Some remarks on fuzzy powerset operators
type: Item
instance of: scholarly article
title: Some remarks on fuzzy powerset operators
zbMATH Open document ID: 1019.18001
DOI: 10.1016/S0165-0114(01)00024-0
author: Cosimo De Mitri
author: Cosimo Guido
published in: Fuzzy Sets and Systems
publication date: 2002-06-24T00:00:00Z
review text: The paper remembers some concepts and properties given in a paper before, that is, present the categories \(\mathcal {A-F}\), \(\mathcal E-F\), \(\mathcal {G-F}\) and \(F\)-\({\mathcal S}et\), reconsiders and redefines the fuzzy powerset operators for each one and lists some properties of these. Then, the authors develop some characterizations of isomorphisms in the categories \(\mathcal {E-F}\), \(\mathcal G-F\) and \(\mathcal {A-F}\), by means of the corresponding powerset operators. They present covering properties in relation to fuzzy points, properties about the image of bold fuzzy points, under the injectivity of the forward powerset operator, and an improve of the above characterization of isomorphisms in \(\mathcal A-F\). Finally, they define the complemented backward powerset operator related to a morphism in anyone of the considered ground categories and the corresponding order reversing involution, and some propositions which relate this operator with both forward and backward powerset operators are proved.
reviewed by: Jesús Medina Moreno
Mathematics Subject Classification ID: 18B05
Mathematics Subject Classification ID: 03E72
zbMATH DE Number: 1758528
zbMATH Keywords: fuzzy powerset
zbMATH Keywords: fuzzy powerset operator
MaRDI profile type: Publication
cites work: Fuzzy topology on fuzzy sets and tolerance topology
cites work: Fuzzy power sets and fuzzy implication operators
cites work: Some results on fuzzy topology on fuzzy sets
cites work: Q4037041
cites work: Functions, equivalence relations, quotient spaces and subsets in fuzzy set theory
cites work: Categories of $V$-sets
cites work: THE SUBSPACE PROBLEM IN THE TRADITIONAL POINT-SET CONTEXT OF FUZZY TOPOLOGY
cites work: POWERSET OPERATOR BASED FOUNDATION FORPOINT-SET LATTICE-THEORETIC (POSLAT) FUZZY SET THEORIES and TOPOLOGIES
cites work: Categorical foundation of variable-basis fuzzy topology
cites work: Fuzzy sets
full work available at URL: s0165-0114(01)00024-0
OpenAlex ID: W2009103718
description: scientific article; zbMATH DE number 1758528