The aim of this package is to provide tools to perform fuzzy formal concept analysis (FCA) from within R. It provides functions to load and save a Formal Context, extract its concept lattice and implications. In addition, one can use the implications to compute semantic closures of fuzzy sets and, thus, build recommendation systems.
The fcaR package provides data structures which allow the user to work seamlessly with formal contexts and sets of implications. More explicitly, three main classes are implemented, using the R6 object-oriented-programming paradigm in R:
FormalContext encapsulates the definition of a formal context \((G, M, I)\), being \(G\) the set of objects, \(M\) the set of attributes and \(I\) the (fuzzy) relationship matrix, and provides methods to operate on the context using FCA tools.
ImplicationSet represents a set of implications over a specific formal context.
ConceptLattice represents the set of concepts and their relationships, including methods to operate on the lattice.
Two additional helper classes are implemented:
Set is a class solely used for visualization purposes, since it encapsulates in sparse format a (fuzzy) set.
Concept encapsulates internally both extent and intent of a formal concept as Set.
Since fcaR is an extension of the data model in the arules package, most of the methods and classes implemented interoperates with the main S4 classes in arules (transactions and rules).
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# Build a formal context
fc_planets <- FormalContext$new(planets)
# Find its concepts and implications
fc_planets$find_implications()
# Print the extracted implications
fc_planets$implications
#> Implication set with 10 implications.
#> Rule 1: {no_moon} -> {small, near}
#> Rule 2: {far} -> {moon}
#> Rule 3: {near} -> {small}
#> Rule 4: {large} -> {far, moon}
#> Rule 5: {medium} -> {far, moon}
#> Rule 6: {medium, large, far, moon} -> {small, near, no_moon}
#> Rule 7: {small, near, moon, no_moon} -> {medium, large, far}
#> Rule 8: {small, near, far, moon} -> {medium, large, no_moon}
#> Rule 9: {small, large, far, moon} -> {medium, near, no_moon}
#> Rule 10: {small, medium, far, moon} -> {large, near, no_moon}