Statistics, Probability and Fuzzy Sets

#102. Old paper by Arnold Neumaier

2010-11-26T20:30:00.002+01:00

From the abstract: "Clouds are a concept for uncertainty mediating between the concept of a fuzzy set and that of a probability distribution. A cloud is to a random variable more or less what an interval is to a number."

Arnold Neumaier (2004). Clouds, fuzzy sets, and probability intervals. Reliable Computing 10, 249–272.

#101. Off-topic

2010-11-11T09:51:00.000+01:00

By virtue of the 4% off-topic rule, here you are the following paper, which will be interesting to those interested in the philosophy of science.

Paul Hoyningen-Huene (2006). More letters by Paul Feyerabend to Thomas S. Kuhn on Proto-Structure. Studies on History and Philosophy of Science 37, 610-632.

It contains four new-found letters, two of which are rather long and discuss issues pertaining Feyerabend's reading of a preliminary version of The structure of scientific revolutions.

#100. CFP for three conferences

2010-11-04T13:11:00.002+01:00

You may be interested in the following conferences for 2011.

1. Linz 2011

The topic of the 32nd Linz Seminar on Fuzzy Set Theory is Decision theory: qualitative and quantitative approaches. Some of the topics covered are

* Decision theory
o Multifactorial evaluation and aggregation operations
o Utility theory
o Cooperative game theory
o Preference structures
o Modelling of preferential independencies
o Revision of preferences
* and applications to
o Multicriteria decision support
o Decision under uncertainty
o Voting procedures
o Recommender Systems
o Electronic commerce

Call for papers
Website
Abstract submission: Nov 14th 2010 (you're still in time).
Conference dates: Feb 1st-5th 2011.
Venue: Linz (Austria).

2. NLMUA 2011

Shoumei Li is the main local organizer of the 1st International Conference on Nonlinear Mathematics, Uncertainty and Applications. Some of the topics covered are:

Nonadditive measures and nonlinear integrals (including Choquet, Sugeno and other type integrals, possibility theory, Dempster-Shafer theory and so on)
Random sets, fuzzy random sets and related statistics
Set-valued and fuzzy stochastic processes, differential inclusions, multi-valued SDE
Imprecise probability theory and related statistical models
Fuzzy mathematics
Nonlinear functional analysis
Information theory
Mathematical finance and risk managements
Decision making under various types of uncertainty
Information fusion and knowledge integration in uncertain environments
Soft computing and intelligent data analysis
Applications in economics, finance, insurance, biology, engineering and others.

Call for papers
Website
Submission: March 15th 2011.
Conference dates: Sep 7th-9th 2011.
Venue: Beijing (China).

3. EYSM 2011

The 17th European Young Statisticians Meeting is intended for researchers under 30 or with a limited research experience. The topic is Statistics and Probability. Two participants per European country are selected (incidentally, the criteria change according to the country's culture; in Spain, the best CVs are selected; in Denmark or the Netherlands, they may be chosen randomly; in Russia, probably a big name in a Moscow university will make the choice).

If you're European or a researcher at an European institution, I strongly encourage you to apply. Not only you'll be able to say that you represented your country in an international event (a good bit for incidental conversation), but the experience is totally unlike a usual conference. I've been involved in the EYSM as both participant of the 14th edition and organizer of the 15th and I can tell you it's extremely enjoyable.

Website
Abstract submission: Apr 17th 2011.
Conference dates: Sep 5th-9th 2011.
Venue: Lisbon (Portugal).

Be aware that the selection process is carried out independently in each country, so you should find your contact here and ask him/her for specific information (if no international organizer is from your country, contact the meeting organization directly). For instance, in Spain you should additionally submit your CV prior to Jan 15th 2011.

#99. Old book by John M. Keynes

2010-11-01T12:39:00.000+01:00

And old book it is.

John Maynard Keynes (1921).
A treatise on probability. Macmillan, London.

#98. Free access to Inventiones, PTRF

2010-10-25T08:36:00.000+02:00

More Springer journals which will be open at the Springer website without subscription until Nov 30th 2010.

Inventiones Mathematicae here.

Probability Theory and Related Fields here.

Inventiones may be quite off-topic to this blog. Even if only out of curiosity, you may want to have a look at the 241-page paper "Chtoucas de Drinfeld et correspondance de Langlands" by Fields medallist Laurent Lafforgue.

#97. Free access to AOR

2010-10-18T17:20:00.002+02:00

In case you are interested, Springer is offering free access to all contents in Annals of Operations Research, from 1980 to the present, here.

This is valid until Nov 30th 2010.

#96. SMPS 2010 abstract book

2010-10-10T23:20:00.001+02:00

The abstract book of the 5th International Conference on Soft Methods in Probability and Statistics is now on the web here.

The sixth edition will take place in Konstanz (Germany).

#95. New journals from Wiley

2010-10-01T10:06:00.001+02:00

Wiley has launched a new collection of online journals: Wiley Interdisciplinary Reviews. They will be publishing survey and overview papers but only on a by-invitation basis. Access is currently free but it will cease to be so in the future.

Already working since 2009 is WIRe: Computational Statistics. You can find its presentation editorial here.

You may want to check the website.

Scheduled to launch in 2011 is WIRe: Data Mining & Knowledge Discovery, whose editor-in-chief is Witold Pedrycz.

#94. New survey paper by Hans-Jürgen Zimmermann

2010-09-24T21:49:00.004+02:00

Hans-Jürgen Zimmermann (2010). Fuzzy set theory. Wiley Interdisciplinary Reviews: Computational Statistics 2, 317–332.

This is a basic overview of fuzzy sets for a `foreign' readership. The contents covered are:

-History [strikingly, it finishes in 1992 with the genetic-neuro-fuzzy thing]
-Basic Definitions and Operations
-The Extension Principle
-Fuzzy Relations and Graphs
-Fuzzy Analysis
-Empirical Evidence
-Fuzzy Logic, Approximate Reasoning, and Plausible Reasoning
-Fuzzy Rule-Based Systems (Fuzzy Expert Systems and Fuzzy Control)
-Fuzzy Data Mining
-Fuzzy Decisions
-Fuzzy Optimization

Most of the material can be routinely found in textbook form. Although published in a statistical collection, no effort seems to have been made to craft the text for an audience of statisticians (in particular, the existence of a solid theory of fuzzy random variables isn't even mentioned).

(Note: According to the Wiley website, free access to the Interdisciplinary Reviews will be discontinued in the future. If you find it has been, please leave a comment and I'll remove the link.)

#93. Old lecture notes by Michael Smithson

2010-09-17T00:25:00.000+02:00

Lecture notes from a short course on uncertainty which took place in 2004. The approach is very general and leans toward philosophical issues.

Lecture 1. Formal uncertainty frameworks: debates and stalemates (14 pp.)
Lecture 2. Fuzzy sets, statistics, and measurement (18 pp.)
Lecture 3. Human judgment and heuristics, rationality debates (21 pp.)

#92. Old paper by Dubois and Prade

2010-05-22T18:27:00.003+02:00

Since everybody knows Dubois and Prade, and knows their work is available at the IRIT website, my linking to their papers is not really necessary.

The main points of the following paper are (assumed to be) well-known for insiders. Unfortunately, the confusions the authors patiently tried to dispel remain alive and kicking today.

Didier Dubois, Henri Prade (2001). Possibility theory, probability theory and multiple-valued logics: a clarification. Annals of Mathematics and Artificial Intelligence 32, 35-66.

