Paper Info
Title
Crisply generated fuzzy concepts
Abstract
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).
Year
DOI
Venue
2005
10.1007/978-3-540-32262-7_19
ICFCA
Keywords
Field
DocType
formal fuzzy concept,fuzzy set,galois connection,fuzzy attribute,formal concept analysis,formal concept,concept lattice,so-called crisply,present example,largest generator,fixed point
Fuzzy concept,Discrete mathematics,Computer science,Fuzzy logic,Fuzzy set,Fixed point,Formal concept analysis
Conference
Volume
ISSN
ISBN
3403
0302-9743
3-540-24525-1
Citations 
PageRank 
References 
52
5.02
7
Authors
3
Name
Order
Citations
PageRank
Radim Bělohlávek136636.09
Vladimír Sklenář2868.97
Jiří Zacpal3746.96