On generating all maximal independent sets
Information Processing Letters
Fuzzy sets and fuzzy logic: theory and applications
Fuzzy sets and fuzzy logic: theory and applications
Discovering knowledge from fuzzy concept lattice
Data mining and computational intelligence
Formal Concept Analysis: Mathematical Foundations
Formal Concept Analysis: Mathematical Foundations
Fuzzy Relational Systems: Foundations and Principles
Fuzzy Relational Systems: Foundations and Principles
Concepts in fuzzy scaling theory: order and granularity
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Reduction and a Simple Proof of Characterization of Fuzzy Concept Lattices
Fundamenta Informaticae
Information Sciences: an International Journal
Relations of attribute reduction between object and property oriented concept lattices
Knowledge-Based Systems
Fuzzy graph representation of a fuzzy concept lattice
Fuzzy Sets and Systems
Attribute reduction in fuzzy concept lattices based on the T implication
Knowledge-Based Systems
Optimal decompositions of matrices with grades into binary and graded matrices
Annals of Mathematics and Artificial Intelligence
Factorization of fuzzy concept lattices with hedges by modification of input data
Annals of Mathematics and Artificial Intelligence
Evaluation of IPAQ questionnaires supported by formal concept analysis
Information Sciences: an International Journal
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
Note on generating fuzzy concept lattices via Galois connections
Information Sciences: an International Journal
Thresholds and shifted attributes in formal concept analysis of data with fuzzy attributes
ICCS'06 Proceedings of the 14th international conference on Conceptual Structures: inspiration and Application
Bisociative discovery in business process models
Bisociative Knowledge Discovery
Concept lattices of incomplete data
ICFCA'12 Proceedings of the 10th international conference on Formal Concept Analysis
Formal concept analysis as a framework for business intelligence technologies
ICFCA'12 Proceedings of the 10th international conference on Formal Concept Analysis
Fundamenta Informaticae - Concept Lattices and Their Applications
Finding Fuzzy Concepts for Creative Knowledge Discovery
International Journal of Intelligent Systems
Axiomatic characterizations of dual concept lattices
International Journal of Approximate Reasoning
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In formal concept analysis of data with fuzzy attributes, both the extent and the intent of a formal (fuzzy) concept may be fuzzy sets. In this paper we focus on so-called crisply generated formal concepts. A concept $\langle{A,B}\rangle \in \mathcal{B}(X, Y, I)$ is crisply generated if A = D↓ (and so B = D↓↑) for some crisp (i.e., ordinary) set D ⊆ Y of attributes (generator). Considering only crisply generated concepts has two practical consequences. First, the number of crisply generated formal concepts is considerably less than the number of all formal fuzzy concepts. Second, since crisply generated concepts may be identified with a (ordinary, not fuzzy) set of attributes (the largest generator), they might be considered “the important ones” among all formal fuzzy concepts. We present basic properties of the set of all crisply generated concepts, an algorithm for listing all crisply generated concepts, a version of the main theorem of concept lattices for crisply generated concepts, and show that crisply generated concepts are just the fixed points of pairs of mappings resembling Galois connections. Furthermore, we show connections to other papers on formal concept analysis of data with fuzzy attributes. Also, we present examples demonstrating the reduction of the number of formal concepts and the speed-up of our algorithm (compared to listing of all formal concepts and testing whether a concept is crisply generated).