The abstract is self-explanatory: `There has been a long-lasting misunderstanding in the literature of artificial intelligence and uncertainty modeling, regarding the role of fuzzy set theory and many-valued logics. The recurring question is that of the mathematical and pragmatic meaningfulness of a compositional calculus and the validity of the excluded middle law. This confusion pervades the early developments of probabilistic logic, despite early warnings of some philosophers of probability. This paper tries to clarify this situation. It emphasizes three main points. First, it suggests that the root of the controversies lies in the unfortunate confusion between degrees of belief and what logicians call "degrees of truth". The latter are usually compositional, while the former cannot be so. This claim is first illustrated by laying bare the non-compositional belief representation embedded in the standard propositional calculus. It turns out to be an all-or-nothing version of possibility theory. This framework is then extended to discuss the case of fuzzy logic versus graded possibility theory. Next, it is demonstrated that any belief representation where compositionality is taken for granted is bound to at worst collapse to a Boolean truth assignment and at best to a poorly expressive tool. Lastly, some claims pertaining to an alleged compositionality of possibility theory are refuted, thus clarifying a pervasive confusion between possibility theory axioms and fuzzy set basic connectives.'

#91. Old paper by Grace and Sawilowsky

2010-05-17T11:09:00.001+02:00

This paper may be useful for Statistics lecturers.

Tammy A. Grace and Shlomo S. Sawilowsky (2009). Data error prevention and cleansing: A comprehensive guide for instructors of statistics and their students. Model Assisted Statistics and Applications 4, 303–312.

#90. Old thesis by Joe Halliwell

2010-05-10T18:07:00.000+02:00

As tends to be the case, looking for something else I came across the following.

Joe Halliwell (2007). Linguistic Probability Theory. Ph.D.Thesis, University of Edinburgh.

Halliwell criticizes some notions of fuzzy probability and presents his own. The application emphasis is in Bayesian networks. Being out of my element, I can't say whether his axioms of fuzzy probability are original, since they are the same properties underlined in e.g. Wolfgang Trutschnig's paper A strong consistency result for fuzzy relative frequencies interpreted as estimator for the fuzzy-valued probability (Fuzzy Sets and Systems 159 (2008) 259 – 269), and I presume similar properties must have been spotted long ago in interval-valued probability.

#89. Books by David Fremlin at lulu.com

2010-03-12T21:26:00.002+01:00

David Fremlin is a well-known measure theorist who has written and (I guess) self-published a six-volume treatise in (of course) Measure Theory. I have always felt that he deserves some special recognition, since his prices are really much smaller than those of any commercial publisher and he needn't undergo the burden of taking care of our not paying unreasonable amounts of money for his work.

So I'd like to take the excuse that I've randomly found him selling at lulu.com to help promote his treatise. (I usually do so by citing him instead of another M.T. book, even if once a journal editor tried to persuade me to drop the citation on the basis that "Torres Fremlin, who knows that publisher?")

lulu.com is a print-on-demand publishing service. You can find some volumes of Fremlin's treatise there. As you will see, Fremlin's prices are astonishingly low for scientific books.

But this is not just a series of cheap thick books: I've always been fully satisfied by its value as a reference work.

#88. Course slides by Didier Dubois

2010-03-04T14:00:00.002+01:00

A summer course on "Soft Computing and Statistics" took place in Lisbon last summer, preceding the IFSA-EUSFLAT conference.

Here you are the slides for Didier Dubois's lectures on Uncertainty theories: a unified view. It contains a whole lot of material (175 slides which might need 500-600 book pages to cover), some of it really recent.

(Aside: I disagree with the claim that imprecise probabilities unify uncertainty theories. `Imprecise probabilities' is, at best, an umbrella label to create a sense of community or to facilitate raising funds. It is like saying: `I put all my toys in a bag and, wow, the bag unified the toys!')

#87. Old paper by Dubois, Foulloy, Mauris and Prade

2010-02-24T12:40:00.003+01:00

As you (may) know, the purpose of this blog is to link to material available for free in the Internet, so papers available only on a pay-a-third-party basis are not talked about (let me note, as an aside, that I fail to understand why Elsevier or whoever may charge somebody with $35 for a PDF file of my paper, of which I will see $0).

Often that means I spend years waiting till somebody uploads an interesting paper.

Didier Dubois, Laurent Foulloy, Gilles Mauris, Henri Prade (2004). Probability-possibility transformations, triangular fuzzy sets,
and probabilistic inequalities. Reliable Computing 10, 273–297.

This is a paper on probability-possibility transformation. It relates triangular fuzzy sets with certain families of probabilities. Although the results have still a tentative nature, it's clear the authors hit something solid with this one. Moreover, the research is carefully justified (as usual in a Dubois-Prade paper).

Further work has been made in the meantime, but still a significant paper.

#86. Old paper by Jonathan Lawry

2010-02-17T11:54:00.001+01:00

The PDF of an interesting paper popped up while looking for something else.

Jonathan Lawry (2004). A framework for linguistic modelling. Artificial Intelligence 155, 1–39.

The topic is modelling linguistic labels. If you are familiar with the Bristol people, you know they tend to favour the random-set interpretation of fuzzy sets, instead of the fuzzy-logic approach. In this case, however, to model a linguistic constraint on a variable they match each individual to a set of appropriate labels, so the mathematical object is a random subset of a finite universe of labels.

Sections 1 and 2 make a long introduction which is informative and carefully written.

#85. Old papers by Huibert Kwakernaak

2010-02-10T11:30:00.002+01:00

Kwakernaak's old papers in which he first defines fuzzy random variables.

Huibert Kwakernaak (1978). Fuzzy random variables- I. Definitions and theorems. Information Sciences 15, 1-29.

Huibert Kwakernaak (1979). Fuzzy random variables- II. Algorithms and examples for the discrete case. Information Sciences 17, 253-278.

There is a very interesting historical issue. The core idea "fuzzy+random" was generated independently a number of times in the late seventies, e.g. Féron's fuzzy random set (1976), Hirota's probabilistic set (1977) and Nahmias's fuzzy variable in a random environment (1979). The question is, why all at the same time and why it was that, particularly, fuzzy random variables triggered other researchers' continued work.

#84. New M.Sc. Thesis by Naimeh Sadeghi

2010-02-03T17:21:00.000+01:00

Naimeh Sadeghi (2009). Combined fuzzy and probabilistic simulation for construction management. University of Alberta, Canada.

Your output is a function of several variables. For some of them you have probability distributions, for other only fuzzy sets (or possibility distributions). The point is how to use Monte Carlo simulations in that situation. The core idea is to simulate the probabilistic variables and pass the fuzzy uncertainty on using an extension principle, thus an artificial sample of fuzzy sets is obtained. Using fuzzy arithmetics, you may calculate then a fuzzy estimate of the expected value of your output. If more information is needed, a fuzzy set of cumulative distribution functions can be calculated and used to estimate quantiles, etcetera. Two applications are presented.

Bonus material: If you're interested, check also the following papers.

Dominique Guyonnet, Bernard Bourgine, Didier Dubois, Helène Fargier, Bernard Côme, Jean-Paul Chilès (2003). A hybrid approach for addressing uncertainty in risk assessments. Journal of Environmental Engineering 129, 68-78.

Cédric Baudrit, Dominique Guyonnet, Didier Dubois, Hélène Fargier (2005). Post-processing the hybrid method for addressing uncertainty in risk assessments. Journal of Environmental Engineering 131, 1750-1754.

Cédric Baudrit, Didier Dubois, Dominique Guyonnet (2006). Joint propagation and exploitation of probabilistic and possibilistic information in risk assessment. IEEE Transactions on Fuzzy Systems 14, 593-608.

#83. Invited session in SMPS 2010

2010-01-27T22:37:00.001+01:00

I am in charge of organizing an invited session on Probabilistic aspects of fuzzy sets for the 5th International Conference on Soft Methods in Probability and Statistics (Mieres and Oviedo, Spain, late September 2010).

If you are interested in submitting a communication for the session, please contact me (teranpedro at uniovi dot es). Relevant topics are fuzzy random variables or any other combinations of probability + fuzzy.

