Just to add to the comments on Formal Concept Analysis, there's further discussion after my post on it at the [n-Category Cafe](https://golem.ph.utexas.edu/category/2013/09/formal_concept_analysis.html). My student Jonathan Elliott wrote [his thesis](http://etheses.whiterose.ac.uk/18342/) on doing this with 'fuzzy truth values' which in this categorical context means not dealing with posets, which are categories enriched over true and false, but dealing with fuzzy posets which are categories enriched over some 'fuzzy truth values' smeared between true and false. Hopefully there wil be a paper soon and I can explain more then...