Why concept lattices are large: extremal theory for generators, concepts, and VC-dimension

2017 ◽  
Vol 46 (5) ◽  
pp. 440-457 ◽  
Author(s):  
Alexandre Albano ◽  
Bogdan Chornomaz
Keyword(s):  
Vc Dimension ◽  
Concept Lattices ◽  
Extremal Theory

scholarly journals Gradation of Fuzzy Preconcept Lattices

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 41
Author(s):  
Alexander Šostak ◽  
Ingrīda Uļjane ◽  
Māris Krastiņš
Keyword(s):  
Fuzzy Information ◽  
Concept Lattices ◽  
Practical Applications ◽  
Fuzzy Concept ◽  
The One ◽  
Practical Nature

Noticing certain limitations of concept lattices in the fuzzy context, especially in view of their practical applications, in this paper, we propose a more general approach based on what we call graded fuzzy preconcept lattices. We believe that this approach is more adequate for dealing with fuzzy information then the one based on fuzzy concept lattices. We consider two possible gradation methods of fuzzy preconcept lattice—an inner one, called D-gradation and an outer one, called M-gradation, study their properties, and illustrate by a series of examples, in particular, of practical nature.

scholarly journals The VC Dimension of Metric Balls under Fréchet and Hausdorff Distances

2021 ◽  
Author(s):  
Anne Driemel ◽  
André Nusser ◽  
Jeff M. Phillips ◽  
Ioannis Psarros
Keyword(s):  
Density Estimation ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Similarity Metrics ◽  
Vc Dimension ◽  
Set Systems ◽  
Polygonal Curves ◽  
The Individual ◽  
Curve Similarity ◽  
Metric Balls

AbstractThe Vapnik–Chervonenkis dimension provides a notion of complexity for systems of sets. If the VC dimension is small, then knowing this can drastically simplify fundamental computational tasks such as classification, range counting, and density estimation through the use of sampling bounds. We analyze set systems where the ground set X is a set of polygonal curves in $$\mathbb {R}^d$$ R d and the sets $$\mathcal {R}$$ R are metric balls defined by curve similarity metrics, such as the Fréchet distance and the Hausdorff distance, as well as their discrete counterparts. We derive upper and lower bounds on the VC dimension that imply useful sampling bounds in the setting that the number of curves is large, but the complexity of the individual curves is small. Our upper and lower bounds are either near-quadratic or near-linear in the complexity of the curves that define the ranges and they are logarithmic in the complexity of the curves that define the ground set.

On context patterns associated with concept lattices

Order ◽  
1993 ◽  
Vol 10 (4) ◽  
pp. 363-373
Author(s):  
Winfried Geyer
Keyword(s):  
Concept Lattices

On multi-adjoint concept lattices based on heterogeneous conjunctors

2012 ◽  
Vol 208 ◽  
pp. 95-110 ◽  
Author(s):  
J. Medina ◽  
M. Ojeda-Aciego
Keyword(s):  
Concept Lattices

On the use of thresholds in multi-adjoint concept lattices

2014 ◽  
Vol 92 (9) ◽  
pp. 1855-1873 ◽  
Author(s):  
M. Eugenia Cornejo ◽  
Jesús Medina ◽  
Eloisa Ramírez-Poussa
Keyword(s):  
Concept Lattices

Distributive laws for concept lattices

1993 ◽  
Vol 30 (4) ◽  
pp. 538-580 ◽  
Author(s):  
Marcel Ern�
Keyword(s):  
Concept Lattices
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