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RE: [Reliable Computing] Re: Intervals "default" for beginners?

Title: RE: [Reliable Computing] Re: Intervals "default" for beginners?
This is actually exactly how fuzzy sets can be interpreted and computed, and this is how it is done in RiskCalc for fuzzy. A fuzzy set can be described as a nested sequence of intervals (alpha-cuts corresponding to different degrees alpha), and operations on fuzzy sets are exactly interval operations for each level.
 
This is not only in RiskCalc, this is how operations with fuzzy numbers are done in most cases, this is why most textbooks on fuzzy start with a chapter on interval computations, and we have cross-polination between our conferences.
 
One way to have nested sets is to take them from confidence intervals as you do, this is what Scott proposed quite some time ago.

From: Ralph [mailto:kelsey@xxxxxxxx]
Sent: Mon 4/27/2009 11:00 AM

However, I now think the best approach is using a sequence of nested
intervals. There are a couple ways you might implement math. But the big
advantage is that all the hard work that has been done in IA is
incorporated for free! A simple version is to have, say, 5 intervals
representing the 1 sigma, ..., 5 sigma intervals, and do calculations using
standard IA. I also carried along the midpoint and standard dev, and
evolved them using the standard engineering methods as a safeguard.

Ralph