplementations. The equivalence of de Morgan BZMV-algebras and Stonian MV-algebras is established.
reviewed by: Hirokazu Nishimura
Mathematics Subject Classification ID: 06D35
Mathematics Subject Classification ID: 03E72
zbMATH DE Number: 1400234
zbMATH Keywords: rough approximations
zbMATH Keywords: fuzzy sets
zbMATH Keywords: de Morgan BZMV-algebras
zbMATH Keywords: distributive de Morgan BZ-lattices
zbMATH Keywords: Brouwerian orthocomplementation
zbMATH Keywords: Boolean algebra
zbMATH Keywords: modal operators
zbMATH Keywords: Stonian MV-algebras
MaRDI profile type: Publication
full work available at URL: s0165-0114(97)00328-x
OpenAlex ID: W1994921377
Recommended article: Fuzzy \(\mathsf{H}_v\mathsf{MV}\)-algebras
Recommended article: On fuzzy B-algebras
Recommended article: \((L,M)\)-fuzzy \(\sigma \)-algebras
Recommended article: Q3978829
Recommended article: Q3090142
Recommended article: Q3220580
Recommended article: Q4820416
Recommended article: Q3333043
Recommended article: Some fuzzy concepts of BCI, BCK and MV-algebras
Recommended article: Q5426346
description: scientific article; zbMATH DE number 1400234