Paper Info
Title
The Linear Algebra in Extended Formal Concept Analysis Over Idempotent Semifields.
Abstract
We report on progress relating K-valued FCA to K-Linear Algebra where K is an idempotent semifield. We first find that the standard machinery of linear algebra points to Galois adjunctions as the preferred construction, which generates either Neighbourhood Lattices of attributes or objects. For the Neighbourhood of objects we provide the adjoints, their respective closure and interior operators and the general structure of the lattices, both of objects and attributes. Next, these results and those previous on Galois connections are set against the backdrop of Extended Formal Concept Analysis. Our results show that for a K-valued formal context (G, M, R)-where vertical bar G vertical bar = g, vertical bar M vertical bar = m and R is an element of K-gxm-there are only two different "shapes" of lattices each of which comes in four different "colours", suggesting a notion of a 4-concept associated to a formal concept. Finally, we draw some conclusions as to the use of these as data exploration constructs, allowing many different "readings" on the contextualized data.
Year
DOI
Venue
2017
10.1007/978-3-319-59271-8_14
Lecture Notes in Artificial Intelligence
Field
DocType
Volume
Galois connection,Residuated lattice,Linear algebra,Discrete mathematics,Combinatorics,Lattice (order),Semifield,Operator (computer programming),Idempotence,Formal concept analysis,Mathematics
Conference
10308
ISSN
Citations 
PageRank 
0302-9743
0
0.34
References 
Authors
6
2
Name
Order
Citations
PageRank
Francisco J. Valverde-Albacete111620.84
Carmen Peláez-moreno213022.07