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Bill Taylor wrote (in part):
>> Some time ago, back in the late seventies to early eighties,
>> there was a brief flurry of interest from fringe mathematicians
>> in "fuzzy math". It was never quite clear what this was, but it
>> still has a small amount of library shelf space, though perhaps
>> little or no presence in math departments in academia.
>> It seemed to be (AFAICT), basically, that joke that
>> used to go around about "Generalized Mathematics" -
MoeBlee wrote (in part):
> Yet I see more and more new books on the shelves every time
> I visit the library that have titles with the word 'fuzzy'
> in them, and these are usually Springer Verlag books,
> including textbooks and collections of articles and
> reportings of conference proceedings. Some of the material
> seems to be computer science, but plenty of it is categorized
> as mathematics. Well, my just saying that there are a lot
> of new books, written by professional mathematicians,
> with the words 'fuzzy' in the title is not an argument
> that fuzzy is an important area of study, but it at
> least gives me some reason to doubt claims that it is
> not currently an important area of study.
If you glance through some of the bound volumes of
Mathematical Reviews, looking at subject areas 26, 28,
and 54 from the mid 1970's to the late 1990's (maybe
glance at one month's issue every two or three years),
you'll find a huge increase in titles with "fuzzy"
in them as the years go by. This might be a bit harsh,
but it almost seems as if certain mathematicians, who
otherwise had done nothing very deep or interesting,
decided they could get a lot of mileage by going
through and fuzzifying certain areas of pure mathematics
(those areas they had graduate courses in). In many cases,
it appears to me that the people writing the papers are
coming from just outside of mathematics (economics,
computer science, etc.) and the papers tend to reflect
where they're at in learning standard graduate mathematics
(i.e. learn about the open mapping theorem, then write
a paper where the theorem and proof receive straightforward
fuzzified translations). Try googling "fuzzy" with various
math words and phrases from analysis and topology:
http://www.google.com/search?q=fuzzy-topology
www.google.com/search?q=fuzzy+open-mapping-theorem">http://www.google.com/search?q=fuzzy+open-mapping-theorem
www.google.com/search?q=fuzzy+Baire-category">http://www.google.com/search?q=fuzzy+Baire-category
www.google.com/search?q=fuzzy+tychonoff-theorem">http://www.google.com/search?q=fuzzy+tychonoff-theorem
www.google.com/search?q=fuzzy-measure-theory">http://www.google.com/search?q=fuzzy-measure-theory
www.google.com/search?q=fuzzy-uniform-space">http://www.google.com/search?q=fuzzy-uniform-space
www.google.com/search?q=fuzzy+Banach-limits">http://www.google.com/search?q=fuzzy+Banach-limits
www.google.com/search?q=fuzzy+convergence-in-measure">http://www.google.com/search?q=fuzzy+convergence-in-measure
www.google.com/search?q=fuzzy+stone-weierstrass-theorem">http://www.google.com/search?q=fuzzy+stone-weierstrass-theorem
www.google.com/search?q=fuzzy-Banach-space">http://www.google.com/search?q=fuzzy-Banach-space
You get the idea, I think.
Dave L. Renfro
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