The submission process will be open between Feb 1st and Mar 1st 2010.
Here you are the conference website. Here you are the full list of invited sessions.

#82. Old paper by Stephan Morgenthaler

2009-12-11T13:26:00.004+01:00

A very interesting survey paper on robust methods, followed by some equally interesting discussions. The survey is highly non-technical and so almost everybody makes insightful remarks, which is very nice to the foreigner.

Stephan Morgenthaler (2007). A survey of robust statistics. Statistical Methods and Applications 15, 271-293.

Here is the list of discussants:
1. Anthony C. Atkinson, Marco Riani and Andrea Cerioli
2. Christophe Croux and Peter Filzmoser
3. Laurie Davies and Ursula Gather
4. Ricardo A. Maronna and Víctor J. Yohai
5. Hannu Oja and Frank Critchley
6. Daniel Peña
7. Peter J. Rousseeuw and Stefan Van Aelst

Filzmoser will be giving one of the plenary lectures at the SMPS 2010, on Soft methods in robust statistics.o

#81. Old papers by Efron and Liang

2009-12-04T19:06:00.000+01:00

In lack of good fuzzy papers* on microarray data and other biology challenges in the frontier of current statistical ability, here you are two non-fuzzy papers.

Bradley Efron (2008). Microarrays, empirical Bayes and the two-groups model. Statistical Science 23, 1-22.

Yulan Liang (2008). Statistical advances and challenges for analyzing correlated high dimensional SNP data in genomic study for complex diseases. Statistics Surveys 2, 43-60.

If you are a curious graduate student, please note: It is much more likely that mainstream statisticians will come to welcome fuzziness if used to solve problems they still don't have good solutions to, than if used to solve problems they think they already solved half a century ago.

*Meaning that my few expeditions have been unfruitful, not that there do not exist any. Feel free to make suggestions in the comments.

#80. New paper by Judea Pearl

2009-11-27T13:53:00.002+01:00

A long survey of Pearl's take on statistics-based causality studies.

Judea Pearl (2009). Causal inference in statistics: an overview. Statistics Surveys 3, 96-146.

#79. Old paper by Andrew Gelman

2009-11-20T14:03:00.001+01:00

Bayesian Analysis recently published and had discussed a short piece by Andrew Gelman in which he played the role of an `anti-Bayesian' (sic) and proposed a number of objections to Bayesian statistics.

There is something inherently wrong when a journal editor asks a statistician to adapt an April Fool's Day blog post for publication and discussion in a (nominally at least) scientific journal, then the statistician (of course) closes the discussion by taking the chance to `dismount' said objections. That can only turn out as an exercise of frivolity or a postmodern parody of a scientific discussion.

This being said, when expert people talk about something they've been thinking about for years, we mere mortals may find something to learn however lightly they gloss over the depths of the subject.

Andrew Gelman (2008). Objections to Bayesian statistics. Bayesian Analysis 3, 445-478 (with discussion by Bernardo, Kadane, Senn and Wasserman).

If you don't feel like downloading each item separately, you can download the whole issue here (3.8 Mb!) and print the parts you're interested in.

Finally, here you are a completely unrelated blog post on the Bayesian-or-Frequentist thing. Additionally, in the comments to that post there are several links which may be of interest.

#78. STMA-Z database

2009-11-10T09:57:00.002+01:00

You can access the database STMA-Z of statistical papers here. STMA stands for `Statistical Theory and Method Abstracts' and Z (presumably) for Zentralblatt, the European equivalent of Mathematical Reviews. For each paper, you have either its abstract or its Zentralblatt review if the latter exists.

You may know that the Zentralblatt database has free online access, although only 3 results will show for each search if your institution does not have a subscription. But if you content yourself with papers having MSC codes 60 and 62 (Probability Theory and Statistics), the access via the STMA-Z website will currently give you all results without restrictions.

Presumably, access will be restricted at some unspecified point in the future.

#77. Off-topic

2009-11-07T20:30:00.002+01:00

Here you can find a truly mindblowing, jaw-dropping, awe-inspiring gallery of Mars pictures from the Mars Reconnaissance Orbiter. Enjoy!

#76. Mathematics Subject Classification 2010

2009-11-03T21:08:00.004+01:00

I ignore whether the 2010 revision of the MSC codes of the American Mathematical Society and the European Mathematical Society has already `officially' superseded the 2000 version. Providing MSC codes for a paper is needed when submitting to some mathematical journals, and they are also used in Mathematical Reviews.

Whether you are an author or a reviewer, you may be interested in the following new codes:

60A86 Fuzzy probability
62A86 Fuzzy analysis in statistics
62B86 Fuzziness, sufficiency, and information
62C86 Decision theory and fuzziness
62E86 Fuzziness in connection with the topics on distributions in this section [i.e. 62E Distribution theory]
62F86 Parametric inference and fuzziness
62G86 Nonparametric inference and fuzziness
62H86 Multivariate analysis and fuzziness
62J86 Fuzziness, and linear inference and regression
62K86 Fuzziness and design of experiments
62L86 Fuzziness and sequential methods
62M86 Inference from stochastic processes and fuzziness
62N86 Fuzziness, and survival analysis and censored data

As you may see, there is a whole new transversal `86' category, which is good because fuzzy + stat papers were being inaccurately labelled 99% of the time (the closest niche for a paper on fuzzy random variables was 60D05 "Geometric probability and stochastic geometry", enough said).

The MSC2010 can be found here.

#75. SMPS 2010 CFP

2009-10-23T15:33:00.002+02:00

The 5th International Conference on Soft Methods on Probability and Statistics (Spain, September-October 2010) already has a website and a preliminary call for papers.

This time, the conference is associated to a COST action from the European Science Foundation which tries to bring together people from the Statistics and Soft Computing communities.

My personal opinion is that, for the SMPS to make sense, it is imperative to become something larger than a mere biannual meeting for fuzzy people working on problems most statisticians don't really care about at all.

I'm happy to see the local organizers heading in that direction. The program commitee includes people working on topics like censored data (Ricardo Cao), robust statistics (Stefan van Aelst), computational econometrics (Manfred Gilli) and others; and the list of featured topics has grown accordingly.

Presently (not in the SMPS but in general), some interface opportunities, like functional data, coarse data, robustness, etc. are not really being exploited, nor sufficient attention is being paid to identifying the points at the frontier of statistical research where fuzzy methods may have something to offer. Or so I think.

#74. Old paper by Mitra et al.

2009-10-09T20:33:00.003+02:00

Being far from safe ground, I can't say anything on the completeness or quality of this survey paper, but it might make a starting point for healthily curious people.

Sushmita Mitra, Sankar K. Pal, Pabitra Mitra (2002). Data Mining in Soft Computing framework: a survey. IEEE Transactions on Neural Networks 13, 3-14.

#73. Old paper by Eyke Hüllermeier

2009-08-14T21:57:00.000+02:00

Hüllermeier gave a nice plenary talk (on fuzzy sets in machine learning and data mining) last month at the IFSA World Congress. Unfortunately, neither his slideshow nor his homonimous paper in Applied Soft Computing seem to be available on the net.

In the meantime, we'll have to do with older material in the same direction.

Eyke Hullermeier (2005). Fuzzy methods in machine learning and data mining: status and prospects. Fuzzy Sets and Systems 156, 387-406.

Further papers of his can be found here.

#72. Martin Sewell's Statistics FAQ website

2009-08-06T20:26:00.002+02:00

You can find a lot of links to interesting papers there.

Sewell seems to be a strong believer in the Bayesian credo. However puzzling his opinions may get, a particularly nice fact is that he also provides links to papers and Internet discussions where opposite views are held, a very much appreciated effort. So you can find there interesting material by all parts.

If you spend some time digging the website, you will find links to a lot of valuable material, not only foundational but also mathematical.

#71. Temporarily free online access to PTRF

2009-07-31T11:42:00.004+02:00

Springer is offering free online access to Probability Theory and Related Fields here.

