There is at present an extensive literature on fuzzy sets and fuzzy logic. I got another brush with the world of fuzzy back in the 1990s when I returned to grad school in a systems engineering program, partly because my adviser was especially interested in applications to decision support and optimal control, and that intersected to a degree — well, as it turns out, not a degree — with my pet project of “inquiry driven systems”.
For reasons I have explained before and will try to explain again later on, I am not especially concerned with the variety of fuzzy, modal, and multi-valued logical systems covered in the literature, but only with the threshold of generalization where we find ourselves drawn from dyadic relations to triadic relations as models for dealing with complex phenomena. Still, I think it’s worth having a look at fuzzy set theory in order to develop ideas about the general thrust of generalization from 2-adic to 3-adic.
Here’s a brief article from PlanetMath that gives a minimal introduction to fuzzy set theory.
The article uses different letters for things than I am using, so I’ll transcribe what I need from it in the next installment.