Tuesday, January 30, 2007

15. New papers on fuzzy p-values

As you may know, the notion of a fuzzy p-value in the sense of Geyer and Meeden has been warmly received by the statistical community (taking into account the cyclic FS-bashing episodes over decades, 'warmly' is a good thing).

Here you are some papers:

Fuzzy p-values in latent variable problems by Elizabeth Thompson and Charles Geyer. Update: Biometrika 94 (2007), 49-60.

Fuzzy p-values and ties in nonparametric tests by Charles Geyer.

Uncertainty in inheritance: assessing evidence for linkage by Elizabeth Thompson.

Interpreting significance in nonparametric linkage analysis: the fuzzy p-value distribution extended to multiple score functions by Lars Ängquist.

Saturday, January 27, 2007

14. Old paper in Test

The Spanish Statistics & OR Society (SEIO) has discontinued the website of their journal Test, which will now be editorially handled by Springer. It looks like, as a more or less tragic (and difficult to explain) consequence, papers published in the last years or forthcoming will no longer be freely accessible.

Here you are a link to the SPFS paper I've been able to rescue using Google. The link will eventually be discontinued as well: Integrals of random fuzzy sets by Volker Krätschmer.

This paper appeared in Test 15 (2006). It contains an extensive study of integrals of fuzzy random variables with convex values, defined via embeddings into Lp spaces.

Update: The SEIO website will temporarily keep accessible Test papers published in 2005 and 2006.

13. Old paper by Masson and Denœux

Another paper from Citeseer.

It is important that attention be paid to adapting modern statistical techniques to fuzzy data. Multidimensional scaling of fuzzy dissimilarity data does so for this technique which aims at visually helpful lower-dimensional representations of dissimilarities between objects. The nutshell idea is that similar objects are plotted as points at close distance, while dissimilar ones are farther apart. In this paper, dissimilarities are modelled by fuzzy numbers, whence objects are represented by fuzzy sets which appear in the plot as nice shadowed areas.

This paper appeared in Fuzzy Sets and Systems 128 (2002), 339-352.

12. Old papers by Körner and Näther

Some years ago I downloaded Ralf Körner's Ph.D. thesis from somewhere in the net but, unfortunately, it seems to have disappeared.

Anyway I have found at Citeseer a couple of papers thereof:

On the variance of fuzzy random variables. This paper by Körner appeared in Fuzzy Sets and Systems 92 (1997), 83-93.

May I bring to your attention that a definition of variance in the non-convex case is lacking.

Linear regression with random fuzzy variables: extended classical estimates, best linear estimates, least squares estimates. This paper by Körner and Näther appeared in Information Sciences 109 (1998), 95-118.

Wednesday, January 10, 2007

11. Two papers in a forthcoming special issue of FSS

The forthcoming special issue of Fuzzy Sets and Systems on Fundamentals of fuzzy logic and soft computing and some applications, edited by Yingming Liu, Mingsheng Ying and Guoqing Chen, will contain seven selected papers from the 11th World Congress of IFSA (Beijing, 2005).

Two of those papers are relevant to this blog:

Representation theorems, set-valued and fuzzy set-valued Ito integral
Shoumei Li and Aihong Ren

Probabilistic foundations for measurement modelling with fuzzy random variables
Pedro Terán

I'll try to talk Shoumei and Aihong into uploading theirs.

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Open-minded readers are urged not to miss Ulrich Höhle's two-part paper on the relationship between fuzzy set theory and sheaf theory, to appear in FSS. Update: FSS 158 (11), 1143-1174 and 1175-1212.

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Readers are reminded that I gladly accept link submissions.

Friday, January 05, 2007

10. Old paper by Gustave Choquet

Happy and prosperous new year!

I've found out that Choquet's mammooth paper is available for free at the French server Numdam: Theory of capacities.

This paper appeared in Annales de l'institut Fourier 5 (1954), 131-295. It is one of those papers divided in chapters, so I will not try to summarize its content.

It suffices to say that it contains a handful of notions and theorems which now carry Choquet's name, including the Choquet integral and the Choquet Theorem which is essential in the theory of random sets (both of which are of minor importance in the overall context of the paper -this gives you an idea of the magnitude of this work).