====== Fuzzy Concept Extractor ======

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) 

^  Fuzzy (or composite) Trait((conceivably, in a case like this example, luminosity could be unconstrained, but the RGB values could be constrained to produce that luminosity.  The RGB values represent a pattern but not a histogram normed to 100%))  ^^^^  Multiple choice \\ (Crisp)  ^^^^ Fuzzy (another) ^^  Binary \\ (explicit)  ^^ Binary \\ (usual compact\\ Y/N)  ^
^  Red  ^  Green  ^  Blue  ^  Luminance  ^  Dog  ^  Cat  ^  Bird  ^  Fish  ^  Day  ^ Night  ^  Day  ^ Night  ^  Day  ^
|  |  |  |  |  |  |  |  |  |  | 1 | 0 | X | daytime |
|  |  |  |  |  |  |  |  |  |  | 0 | 1 | _ | night time |
|  |  |  |  |  | 1 |  |  | 60% | 40% |  |  |  | evening?  dawn? |
|  |  |  |  |  |  |  |  |  |  |  |  |  |
|  |  |  |  |  |  |  |  |  |  |  |

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"

====== Classes and Pseudocode ======

  * 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.


===== Algorithm =====

  * 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.