Editing Formal concept analysis (section)

== Example ==
[[File:FCA body of water.svg|thumb|Line diagram corresponding to the formal context ''bodies of water'' shown in the example table]]
The data in the example is taken from a semantic field study, where different kinds of [[Body of water|bodies of water]] were systematically categorized by their attributes.<ref>{{citation |first1=Peter Rolf |last1=Lutzeier |title=Wort und Feld: wortsemantische Fragestellungen mit besonderer Berücksichtigung des Wortfeldbegriffes: Dissertation |series=Linguistische Arbeiten 103 |publisher=Niemeyer |location=Tübingen |oclc=8205166 |date=1981 |language=de |doi=10.1515/9783111678726.fm}}</ref> For the purpose here it has been simplified.

The data table represents a ''formal context'', the ''line diagram'' next to it shows its ''concept lattice''. Formal definitions follow below.

{| class="wikitable" style="text-align: center; margin-right: 2em; float: left; font-size: 80%"
|+ Example for a formal context: "bodies of water"
|-
! rowspan="2" colspan="2"| bodies of water !! colspan="8" | attributes
|-
! ''temporary'' !! ''running'' !! ''natural'' !! ''stagnant'' !! ''constant'' !! ''maritime''
|-
! rowspan="18" {{verth|va=middle|objects}}
! {{rh}} | [[canal]]
| || {{ya}} || || || {{ya}} ||
|-
! {{rh}} | [[Channel (geography)|channel]]
| || {{ya}} || || || {{ya}} ||
|-
! {{rh}} | [[lagoon]]
| || || {{ya}} || {{ya}} || {{ya}} || {{ya}}
|-
! {{rh}} | [[lake]]
| || || {{ya}} || {{ya}} || {{ya}} ||
|-
! {{rh}} | [[maar]]
| || || {{ya}} || {{ya}} || {{ya}} ||
|-
! {{rh}} | [[puddle]]
| {{ya}} || || {{ya}} || {{ya}} || ||
|-
! {{rh}} | [[pond]]
| || || {{ya}} || {{ya}} || {{ya}} ||
|-
! {{rh}} | pool
| || || {{ya}} || {{ya}} || {{ya}} ||
|-
! {{rh}} | [[reservoir]]
| || || || {{ya}} || {{ya}} ||
|-
! {{rh}} | [[river]]
| || {{ya}} || {{ya}} || || {{ya}} ||
|-
! {{rh}} | [[rivulet]]
| || {{ya}} || {{ya}} || || {{ya}} ||
|-
! {{rh}} | [[Stream|runnel]]
| || {{ya}} || {{ya}} || || {{ya}} ||
|-
! {{rh}} | [[sea]]
| || || {{ya}} || {{ya}} || {{ya}} || {{ya}}
|-
! {{rh}} | [[stream]]
| || {{ya}} || {{ya}} || || {{ya}} ||
|-
! {{rh}} | [[Tarn (lake)|tarn]]
| || || {{ya}} || {{ya}} || {{ya}} ||
|-
! {{rh}} | torrent
| || {{ya}} || {{ya}} || || {{ya}} ||
|-
! {{rh}} | trickle
| || {{ya}} || {{ya}} || || {{ya}} ||
|}


{{Clear}}

The above line diagram consists of circles, connecting line segments, and labels. Circles represent ''formal concepts''. The lines allow to read off the subconcept-superconcept hierarchy. Each object and attribute name is used as a label exactly once in the diagram, with objects below and attributes above concept circles. This is done in a way that an attribute can be reached from an object via an ascending path if and only if the object has the attribute.

In the diagram shown, e.g. the object ''reservoir'' has the attributes ''stagnant'' and ''constant'', but not the attributes ''temporary, running, natural, maritime''. Accordingly, ''puddle'' has exactly the characteristics ''temporary, stagnant'' and ''natural''.

The original formal context can be reconstructed from the labelled diagram, as well as the formal concepts. The extent of a concept consists of those objects from which an ascending path leads to the circle representing the concept. The intent consists of those attributes to which there is an ascending path from that concept circle (in the diagram). In this diagram the concept immediately to the left of the label ''reservoir'' has the intent ''stagnant'' and ''natural'' and the extent ''puddle, maar, lake, pond, tarn, pool, lagoon,'' and ''sea''.