Lattice-valued topological systems as a framework for lattice-valued formal concept analysis
type: Item
instance of: scholarly article
title: Lattice-valued topological systems as a framework for lattice-valued formal concept analysis
zbMATH Open document ID: 1403.06009
DOI: 10.1155/2013/506275
author: Sergejs Solovjovs
published in: Journal of Mathematics
publication date: 2013-07-25T00:00:00Z
review text: Summary: Recently, \textit{J. T. Denniston} et al. [Fuzzy Sets Syst. 216, 52--90 (2013; Zbl 1320.06004)] presented a new categorical outlook on a certain lattice-valued extension of Formal Concept Analysis (FCA) of \textit{B. Ganter} and \textit{R. Wille} [Formale Begriffsanalyse. Mathematische Grundlagen. Berlin: Springer (1996; Zbl 0861.06001)]; their outlook was based on the notion of lattice-valued interchange system and a category of Galois connections. This paper extends the approach of Denniston et al. [loc. cit.] clarifying the relationships between Chu spaces of \textit{V. Pratt} [in: School on category theory and applications. Lecture notes of courses, Coimbra, Portugal, July 13--17, 1999. Coimbra: Universidade de Coimbra, Departamento de Matemática. 39--100 (1999; Zbl 0954.18002)], many-valued formal contexts of FCA, lattice-valued interchange systems, and Galois connections.
Mathematics Subject Classification ID: 06B23
Mathematics Subject Classification ID: 06A15
Mathematics Subject Classification ID: 06B30
Mathematics Subject Classification ID: 18B30
Mathematics Subject Classification ID: 68T30
zbMATH DE Number: 6191165
Wikidata QID: Q59015495
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/506275
OpenAlex ID: W2064877230
cites work: Variable-basis topological systems versus variable-basis topological spaces
cites work: Q3994458
cites work: Functorial relationships between lattice-valued topology and topological systems
cites work: Categorical foundation of variable-basis fuzzy topology
cites work: Fuzzy points and attachment
cites work: A note on the hypergraph functor
cites work: Interweaving algebra and topology: lattice-valued topological systems
cites work: Q4144755
cites work: Q4501691
cites work: *-autonomous categories. With an appendix by Po-Hsiang Chu
cites work: Formal concept analysis and lattice-valued Chu systems
cites work: Foundations of quantum physics: a general realistic and operational approach
cites work: State property systems and closure spaces: a study of categorical equivalence
cites work: On the amnestic modification of the category of state property systems
cites work: On a generalization of the concept of state property system
cites work: Hypergraph functor and attachment
cites work: Categorical foundations of variety-based topology and topological systems
cites work: Localification of variable-basis topological systems
cites work: Bitopological Spaces
cites work: On the quantisation of points
cites work: On the quantisation of spaces
cites work: Composite variety-based topological theories
cites work: Generalized fuzzy topology versus non-commutative topology
cites work: Lattice-valued soft algebras.
cites work: Q4877294
cites work: Q3794367
cites work: Algebraic and Categorical Aspects of Quantales
cites work: Q3996704
cites work: Q5493135
cites work: Q4316881
cites work: Fuzzy Galois Connections
cites work: Fuzzy Galois connections categorically
cites work: Q4693062
cites work: Q5430142
cites work: Q4215784
cites work: Q3910579
cites work: Q3890747
cites work: Tensor Products and Bimorphisms
cites work: Q4123496
cites work: Q3965241
cites work: Relationship of algebraic theories to powerset theories and fuzzy topological theories for lattice-valued mathematics
cites work: Continuous Lattices and Domains
cites work: POWERSET OPERATOR BASED FOUNDATION FORPOINT-SET LATTICE-THEORETIC (POSLAT) FUZZY SET THEORIES and TOPOLOGIES
cites work: Powerset operator foundations for poslat fuzzy set theories and topologies
cites work: Relationship of algebraic theories to powersets over objects in \(\mathbf {Set}\) and \(\mathbf {Set}\times C\)
cites work: Q4915485
cites work: Q5446380
cites work: Sums, products and negations of contexts and complete lattices
cites work: Relational Galois Connections
cites work: Functorial Properties of Formal Concept Analysis
cites work: The concept lattice functors
cites work: Fuzzy Galois connections under weak conditions
cites work: Transporting many-valued sets along many-valued relations
description: scientific article; zbMATH DE number 6191165