Wednesday, 7 May 2008

On convergence in necessity and its laws of large numbers

P. Terán (2008). In: Soft Methods for Handling Variability and Imprecision, 289--296. Springer, Berlin.

[Proceedings of the 4th Intl. Conf. on Soft Methods in Statistics and Probability]

An interesting question is what happens to random variables when the probability measure is replaced by a non-additive measure. That topic has been intermitently studied in the fuzzy literature for over 20 years, and has also received attention from economy theorists.

I've had a few ideas about that for some time. I took the opportunity to give an invited lecture at the University of Extremadura to put them in order and start writing a paper -which, however, won't be ready until the long awaited 36-hour-day regulations will be enforced.

This paper presents some convergence results, in an attempt to clarify the difference between LLNs for possibilistic variables and LLNs for their distributions identified with fuzzy sets.

It also shows that usual techniques, relying on shape assumptions related to the t-norm generators, can be effectively replaced by other techniques independent of the particularities of the t-norm modelling the interactivity between the variables.

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

Down the line:
An evolution of this paper with proofs and new results will be typed later this year. (I don't think that will happen. It's 2013 now and I doubt a journal would be excited to publish a full-length version of a 2008 conference paper. Why bother typing it then?- PT, Mar 18th 2013)

To download, click on the title or here.

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