Monday, 20 April 2009

Probabilistic foundations for measurement modelling with fuzzy random variables

P. Terán (2007). Fuzzy Sets and Systems 158, 973-986.

For some reason, I never wrote an entry for this paper when I started this blog.

It appeared in the FSS special issue Selected papers from IFSA 2005, 11th World Congress of International Fuzzy Systems Association, for which 7 papers were selected out of the 340 conference communications (I made it into the 2% cut, showing that events with probability zero do happen. To me, it was already a big success to make it into an invited session in Something's World Congress.)

It shows how to use fuzzy random variables to model measurements, in the most simple situation: the final estimate of the measurand is the average of the measurements. The measurand is assumed to be crisp; fuzziness appears due to uncertainty in measurement. Uncertainty is propagated using a t-normed extension principle with an Archimedean t-norm.

The paper points out a lot of things that remain to be done. This research was nice but it's hard for me to go on with it after I realized that I didn't know how to persuade a practitioner that this theoretical framework was simple enough to deserve their consideration.

Up the line:
·Strong law of large numbers for t-normed arithmetics (2008).

Down the line:
There are ideas for a sequel which I planned to submit to a metrology journal but, as I said, I've never found the words to convince them that it's worth reading.

To download, click on the title or here. There are some typos I hope were caught in proof-editing.

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