This is valid until Aug 31st 2009.

PTRF is a top journal (maybe the top journal) in Probability Theory, so go ahead and have a look.

#70. New paper by Grigorii Melnichenko

2009-07-30T21:13:00.004+02:00

Stop the press, here comes an unexpected paper!

JMVA is going to publish yet another fuzzy paper; particularly, a paper on quantum logic.

Grigorii Melnichenko. Energy discriminant analysis, quantum logic, and fuzzy sets. Journal of Multivariate Analysis, to appear. Update: JMVA 101 (2010), 68-76.

As you may or may not know, broadly speaking there are two main approaches to what a physicist might call non-Kolmogorovian probability. One uses operator-valued probabilities and has led to a quite fruitful field of research called non-commutative or free probability. The other goes back to work by Birkhoff and von Neumann in the 30's, and uses real-valued probabilities but defined on structures poorer than sigma-algebras (e.g. orthomodular lattices; in the original work, events are defined as closed subspaces of a Hilbert space).

While the first-mentioned approach has found strong supporters among statisticians, notably Richard Gill (who has a lot of interesting work on `quantum statistics'), I had never seen a paper from the second strand in a Statistics journal (only in Theoretical Physics journals). But there's a first time for everything...

#69. New paper by Steven Vickers

2009-07-29T16:41:00.003+02:00

The connection between this paper and the topics covered in this blog could admittedly not be evident.

Steven Vickers. Fuzzy sets and geometric logic. Fuzzy Sets and Systems, to appear.

The paper follows up Höhle's recent papers (already mentioned here) on the relationship between fuzzy sets and sheaves.

The reason why I am, in a broad sense, interested in this may be clearer in the following paper.

Steven Vickers (2007). Locales and toposes as spaces. In: Marco Aiello, Ian E. Pratt Hartmann, and Johan F.A.K. van Benthem, editors, Handbook of Spatial Logics, 429-496 (chapter 8). Springer.

Sooner or later, we will all formalize events using those and similar tools.

#68. New book by Krzysztof Burdzy

2009-07-13T21:36:00.005+02:00

I have randomly learnt that Burdzy has found a publisher for his book

Krzysztof Burdzy (2009). The search for certainty. On the clash of science and philosophy of probability. World Scientific.

(before that, it was available at his website for some time).

Here at the publisher's website for the book, you can download some material, including the introduction chapter.

Here at the author's website, you can find further material including a link to the book's blog and a promotional code for a 20% discount if you buy the book before August 31st.

#67. Old paper by Colubi et al.

2009-06-26T23:52:00.001+02:00

A survey on fuzzy random variables from the point of view of Statistics.

Ana Colubi, Renato Coppi, Pierpaolo D'Urso, María Ángeles Gil (2007). Statistics with fuzzy random variables. Metron 65, 277-303.

It gives a good overview of what the Oviedo group has been doing for many years now, anyway I feel the survey is maybe too self-centered to be fair to other researchers.

#66. Old paper by Shafer and Vovk

2009-06-20T22:08:00.003+02:00

I presume you have heard about Glenn Shafer and Vladimir Vovk's game-theoretic approach to probability, so this one travels a different (but not really disjoint) path.

In this paper they trace the early history of measure-theoretical probability culminating in Kolmogorov's well-known book.

Glenn Shafer, Vladimir Vovk (2006). The sources of Kolmogorov’s Grundbegriffe. Statistical Science 21, 70--98.

Their account is nice and very informative, not avoiding technical details. It's a pity people don't pay historical issues more attention.

#65. Old papers by Volker Krätschmer

2009-06-06T11:25:00.002+02:00

You can find Krätschmer's papers here at his website.

After working for some years on fuzzy random variables and related problems, Volker, like a number of other capable researchers, recently moved on to greener pastures (probability in finance).

Specially interesting are his four papers published in 2006.

In his Test paper he discusses at length several extensions of known vector-valued integrals (Bochner and Pettis) to fuzzy random variables. The other three papers, two of them in the Journal of Multivariate Analysis, are on least squares estimation with fuzzy random variables, including "sqrt n" consistency and limit distributions, which I have never seen discussed elsewhere.

#64. Forthcoming book by Reinhard Viertl

2009-05-30T21:49:00.001+02:00

A number of online sellers are already accepting preorders of Reinhard Viertl's new book Fuzzy data and Statistics, seemingly to appear in Dec 2009 in Wiley.

As the name `Wiley' may suggest, this will be the third time (to the best of my knowledge) that fuzzy material makes it into the Wiley Series on Probability and Statistics.

First, Finding groups in data: an introduction to cluster analysis (1990, by Kaufman and Rousseeuw) discussed fuzzy and nonfuzzy clustering on equal footing.

Second came Statistical applications using fuzzy sets (1994, by Manton, Woodbury and Tolley), whose grade-of-membership method made heavy use of fuzzy partitions (although, it looks like currently the fuzzy interpretation has been expurgated from the theory).

#63. Old paper by Coppi, Gil and Kiers

2009-05-23T21:08:00.000+02:00

This paper introduced the CSDA special issue on The fuzzy approach to Statistics. Before presenting the papers in that issue, it presents Coppi's self-called `informational paradigm' which inserts Statistics in a wider landscape of information management and knowledge acquisition tasks.

Renato Coppi, María Ángeles Gil, Henk A. L. Kiers (2006). The fuzzy approach to statistical analysis. Computational Statistics and Data Analysis 51, 1-14.

Here you are another document, now found at the Italian Statistical Association website, in case it is clarifying:

Renato Coppi (2007?). The treatment of different sources of uncertainty affecting the data and the statistical models according to the Informational Paradigm.

#62. Old paper by Laviolette and Seaman

2009-05-16T19:50:00.002+02:00

Luckily, I've found another paper I have wanted to link to since I started this blog.

I have very little good to say about it and I believe it did do a serious disservice to its cause. Anyway, it has considerable historical interest.

Michael Laviolette, John W. Seaman Jr. (1994). The efficacy of fuzzy representations of uncertainty. IEEE Transactions on Fuzzy Systems 2, 4-15.

This paper was discussed in pages 16-42 as you can see here.

#61. Old papers on fuzzy set elicitation

2009-05-09T17:45:00.001+02:00

There are plenty of papers on how to elicit fuzzy sets. These have a strong emphasis on measurement-theoretical aspects.

Feel free to suggest in the comments more interesting papers like these (or with a different emphasis).

Jay Verkuilen (2005). Assigning membership in a fuzzy set analysis. Sociological Methods and Research 33, 462--496.

(A recent survey with a social science twist.)

Taner Bilgiç, Burhan Turksen (1999). Measurement of membership functions: theoretical and empirical work. Chapter 3 in Fundamentals of Fuzzy Sets (Didier Dubois, Henri Prade, editors), 195-230.

(I presume everybody knows this one, an excellent starting point.)

#60. Old paper by Witold Pedrycz

2009-04-30T23:03:00.001+02:00

I presume a thorough search would discover many interesting papers by Pedrycz in the net. This one makes a nice reading:

Witold Pedrycz (2007). Collaborative and knowledge-based fuzzy clustering. International Journal of Innovative
Computing, Information and Control 3, 1-12.

The content is much more `philosophical' than `technical', explaining some ideas from his `human-centric' view of clustering techniques. I recall distinctly Pedrycz's talk at IFSA'05 (Dubois's as well, but that's material for another post). A catchy example of Pedrycz's was a system which would learn to classify your digital picture collection. I thought: Now that's definitely a clustering problem and how far it is from the typical view of clustering in statistical books and journals!

More technical material can be found in Pedrycz's book (link to Google Books).

Witold Pedrycz (2005). Knowledge-based clustering: from data to information granules. Wiley, Hoboken.

