Liminf convergence in &OHgr;-categories
Theoretical Computer Science
Generalized metric spaces: completion, topology, and power domains via the Yoneda embedding
Theoretical Computer Science
Construction of the L-fuzzy concept lattice
Fuzzy Sets and Systems
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Formal Concept Analysis: Mathematical Foundations
Formal Concept Analysis: Mathematical Foundations
On the Yoneda completion of a quasi-metric space
Theoretical Computer Science
Fuzzy Relational Systems: Foundations and Principles
Fuzzy Relational Systems: Foundations and Principles
A Triadic Approach to Formal Concept Analysis
ICCS '95 Proceedings of the Third International Conference on Conceptual Structures: Applications, Implementation and Theory
Pattern Structures and Their Projections
ICCS '01 Proceedings of the 9th International Conference on Conceptual Structures: Broadening the Base
Concept Data Analysis: Theory and Applications
Concept Data Analysis: Theory and Applications
Network as a computer: ranking paths to find flows
CSR'08 Proceedings of the 3rd international conference on Computer science: theory and applications
Formal concept analysis in knowledge discovery: a survey
ICCS'10 Proceedings of the 18th international conference on Conceptual structures: from information to intelligence
Mining gene expression data with pattern structures in formal concept analysis
Information Sciences: an International Journal
Quantifying and qualifying trust: spectral decomposition of trust networks
FAST'10 Proceedings of the 7th International conference on Formal aspects of security and trust
What is a fuzzy concept lattice? II
RSFDGrC'11 Proceedings of the 13th international conference on Rough sets, fuzzy sets, data mining and granular computing
Proceedings of the Third international conference on Formal Concept Analysis
ICFCA'05 Proceedings of the Third international conference on Formal Concept Analysis
Revisiting numerical pattern mining with formal concept analysis
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
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Formal Concept Analysis (FCA) begins from a context, given as a binary relation between some objects and some attributes, and derives a lattice of concepts, where each concept is given as a set of objects and a set of attributes, such that the first set consists of all objects that satisfy all attributes in the second, and vice versa. Many applications, though, provide contexts with quantitative information, telling not just whether an object satisfies an attribute, but also quantifying this satisfaction. Contexts in this form arise as rating matrices in recommender systems, as occurrence matrices in text analysis, as pixel intensity matrices in digital image processing, etc. Such applications have attracted a lot of attention, and several numeric extensions of FCA have been proposed. We propose the framework of proximity sets (proxets), which subsume partially ordered sets (posets) as well as metric spaces. One feature of this approach is that it extracts from quantified contexts quantified concepts, and thus allows full use of the available information. Another feature is that the categorical approach allows analyzing any universal properties that the classical FCA and the new versions may have, and thus provides structural guidance for aligning and combining the approaches.