While “Fuzzy Concept Extractor” might seem like a specialization of “Concept Extractor”, it is a generalization compared to concept extractors for binary relations and multivalued crisp relations (“one value among”–think radio buttons).

If a fuzzy trait can have several modalities to varying degrees, with the sum of degrees (or affinities)

So (for quantified descriptors)

• a rated pattern is an ordered set of numeric values associated with descriptors
  • a normed histogram (or affinities or belief weights?) is a pattern whose descriptors must add to 100%
    • a multi-valued (scaled) attribute is a histogram which concentrates the 100% on a single modality
      • a binary-valued attribute is a multi-valued attribute with only two modalities
        • mostly abbreviated as “on/off”

• FuzzyConceptExtractor
  • input : file of context to analyse, or
  • FuzzyContext
    • Trait*Modality framework
      • Traits
        • Modalities
        • Norm Constraint (if sum of affinities must equal a set value: 100 for percents, 1000 for per mil, etc.)
        • Trait-Modalities segmentation : for decoding (segmenting, parsing) the serialized affinities and applying the norm constraints.
      • Specimens : TreeSet
        • Specimen.name
        • Specimen.affinities: serialized affinities for each trait.modality, in order
        • Constructors
          • TreeSet (Specimins is not a specialized class); Specimen have a lexicographic compareTo().
  • FuzzyConcepts <TreeSet> : output
    • FuzzyConcept
      • Constructors
        • FuzzyConcept(FuzzyConcept prior, FuzzyContext context, Specimen candidate) :
          • FuzzyIntent of prior relaxed to admit candidate
          • FuzzyExtent closed with respect to new FuzzyIntent for context.specimens.
        • FuzzyConcept(FuzzyContext context, Specimen candidate)
          • FuzzyIntent(Specimen candidate)
          • FuzzyExtent(FuzzyIntent intent, FuzzyContext context, Specimen currentSpecimen)
      • FuzzyIntent
        • minAffinities : integer vector
        • maxAffinities : integer vector
        • Constructors
          • FuzzyIntent(Specimen founder) : create an intent from a specimen (min=max=specimen.affinities)
          • FuzzyIntent(FuzzyIntent prior, Specimen candidate) : create an intent from prior, relaxed to admit candidate.
      • FuzzyExtent
        • TreeSet <Specimen>
        • Constructors
          • FuzzyExtent(FuzzyIntent intent, FuzzyContext context) : list of all specimens in context which intent.admits().
          • FuzzyExtent(FuzzyIntent intent, FuzzyContext context, Specimen currentSpecimen) :
            • list of all specimens in context which intent.admits() if none are predecessors of currentSpecimen,
            • null otherwise.
          • FuzzyExtent(FuzzyIntent intent, FuzzyContext context, Specimen currentSpecimen, FuzzyExtent prior) :
            • prior plus list of all other specimens in context which intent.admits() if none are predecessors of currentSpecimen,
            • null otherwise.

• FuzzyConceptExtractor constructs FuzzyContext with normed affinities, specimens sorted by normed affinities in lexicographic order.
• For each specimen in FuzzyContext, FCE generates its FuzzyConcept
  • If new (not redundant)
    • For each successor specimen, derive relaxed FuzzyConcept – FuzzyConcept(FuzzyConcept prior, FuzzyContext context, Specimen candidate) – to include the candidate. If new, continue recursively. This will have to be done either via a FCE method or passing the FCE concept tree as an argument to be able to add each new concept to the tree.