#59. Old paper by Lotfi Zadeh

2009-04-25T03:47:00.006+02:00

Related to the Singpurwalla-Booker paper just below is, of course, Zadeh's original paper on probability of fuzzy events.

Lotfi A. Zadeh (1968). Probability measures of fuzzy events. Journal of Mathematical Analysis and Applications 23, 421-427.

More papers by Zadeh can be found here.

A nice Powerpoint presentation based on (the short version of) Dubois and Prade's Fuzzy sets and probability: Misunderstandings, bridges and gaps, where fuzzy events play a role, can be found here.

If that weren't enough, Gert de Cooman recently discussed the issue here in his blog.

#58. Old paper by Singpurwalla and Booker

2009-04-24T18:51:00.004+02:00

I have often googled to find a free copy of this paper since I started this blog.

Nozer Singpurwalla, Jane A. Booker (2004). Membership functions and probability measures of fuzzy sets. Journal of the American Statistical Association 99, 867-877.

Here is my review of it for Mathematical Reviews.

As I say there, I believe that it will be remembered as the first attempt to transmute fuzzy sets into something palatable to hardcore Bayesians.

#57. Old chapter by Thoralf Skolem

2009-04-24T18:20:00.002+02:00

Via Project Euclid, one can access Skolem's Abstract set theory (70-page lecture notes published by the University of Notre Dame). Its Chapter 18 summarizes very briefly Skolem's approach to proving the consistency of set theory within Lukasiewicz [0,1]-valued logic.

Just a curiosity, but--

Thoralf Skolem (1962). The possibility of set theory based on many-valued logic.

The whole volume can be downloaded chapter by chapter here.

#56. Old paper by Glen Meeden

2009-04-21T01:31:00.002+02:00

Meeden co-authored the paper on fuzzy p-values which sadly seems to have made little or no impact in the fuzzy statistics community.

In this recent paper, he discusses his views on probability-possibility `translation'. In spite of the title, I say so because I think he means a possibility distribution when he says 'a fuzzy set'.

Meeden seems to be unaware of the literature in this topic, but anyway his approach has a rather Bayesian flavour by making it a loss-driven decision, and that's nice (although, a criticism in point is that his loss functions lack a fuzzy interpretation).

Glen Meeden (2008). Fuzzy set representation of a prior distribution. In: Pushing the limits of contemporary Statistics: Contributions in honor of Jayanta K. Ghosh, 82-88. Published by the IMS.

One further fuzzy preprint is:

Glen Meeden, Siamak Noorbaloochi. Hypotheses testing as a fuzzy set estimation problem. Available as a technical report from the University of Minnesota.

More papers of his can be found here.

#55. Old book by Nguyen and Wu

2009-04-15T12:39:00.004+02:00

As it turns out, someone has uploaded Hung Nguyen and Berlin Wu's Fundamentals of statistics with fuzzy data (Springer, 2006) to direct download servers. I didn't put it there and I ignore who did it, in particular if he had the legal right to do so. If you are uncomfortable with that, or think that downloading the book may be illegal in your country, just use Google Books or inter-library loan instead.

Instructions: In this page, follow the "Rapidshare" link (if it doesn't work, try the "File Factory" link but the process is then more complex), then click on the button "Free user", wait for as long as you're asked to do, finally a button "Download" will appear, click on it. The PDF is compressed as a RAR file, so you will need a decompressor for it. If you haven't any, google for e.g. WinRAR and download a shareware version for free.

#54. Special issue on Fuzzy Sets and Statistics (CFP)

2009-04-07T13:00:00.004+02:00

Computational Statistics and Data Analysis is preparing their second special issue on Fuzzy Sets and Statistics, this time with Ana Colubi, Didier Dubois and Frank Klawonn serving as guest editors.

The deadline is December 15th, 2009. However you may also be interested in submitting a conference version of the paper to the track Fuzzy Statistical Analysis of the 2nd International Workshop of the ERCIM Working Group on Computing & Statistics, in which case a prior deadline for 1-page abstracts is June 1st, 2009.

Update: July 31st, 2009.

Further info here and here, respectively.

#53. Essay at edge.org

2009-01-19T12:07:00.003+01:00

This is an interesting essay I found while surfing the net.

Nassim Nicholas Taleb (2008). The fourth quadrant. A map of the limits of statistics.

The main point is that mind habits (got by osmosis or lack of deep understanding) obtained in ordinary statistics courses are dangerous in decision-making with extreme value distributions. The text leans towards the role of extreme events in wrong risk assessment leading to the current economic crisis.

Although the point of view is strictly probabilistic, there is a resonance with some important ideas behind `alternative' uncertainty modelling. For instance,

"Are we using models of uncertainty to produce certainties?"

"Given a set of observations, plenty of statistical distributions can correspond to the exact same realizations—each would extrapolate differently outside the set of events on which it was derived."

---
If you find the essay interesting: in the last SMPS, Dominique Guyonnet gave a keynote lecture on possibilistic risk analysis for enviromental decisions which is very nice to follow. The paper is in the conference proceedings.

#52. New special issue of FSS

2008-12-26T12:26:00.007+01:00

Issue 160(3) of Fuzzy Sets and Systems (February 2009), guest edited by Erich Peter Klement and Radko Mesiar, is a special issue with selected papers from Linz 2007. The topic is Fuzzy sets, probabilities, and statistics: gaps and bridges.

The table of contents is as follows.

Editorial
Page 291
Erich Peter Klement, Radko Mesiar

Fuzzy inclusion and similarity through coherent conditional probability
Pages 292-305
Romano Scozzafava, Barbara Vantaggi

T-conditional possibilities: Coherence and inference
Pages 306-324
Giulianella Coletti, Barbara Vantaggi

A concept of duality for multivariate exchangeable survival models
Pages 325-333
Fabio Spizzichino

On a class of transformations of copulas and quasi-copulas
Pages 334-343
Elisabetta Alvoni, Pier Luigi Papini, Fabio Spizzichino

Statistical inference about the means of fuzzy random variables: Applications to the analysis of fuzzy- and real-valued data
Pages 344-356
Ana Colubi

Estimation of a simple linear regression model for fuzzy random variables
Pages 357-370
Gil González-Rodríguez, Ángela Blanco, Ana Colubi, M. Asunción Lubiano

Uncertainty measures—Problems concerning additivity
Pages 371-383
Siegfried Weber

The issue also contains the following regular paper, which anyway is on-topic so I include it here as well.

A Monte Carlo-based method for the estimation of lower and upper probabilities of events using infinite random sets of indexable type
Pages 384-401
Diego A. Alvarez

---
The proceedings of the seminar can be found here.

#51. Old paper by Dubois and Hüllermeier

2008-07-18T14:00:00.004+02:00

No time lately.

Didier Dubois, Eyke Hüllermeier (2007). Comparing probability measures using possibility theory: A notion of relative peakedness. Int. J. Approx. Reasoning 45, 364-385.

#50. Off-topic

2008-03-11T17:13:00.003+01:00

For the interested readers, you can download the mamooth paper of Anton Kapustin and Edward Witten, 231 pages widely known as the Kapustin-Witten paper, from the net.

Electric-magnetic duality and the geometric Langlands program (2006).

That was written in 2006 and, as far as I know, is still unpublished or was never meant to be published traditionally.

You can also download the more recent lectures notes of Kapustin on the same topic, based on a 2007 course. They amount to a mere 38 pages and may be more readable.

Lectures on electric-magnetic duality and the geometric Langlands program

And no, I don't understand a word of what these gentlemen say but I will make my way through it anyway.

49. Editorial post

2008-03-11T12:46:00.004+01:00

We are about to reach fifty posts and one year and a half on the net.

When I started this blog, I thought I'd send an e-mail informing each cited researcher. However, I felt that if only few posts were available, they would classify the blog as an anecdote of little use and probably not be back. So I sent the blog's address only to close friends and colleagues.

