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I had a very big doubt in my mind about Fuzzyness. When statistics is answering all the questions, which we see generally in Fuzzy theory. Then why one SHOULD learn Fuzzy Theory. Or is there any gap in statistics, I mean:

Is there any problems which can be solved by Fuzzy theory and not by statistics?

Please clarify with examples.

Thanks in advance.

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closed as not constructive by Will Jagy, Hans Lundmark, Austin Mohr, Sam, Willie Wong Jun 27 '12 at 13:48

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As an analogy, every problem that can be solved with multiplication can be solved with addition, and yet it is still important to learn multiplication. Even if every fuzzy logic problem could be solved some other way (I do not know whether this is the case), it could be that fuzzy logic provides a simpler approach. – Austin Mohr Jun 25 '12 at 19:20

There are plenty of domains in mathematics that bring no general interesting new theorem but that are interesting in themselves, in that they bring new tools to prove things. One of the greatest contributions of number theory, for me, is that it gave birth to modern algebra by studying the groups $\mathbb Z / n\mathbb Z$ and $(\mathbb Z / n\mathbb Z)^{\times}$. Even though these are the simplest groups of all time (they are cyclic or direct products of cyclic groups), their study as number-theoretic objects also gave rise to the theory of characters. If you have read a little bit Dirichlet's proof on the infinity of primes in congruences classes, you see that it is also a wonderful use of complex analysis that one didn't expect to happen on questions about prime numbers, at the time the proof was first written.

And if my memory serves me well, I think fuzzy logic is used in developping artifical intelligence algorithms. Here's a Wikipedia link that confirms my doubts :

And maybe you don't see any interest as a statistician, but that only means it has no interest to you, and that is okay, but still, some people might need it. I don't need much statistics in what I do, still I think that statistics are very useful to other people.

Hope that helps,

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! good answer you was given, Can you suggest a problem, which is done in only bu Fuzzy and not by statistics?... – KRRG-BITS Jun 26 '12 at 3:32
Downvoters... Seriously? Man. Sometimes I think people are just out there to hate. @KRRG-BITS : Unfortunately I am not a specialist in fuzzy logic, I've just heard about it and read a few lines online, but that's it. I think I helped you as much as I can. – Patrick Da Silva Jun 26 '12 at 6:33
@I want more clarifications on my question by examples if possible. – KRRG-BITS Jun 26 '12 at 13:11
I didn't downvote, but I'll be happy to give you an upvote if you remove / amend your statement that the group $(\mathbb{Z}/n\mathbb{Z})^{\times}$ is cyclic: sometimes it is and sometimes it isn't! – Pete L. Clark Jun 27 '12 at 7:11
@Pete L. Clark : I was working on other things where I assumed that $n$ is prime and confused statements. Thanks for noticing. – Patrick Da Silva Jun 28 '12 at 6:26

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