When you switch to using these numbers to differentiate between “short” and “extremely short”, that’s not probability. But then you’re no longer talking about truth values.
That is in fact precisely what I mean by “truth value”. What does “truth value” mean in your book?
It means that Bill is pretty nearly 3 feet tall, but not exactly. Perhaps it means that for half of all practical purposes, Bill is 3 feet tall; that may be a good formalization.
I’ll mention now that I don’t know if normal treatments of fuzzy logic insists that truth value functions be continuous. Mine does, which may make it ordinary, substandard, quirky, or insightful.
That is in fact precisely what I mean by “truth value”. What does “truth value” mean in your book?
Then what does it mean in fuzzy-logic to say “The truth value of ‘Bill is 3 feet tall’ is .5” ?
It means that Bill is pretty nearly 3 feet tall, but not exactly. Perhaps it means that for half of all practical purposes, Bill is 3 feet tall; that may be a good formalization.
I’ll mention now that I don’t know if normal treatments of fuzzy logic insists that truth value functions be continuous. Mine does, which may make it ordinary, substandard, quirky, or insightful.