Attribute exploration with background knowledge
Theoretical Computer Science
Formal Concept Analysis: Mathematical Foundations
Formal Concept Analysis: Mathematical Foundations
A partition-based approach towards constructing Galois (concept) lattices
Discrete Mathematics
Computing iceberg concept lattices with TITANIC
Data & Knowledge Engineering
Information Sciences—Informatics and Computer Science: An International Journal
Formal concept analysis for general objects
Discrete Applied Mathematics - Special issue: The 1998 conference on ordinal and symbolic data analysis (OSDA '98)
Off to new shores: conceptual knowledge discovery and processing
International Journal of Human-Computer Studies
Concept Data Analysis: Theory and Applications
Concept Data Analysis: Theory and Applications
A multi-level conceptual data reduction approach based on the Lukasiewicz implication
Information Sciences: an International Journal - Special issue: Information technology
Monotone concepts for formal concept analysis
Discrete Applied Mathematics - Discrete mathematics & data mining (DM & DM)
Fuzzy inference based on fuzzy concept lattice
Fuzzy Sets and Systems
Information Sciences: an International Journal
Topological approaches to covering rough sets
Information Sciences: an International Journal
Artificial Intelligence
Attribute reduction in decision-theoretic rough set models
Information Sciences: an International Journal
Formal concept analysis via multi-adjoint concept lattices
Fuzzy Sets and Systems
Relationship between generalized rough sets based on binary relation and covering
Information Sciences: an International Journal
Concept lattices of fuzzy contexts: Formal concept analysis vs. rough set theory
International Journal of Approximate Reasoning
Linguistic Values-based Intelligent Information Processing: Theory, Methods, and Applications
Linguistic Values-based Intelligent Information Processing: Theory, Methods, and Applications
Learning concept hierarchies from text corpora using formal concept analysis
Journal of Artificial Intelligence Research
FCA-MERGE: bottom-up merging of ontologies
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
On the topological properties of fuzzy rough sets
Fuzzy Sets and Systems
Topological space for attributes set of a formal context
RSKT'07 Proceedings of the 2nd international conference on Rough sets and knowledge technology
A new algebraic structure for formal concept analysis
Information Sciences: an International Journal
Reduction-Based approaches towards constructing galois (concept) lattices
RSKT'06 Proceedings of the First international conference on Rough Sets and Knowledge Technology
Ontology-based concept similarity in Formal Concept Analysis
Information Sciences: an International Journal
Fuzzy logic = computing with words
IEEE Transactions on Fuzzy Systems
A Categorical View on Algebraic Lattices in Formal Concept Analysis
Fundamenta Informaticae
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Formal concept analysis (FCA) concerns the hierarchical structures induced by a binary relation between a pair of sets, it is widely applied in data analysis, information retrieval, and knowledge discovery. Within the framework of FCA, computing all formal concepts is the main challenge due to its exponential complexity. It has be proved that all formal concepts is a closure system on objects, hence, the closure operator on objects are general used to generate all formal concepts of a formal context. In the lexicographic tree approach, a base on objects is used to generate extensions of all formal concepts and construct the formal concept lattice. Inspired from the approach, we concentrate a base on attributes and generate intensions of all formal concepts in this paper. To this end, we firstly analyze an example, the lexicographic tree approach is used to generate all formal concepts, from the time complexity point of view, we present that it is not trivial to generate the base on attributes by a simple symmetrical way from the methods based on objects. Then, we deduce a set-valued mapping from attributes to the power set of attributes in a formal context and define a binary relation on attributes by the set-valued mapping. Using the binary relation on attributes, we construct an approximation space and a topology for attributes, respectively, and obtain a base for the topology. We prove that intensions of all formal concepts are included in the topology for attributes, this means that the base can be used to generate intensions of all formal concepts of the formal context and construct the formal concept lattice. More general, our results represent relationships and the hierarchical structures among attributes of the formal context, we present some typical applications, in which the topology for attributes and the base for the topology are applied for association rules discovery from a formal context and linguistic concept analysis.