Fuzzy sets as texture spaces. I: Representation theorems
type: Item
instance of: scholarly article
title: Fuzzy sets as texture spaces. I: Representation theorems
zbMATH Open document ID: 0953.54010
DOI: 10.1016/S0165-0114(98)00157-2
author: Lawrence M. Brown
author: Rıza Ertürk
published in: Fuzzy Sets and Systems
publication date: 2000-08-29T00:00:00Z
review text: For \(S\) a set, if \({\mathcal L}\) is a completely distributive sublattice of the power set of \(S\) (with unions as suprema and with intersections as infima) which separates points of \(S\) (i.e., given \(s_1\neq s_2\) in \(S\), there exists \(L_i\in{\mathcal L}\) such that \(s_i\in L_i\) and \(s_j\not\in L_i\) for \(i,j= 1,2\), \(i\neq j\)), then \((S,{\mathcal L})\) is called a texture space. It has a complementation if there exists an inclusion-reversing involution on \({\mathcal L}\). Representation theorems for fuzzy sets, completely distributive lattices with an order-reversing involution, generalized fuzzy sets and intuitionistic sets by complemented texture spaces are presented.
Mathematics Subject Classification ID: 54A40
Mathematics Subject Classification ID: 54E55
Mathematics Subject Classification ID: 06D72
zbMATH DE Number: 1423468
zbMATH Keywords: generalized fuzzy set
zbMATH Keywords: intuitionistic fuzzy set
zbMATH Keywords: texture space
reviewed by: Tomasz Kubiak
MaRDI profile type: Publication
cites work: Intuitionistic fuzzy sets
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description: scientific article; zbMATH DE number 1423468