Triadic Relations, Intentions, Fuzzy Subsets • Discussion 1

Re: Peirce List DiscussionStefan Berwing

Frequencies, histograms, and probabilities are one way to think about degrees of membership in a fuzzy subset, but there are cautions to be observed in doing that.

Consider the following triadic relations:

  • xr S   =   x is in S to the degree r
  • xj S   =   x is in S to the judge j

And consider their intensional counterparts:

  • x isr P   =   x is P to the degree r
  • x isj P   =   x is P to the judge j

These relations are all defined abstractly enough that you could probably fit them out with almost any reasonable statistical model.

One adds concreteness to these abstractions by specifying how the triadic relations combine under operations analogous to the usual set-theoretic and logical operations.  It’s been a while since I studied it but I seem to recall that most of the fuzzy literature works with rules for combining degrees that cannot be interpreted as probabilities, rather as what they like to call possibilities.

How one combines interpreters is a really good question.  This may be another one of those places where we have to turn Peirce’s trick of replacing interpreters with interpretants.

Advertisements
This entry was posted in C.S. Peirce, Fuzzy Logic, Fuzzy Sets, Intentional Contexts, Intentional Objects, Intentionality, Intentions, Logic, Mathematics, Peirce, Relation Theory, Semiotics and tagged , , , , , , , , , , , . Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s