Now, the blog has received 1,349 visits and ranks in fifth position (over 280,000 search results) when you google for "fuzzy sets"+"statistics". One thousand visits is a modest number for a common blog (my personal blog has had 19,000 page loads in the same time, and it's a modest one) but maybe not so when the information delivered is so highly specialized and arrives at a slow rate of two posts per month.

The blog looks quite serious now and contains many links to interesting papers and books. As an important development, I have added a box in the right column so that readers can have the new posts delivered at their e-mail address. So I think it's about time to undertake the task of promoting the SPFS blog by informing all cited researchers that their work has been linked here.

As to `editorial' decisions to be announced at a moment like this, there are three of those.

1. Post 25 was off-topic and I have decided that a 4% of off-topic posts is OK.

2. Begining with post 51, a number of entries will be devoted to linking to the SPFS material in Google Books. If you know, Google has been digitalizing books for some time, with or without permission from copyright owners, and I've been shocked to find out how much material is there. It will take some time to make a careful search and organize the results, though.

3. Some effort in the following direction will be made: posting about applications and presence of fuzzy statistical methods in different fields. For instance, I have long wanted to write a post about fuzzy methods for microarray data (I downloaded a couple of papers but were not very good).

And, finally, an observation. If you remember, only links to publicly accessible papers are posted, so it's a little frustrating to me when I find good new papers that can be accessed only on a pay-a-third-party basis. I bring to everybody's attention that currently many publishers will let you retain the right to post your papers at your website, or at a public repository. You needn't go through creating and maintaining a website to have them accessible to everyone: a blog and a file hosting service is all you need, and there are plenty of free providers for both things. Actually, you can get started in less than ten minutes.

48. New paper by Arnold Shapiro

2008-02-29T17:50:00.002+01:00

An introduction to fuzzy random variables, intended for an actuarial science audience.

Arnold F. Shapiro. A fuzzy random variable primer.

It may be worth pointing out that Shapiro was awarded the second-best-presentation award in the 42nd Actuarial Research Conference (August 2007) for this paper.

47. Old book by Edwin Jaynes

2008-02-13T12:49:00.002+01:00

I thought the `preprint' version of Jaynes's book had been removed from the Internet when it was published in paper. Either I was wrong, or it is back there anyway. It can be downloaded, chapter by chapter (30 chapters plus 9 appendices), as PS files. Be aware that these files are not final (or they weren't the first time I found them) as Jaynes died before finishing the book, leaving some parts unfinished, and the final version was prepared by Larry Bretthorst.

Edwin T. Jaynes (2003). Probability Theory. The logic of science. Cambdridge Univ. Press, Cambridge.

Sometimes lucid, sometimes irritating, sometimes enlightening, often misguiding.

46. Old theses by Körner, Hébert and myself

2008-02-05T17:48:00.001+01:00

I finally found Ralf Körner's thesis

Ralf Körner (1997). Linear models with random fuzzy variables

at his old website at Freiberg. Some preprints can be found there too.

Moreover, I've found P.-A. Hébert's

Pierre-Alexandre Hébert (2004). Analyse de données sensorielles : une approche ordinale floue (Sensorial data analysis: an ordinal fuzzy approach).

It seems fair enough to add my own thesis here, even if it were only to make this really multi-language.

Pedro Terán (2003). Teoremas de aproximación y convergencia para conjuntos y funciones aleatorias (Approximation and convergence theorems for random sets and random functions).

45. Old papers by Thierry Denœux and co-workers

2008-02-05T17:37:00.000+01:00

Denœux works, among other things, on fuzzy data analysis. He is one of several people who have started devising methods for fitting fuzzy measures to empirical data.

Some papers of his can be found here at his website.

44. Old paper by Baudrit, Couso and Dubois

2008-02-03T21:19:00.000+01:00

Hybrid methods for uncertainty modelling are in their infancy. I suspect we might be missing a whole layer of deeper concepts underlying the familiar notions of probability, possibility, etcetera.

The near future, hierarchical Bayesian modelling rising exponentially, may be dark for some time for realistic approaches. Ideally, we'd need a compelling foundation* which would suggest simple practical implementations, reasonable for practitioners.

Cédric Baudrit, Inés Couso, Didier Dubois (2007). Joint propagation of probability and possibility in risk analysis: towards a formal framework. Int. J. Approx. Reasoning 45, 82-105.

* No, I don't find Bayesian foundations compelling at all.

43. SMPS'08: Deadline extended

2008-02-01T11:10:00.000+01:00

The deadline for paper submission to the 4th International Conference on Soft Methods in Probability and Statistics has moved from Feb 1st to Feb 11th.

42. Advice on starting to get published in Statistics and Probability journals

2008-01-15T12:52:00.000+01:00

Unfortunately, there is little mutual interest or communication between typical fuzzy researchers and typical statistics researchers.

There seem to be two positions among SPFS researchers. Some of them think it's fine to have all their papers published in, say, FSS or INS or IEEE:TFS. That, I acknowledge, is good for their position within the fuzzy community, since many people just don't check non-fuzzy journals and so the efficacy of their efforts to get visible is undivided. Others think that publications should be allocated among fuzzy and non-fuzzy journals alike.

In order to do the latter, one needs to know which Statistics journals are better than others, and which give fuzzy papers a fair chance.

My advice is: you will lose less time if you don't bother to submit to journals which haven't published fuzzy papers for some time. On the other hand, some statistical journals have sustainedly published fuzzy material or don't have bizarre objections to it, for instance (in no particular order; more names will be added as they come to my mind)

Computational Statistics and Data Analysis
Metrika
Statistics and Probability Letters
Test

Publishing fuzzy in JCR-covered Probability journals is extremely hard, and although winning the lottery may need more luck, I'm not sure. They are very few, of good quality and they prefer their own fashionable topics. An exception is Stochastic Analysis and Applications, which has published some fuzzy material of a very specific nature.

Thus you would do better, paradoxically, in general math journals. A couple of journals I've had a very pleasant experience publishing with are

Journal of Approximation Theory
Proceedings of the American Mathematical Society

I recommend that you avoid the Journal of Mathematical Analysis and Applications. Not only it will avoid you anyway if you don't, but it's by large the less serious journal I've ever submitted to.

As far as journal quality or prestige is concerned, if you look at the journals' editorial boards without recognizing any name on it, you may want to trust me on the following recommendation.

First, download this document. It contains the tables in the following paper:

V.Theoharakis, M.Skordia (2003). How Do Statisticians Perceive Statistics Journals? American Statistician 57, 115-123.

You may also get the paper, but the tables contain all the information. As you will see, they are very informative.

Second, if you wish to use an objective ranking, my advice is that you may like the Article Influence indicator calculated by eigenfactor.org rather than the well-known company-owned Impact Factor. The AI can be accessed free and is calculated from the same data. It uses the Page Rank algorithm developed by Google to rank websites.

I know of three such rankings:
-The Impact Factor introduces some serious distortions in the ranking.
-The brand new SCImago ranking (which uses the SCOPUS database) is seriously wrong. However the SCImago website will provide you with an SCOPUS-based Impact Factor which you can access for free, and also a sort of Hirsch index for the journals.
-The Article Influence gives the least bad ranking, in fact it's quite good, but it fails for journals with few papers a year, so only about 50 journals are listed, as opposed to about 90 for the other two.

---
Readers' comments and further advice for beginners are welcome.

41. Old tutorial by José Miguel Bernardo

2007-11-22T21:16:00.000+01:00

You may take Bayesianism as a methodology or as a religion (you know, the "...the very guide of life" thing). Both aspects are blended. Everything that makes it fascinating as a methodology is also evidence that, as a religion, it qualifies at the crackpot level.

