Re: Objective Meaning of Fuzzy sets

Sam Sengupta (sengupta@fang.cs.sunyit.edu)
Fri, 8 Mar 1996 19:56:00 +0100


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May you have a wonderful day!
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On Tue, 5 Mar 1996, Hans Wehn wrote:

> I am relatively new to Fuzzy Logic. One thing that always puzzled
> me is the apparent absense of an objective experimental meaning of fuzzy sets.
> For example, can I perform an objective experiment that lets me conclude that the
> membership degree of a 1.80m tall man in the set of "tall" men is, say, 0.8 rather
> than 0.001 ? In other words, when all I tell you is that I know a man has a
> membership of 0.8 in the set of tall men, then do I actually convey to you
> any information at all ?
>

Sure, some information is conveyed. But that may not be as crisp as the
proposition x is 3.089. Why do we insist that the information conveyed has
to be crisp? Think about a dictionary. How does it handle non-crisp entities
like 'tall', 'short' etc?

> One idea I had is to conduct a poll and ask people what membership degree
> they would give a 1.80m tall man in the set of "tall" men. Then take the average
> value as the true objective membership degree. Does this makes any sense ?

No, it would be with reference to a specific sampling domain and it would be
too crisp. What makes you think that in my mind, or in X's mind the average
of a set of data is the most meaningful way of representing the prototypical
data in the set? Why not the mode? Better still, why not leave the problem
of measure and inference to the person or entity who has to understand it.

> Hans
>
>

Warmest regards

Saumen (sengupta@sunyit.edu)
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