tea.mathoverflow.net - Discussion Feed ("Is fuzzy mathematics useful in pure mathematics?")

Kevin Lin comments on ""Is fuzzy mathematics useful in pure mathematics?"" (12662)

Kevin Lin — Mon, 17 Jan 2011 14:45:50 -0800

I agree with Tom, and I cast one of the votes to reopen.

Tom LaGatta comments on ""Is fuzzy mathematics useful in pure mathematics?"" (12661)

Tom LaGatta — Mon, 17 Jan 2011 14:43:41 -0800

Zev, "my" formulation is actually straight from the question itself.

unknown (yahoo): I would suggest that you remove the last three paragraphs of your question. Note that this would roll back the question to Edit #2.

Zev Chonoles comments on ""Is fuzzy mathematics useful in pure mathematics?"" (12660)

Zev Chonoles — Mon, 17 Jan 2011 14:33:18 -0800

I agree that the question is interesting and should be reopened, but I'm not sure I like the OP's actual phrasing of the question - in particular, the word "madder" seems argumentative, or at least unnecessary. Both Todd's and Tom's formulations would be good replacements, in my opinion.

Tom LaGatta comments on ""Is fuzzy mathematics useful in pure mathematics?"" (12659)

Tom LaGatta — Mon, 17 Jan 2011 14:09:01 -0800

It should be reopened. The question ("Are there any proofs of theorems in pure mathematics of a non-fuzzy nature that make use of fuzzy concepts ?") is straightforward, and an expert should easily be able to answer it yes or no.

Todd Trimble comments on ""Is fuzzy mathematics useful in pure mathematics?"" (12658)

Todd Trimble — Mon, 17 Jan 2011 13:30:31 -0800

I'm not that enthusiastic about the question, but it doesn't seem to me any less reasonable than many other questions on MO. The question is: are there results in the language of non-fuzzy mathematics whose proofs significantly use fuzzy mathematics; this is analogous to: are there results in the language of standard analysis proved using nonstandard analysis? The latter question would be perfectly reasonable if the answer weren't so well-known, and answers to the former question are not known to me.

Some category theorists I know of have looked at fuzzy set theory, recasting aspects of it to bring it closer to mainstream or more recognizable concepts (for example, in the language of toposes or quasitoposes, where fuzzy set theory is brought into contact with sheaves or separated presheaves on locales). As I read it, these are mostly exercises in demystification, not born of any particular enthusiasm for fuzzy sets.

Yemon Choi comments on ""Is fuzzy mathematics useful in pure mathematics?"" (12655)

Yemon Choi — Mon, 17 Jan 2011 12:00:19 -0800

This question was closed, has been edited, and now has two votes to re-open. I'm starting a thread here in case people want to argue the case one way or another.