More precisely, if you accept a number of axioms, then you can solve every problem, and the way to solve them is the same, universally. Bayesianism provides a full theory of uncertainty working under a number of specified assumptions. Of course, it is very difficult (to me) to imagine how those assumptions could be met except in a tiny minority of the problems involving uncertainty.

Some people have a much more powerful imagination than mine, but except for that important excess and its consequences they are a joy to read.

J.M. Bernardo. Bayesian Statistics.

This is a fast-paced introduction to Bayesian Statistics, including a lot of the somewhat deeper technical material, often absent from introductions, which unbelievers should at least know and understand.

His style, though, is at times an unpleasant and dogmatic one.

More papers by José Miguel Bernardo, including several published revamps (some earlier, some later) of this document, can be found here at his website. Don't miss the Test paper on intrinsic regions.

40. Old survey papers by Grzegorzewski and Hryniewicz, and Taheri

2007-11-22T17:10:00.000+01:00

I bring you two papers surveying different aspects of fuzzy statistics. Unfortunately, they are no longer representative of what's currently being done, and I'd rather call this `old Fuzzy Statistics' (but that's another story). In any case, they can be a good source for old references.

Przemyslaw Grzegorzewski, Olgierd Hryniewicz (1997). Testing statistical hypotheses in a fuzzy environment. Mathware & Soft Computing 4, 203-217.

S. Mahmoud Taheri (2003). Trends in Fuzzy Statistics. Austrian Journal of Statistics 32, 239-257.

It must be noted that the second paper covers favorite topics developed within the `fuzzy+statistics' community but makes no attempt at discussing the non-fuzzy literature, thus ignoring important topics like fuzzy clustering, to name just an instance.

39. Old paper by Matteo Paris

2007-11-22T16:53:00.000+01:00

A curious paper which uses fuzzy hypothesis testing.

Matteo G. A. Paris (2001). Nearly ideal binary communication in squeezed channels. Physical Review A 64, paper 014304, 1-4.

38. New paper by Kulinskaya and Lewin

2007-11-15T16:11:00.000+01:00

Fuzzy p-values continue to attract researchers (see more papers here).

On fuzzy FWER and FDR procedures for discrete distributions by Elena Kulinskaya and Alex Lewin.

37. New theme-oriented issue of FSS

2007-11-15T15:24:00.000+01:00

Volume 159 issue 3 of Fuzzy Sets and Systems (February 2008) is devoted to the theme Probability and Statistics. This is not a guest-edited special issue but an ordinary issue where all papers are on the same topic.

FSS has been doing this for a while; it is more practical as it makes harder to miss a paper on your topic, but at the same time it implicitly acknowledges that `fuzzy' has become too broad to be much of a unitarily focused discipline.

The table of contents is as follows.

·Probability and fuzzy sets

1. Higher order models for fuzzy random variables
Pages 237-258
Inés Couso and Luciano Sánchez

2. A strong consistency result for fuzzy relative frequencies interpreted as estimator for the fuzzy-valued probability
Pages 259-269
W. Trutschnig

·Random sets

3. Approximation techniques for the transformation of fuzzy sets into random sets
Pages 270-288
Mihai Cristian Florea, Anne-Laure Jousselme, Dominic Grenier and Éloi Bossé

4. Nonspecificity for infinite random sets of indexable type
Pages 289-306
Diego A. Alvarez

·Applications

5. Fuzzy universal generating functions for multi-state system reliability assessment
Pages 307-324
Yi Ding and Anatoly Lisnianski

6. Optimal selection of the service rate for a finite input source fuzzy queuing system
Pages 325-342
María José Pardo and David de la Fuente

·Mathematical aspects

7. Strong law of large numbers for t-normed arithmetics
Pages 343-360
Pedro Terán

8. Statistical convergence in fuzzy normed linear spaces
Pages 361-370
C. Şençı˙men and S. Pehlı˙van

(Curiously, nothing less than three papers by people from, or educated in, the University of Oviedo!)

36. Old papers in AoMS (I)

2007-11-14T17:49:00.000+01:00

This is the first in a series of entries on highly cited papers originally published in the Annals of Mathematical Statistics (1930-1972), now available at Project Euclid. I got the citation info from the ISI database.

These papers need not have any relationship, direct or whatsoever, with fuzzy sets-- but don't let that bother you.

Let us begin with the ten highest cited papers from that journal.

1. (2249 citations) Mann and Whitney on the Mann-Whitney-Wilcoxon test.
2. (1430 citations) Parzen on density estimation.
3. (1047 citations) Kullback and Leibler on Kullback-Leibler divergence.
4. (904 citations) Huber on robust estimation.
5. (815 citations) Box and Muller on the Box-Muller transform.
6. (811 citations) Robbins and Monro on the Robbins-Monro stochastic approximation method.
7. (783 citations) Chernoff on asymptotic efficiency (including the germ of the Chernoff bound, see Theorem 1).
8. (699 citations) Levene on `a matching problem arising in Genetics'.
9. (677 citations) Dempster on upper and lower probabilities (later to become a part of Dempster-Shafer theory).
10. (629 citations) Geisser and Greenhouse on the Geisser-Greenhouse correction.

This list strongly suggests that it was naive on Parzen and Huber's part to propose the names `kernel' and `M-estimator'. Don't name things too hastily!

35. Copula wiki website

2007-11-13T18:47:00.000+01:00

It looks like there's a wiki for everything, copulas included.

34. New paper by McNeil and Nešlehová

2007-11-12T18:15:00.001+01:00

A paper on Archimedean copulas with some new ideas, maybe worth scanning for people working on t-norms.

Alexander J. McNeil, Johanna Nešlehová. Multivariate Archimedean copulas, d-monotone functions and l1-norm symmetric distributions. Annals of Statistics, to appear. Update: AoS 37 (2009), 3059-3097.

33. Book chapter by Jon Williamson

2007-11-12T17:44:00.000+01:00

Although Williamson is not the kind of philosopher I would trust to guide me through a minefield (and what else is a philosopher's duty?), the following is interesting as an introduction to the various interpretations of probability.

J. Williamson (2006). Philosophies of probability: objective Bayesianism and its challenges, in Andrew Irvine (ed.): Handbook of the Philosophy of Mathematics, Volume 4 of the Handbook of the Philosophy of Science, Elsevier.

The reference comes from Williamson's website, yet it may well be wrong in the light of this.

Note also that Williamson's usage of the term `objective Bayesianism' differs from the common one in Statistics. Thus his prototype of an objective Bayesian is Jaynes, not Bernardo. It is unclear whether Williamson would call Bernardo a Bayesian at all.

More papers by Jon Williamson can be found here.

32. Old papers by Gordaliza, Matrán et al.

2007-11-08T19:44:00.001+01:00

I have run this blog for a year without remembering AoS had published these two papers where probability of fuzzy events plays a role. OK, here you are now.

J.A. Cuesta-Albertos, A. Gordaliza, C. Matrán (1997). Trimmed k-means: an attempt to robustify quantizers, Annals of Statistics 25, 553-576.

L.A. García-Escudero, A. Gordaliza, C. Matrán (1999). A central limit theorem for multivariate generalized trimmed k-means. Annals of Statistics 27, 1061-1079.

Let me quote from the first paper: Notice that the functions ... are a natural generalization of the indicator functions of sets which have probability α (resp. at least α) obtained by introducing the possibility of partial participation of the points in the trimmings.

31. Old papers in Statistical Science

2007-11-08T18:08:00.001+01:00

In its early days (2, 1-44, 1987), Statistical Science published a `multi-discussion' on uncertainty modelling in Artificial Intelligence. Old journal material is now freely available and you can access the papers here at Project Euclid.

