Images and preimages of \(L\)-filterbases
type: Item
instance of: scholarly article
title: Images and preimages of \(L\)-filterbases
zbMATH Open document ID: 1111.54005
author: Yong Chan Kim
author: Jung Mi Ko
published in: Fuzzy Sets and Systems
publication date: 2006-11-15T00:00:00Z
review text: The paper is concerned with the notion of \(L\)-filterbase formed on a strictly two-sided, commutative quantale lattice \(L\). Considering that \(L\) is a complete lattice and \(\phi\) is a function \(\phi: X\to Y\), the Zadeh image and preimage operators are defined in the form \[ \phi^{\rightarrow}_L(f)(y)= \bigvee\{f(x)\mid\phi(x)= y\},\qquad \phi^{\leftarrow}_L(g)= g\circ\phi. \] Second-order powerset operators are introduced (the image and preimage operators \(\phi^{\rightrightarrows}\) and \(\phi^{\leftleftarrows}\)) and their properties studied.
Mathematics Subject Classification ID: 54A40
Mathematics Subject Classification ID: 54B10
zbMATH DE Number: 5073274
zbMATH Keywords: \(L\)-filters
zbMATH Keywords: image
zbMATH Keywords: preimage
zbMATH Keywords: commutative quantale lattice
reviewed by: Witold Pedrycz
MaRDI profile type: Publication
full work available at URL: j.fss.2005.12.012
OpenAlex ID: W2001138407
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DOI: 10.1016/J.FSS.2005.12.012
description: scientific article; zbMATH DE number 5073274