The contents are as follows:

In This Issue
1-2 [contains interesting background info]

Probability Judgment in Artificial Intelligence and Expert Systems
Glenn Shafer; 3-16

The Probability Approach to the Treatment of Uncertainty in Artificial Intelligence and Expert Systems
Dennis V. Lindley; 17-24

Probabilistic Expert Systems in Medicine: Practical Issues in Handling Uncertainty
David J. Spiegelhalter; 25-30

[Probabilistic Expert Systems in Medicine: Practical Issues in Handling Uncertainty]: Comment
Stephen R. Watson; 30-32

[Probabilistic Expert Systems in Medicine: Practical Issues in Handling Uncertainty]: Comment
A. P. Dempster and Augustine Kong; 32-36

[Probabilistic Expert Systems in Medicine: Practical Issues in Handling Uncertainty]: Comment
Glenn Shafer; 37-38

[Probabilistic Expert Systems in Medicine: Practical Issues in Handling Uncertainty]: Comment: A Tale of Two Wells
Dennis V. Lindley; 38-40

[Probabilistic Expert Systems in Medicine: Practical Issues in Handling Uncertainty]: Comment
David J. Spiegelhalter; 40-41

[Probabilistic Expert Systems in Medicine: Practical Issues in Handling Uncertainty]: Rejoinder
Glenn Shafer; 41-42

[Probabilistic Expert Systems in Medicine: Practical Issues in Handling Uncertainty]: Rejoinder
Dennis V. Lindley; 42-43

[Probabilistic Expert Systems in Medicine: Practical Issues in Handling Uncertainty]: Rejoinder
David J. Spiegelhalter; 43-44

30. SMPS'08 CFP

2007-10-30T16:39:00.000+01:00

As you may know, the 4th International Conference on Soft Methods in Statistics and Probability will be in Toulouse (France), September 2008.

Here you are the call for papers. The submission deadline is February 1st.

29. Old paper by Genest and Favre

2007-10-30T16:07:00.000+01:00

Copulas are currently a very important interface between Fuzzy Sets and Statistics. They used to be quite obscure and exotic to the average statistician (conditional on his ever having heard about them), but recent years are witnessing a sudden eclosion of interest and systematic application to dependence modelling, specially in areas like Finance.

The following is an interesting introduction to the statistical side of the subject.

C. Genest, A.-C. Favre (2007). Everything you always wanted to know about copula modeling but were afraid to ask. Journal of Hydrologic Engineering 12, 347-368.

A full list of Christian Genest's recent publications, with many links, is here.

28. Scholarpedia entries

2007-10-30T15:35:00.000+01:00

I've just found out that there is something called Scholarpedia which is essentially an elitist version of the popular Wikipedia. I'm no big fan of this idea, even if scientific articles in the Wikipedia may contain serious errors. In any case, it must be admitted that many choices of authors are simply right (e.g. Berger for `Bayesian Statistics' or Dubois-Prade for `Possibility Theory').

Here you are a list of on-topic articles (actually, only a small number of articles have been written so far).

Fuzzy C-Means Cluster Analysis (James C. Bezdek)
Fuzzy logic (Lotfi A. Zadeh)
Fuzzy sets (Milan Mares)
Possibility Theory (Didier Dubois, Henri Prade)
Random sets (Hung T. Nguyen)

27b. New paper by Mark Colyvan

2007-09-20T11:14:00.001+02:00

Yet Lindley must not have made such a convincing case when, two decades later, papers like the following continue to be published.

M.Colyvan. Is probability the only coherent approach to uncertainty?, Risk Analysis, to appear.

Colyvan examines the Cox theorem from the logical point of view, more deeply than he did in an IJAR paper some years ago. Unfortunately, it is obvious from reading Lindley's testament Understanding uncertainty (Wiley, 2006) that Lindley never came to understand or accept that discussing the underlying logical assumptions is very pertinent and necessary here.

That explains that Lindley speaks of the "self-evidentiary nature" of "rules whose violation would look ridiculous" and are "dictated to us by the inexorable laws of logic" (here, p.19), whereas Colyvan puts it as follows: "Anyone wishing to argue against fuzzy methods, for instance, must not simply beg the question against those methods. To use a theorem such as Cox's theorem that is based on assumptions that fuzzy logic rejects is thus unappropriate unless the assumptions in question can be independently defended. But then the appeal to Cox's theorem is redundant" (p.11).

It is quite transparent, from the very first page of Understanding uncertainty, that Lindley lives in a world where events either happen or not happen. Thence, invoking the "inexorable laws of logic" his opponents do deny is just question-begging.

27a. Old paper by Dennis Lindley

2007-09-20T11:05:00.000+02:00

Lindley's famous paper (mostly on the basis of Zadeh's systematic citation campaign) is available online:

D.V.Lindley (1987). The probability approach to the treatment of uncertainty in Artificial Intelligence and Expert Systems. Statistical Science 2, 3--44.

This is where the well-known paragraph "The only satisfactory description of uncertainty is probability. By this is meant that every uncertainty statement must be in the form of a probability; that several uncertainties must be combined using the rules of probability; and that the calculus of probabilities is adequate to handle all situations involving uncertainty" comes from.

26. Old chapter by Ross, Booker and Parkinson

2007-09-19T15:41:00.000+02:00

A quite interesting sample chapter from the book Fuzzy logic and probability applications: bridging the gap (SIAM, 2002), edited by Timothy J. Ross, Jane M. Booker and W. Jerry Parkinson is freely available.

Chapter 1: Introduction, authored by the editors.

25. Off-topic

2007-07-11T10:19:00.001+02:00

Every rule calls for an exception, or so they say.

For the interested readers, you can download the book Noncommutative Geometry, Quantum Fields and Motives by Alain Connes and Matilde Marcolli (645-page, july 2007 version) here.

Update: the book has been published by the American Mathematical Society.

24. Old paper by Tversky and Kahneman

2007-07-10T18:08:00.000+02:00

Another interesting old paper found while looking for something else:

A. Tverski, D. Kahneman (1983). Extensional versus intuitive reasoning: the conjunction fallacy in probability judgment. Psychological Review 90, 293-315.

23. Old theses at the Université de Savoie

2007-07-10T11:14:00.000+02:00

You can find here a list of the theses presented at the LISTIC laboratory of the Université de Savoie, including the following (in French).

Virginie Lasserre (1999). Modélisation floue des incertitudes de mesures de capteurs (Fuzzy modelling of measurement uncertainties in sensors).

Lotfi Khodja (1997). Contribution à la classification floue non supervisée (A contribution to unsupervised fuzzy classification).

22. Linz 2007 abstract book

2007-06-15T19:11:00.000+02:00

The abstract book from the 28th Linz Seminar, entitled Fuzzy Sets, Probability and Statistics - Gaps and bridges, can be downloaded here.

21. SMPS'08

2007-06-15T18:45:00.000+02:00

Early news about the 4th International Conference on Soft Methods in Probability and Statistics are as follows:

Spatio-temporal coordinates: Toulouse (France), September 8-10, 2008.

Submission deadline: February 1, 2008.

20. Special issue on Imprecision (CFP)

2007-05-26T12:45:00.000+02:00

The Journal of Statistical Theory and Practice is calling for papers for its special issue on Imprecision. Guest editors are Thomas Augustin, Frank Coolen, Pauline Coolen-Schrijner and Matthias Troffaes. The deadline for submission is October 31, 2007.

Please find all the information here. Also find a valuable bibliography list on the topic here.

19. Old papers by Gert de Cooman

2007-05-24T18:57:00.000+02:00

Preprint versions of De Cooman's papers on imprecise probabilities are here.

I'll update this entry to provide direct links to some of them.

18. Old papers by Yuhu Feng

2007-05-08T12:25:00.000+02:00

Feng's papers on fuzzy random variables are online here.

The link points to file 26.pdf; just go backwards to 1.pdf to find the others. The papers are not ordered cronologically. A few links are broken.

I feel obliged to comment that some of Feng's papers contain wrong proofs or/and results.

17. Uncertainty in Engineering website

2007-05-03T12:13:00.000+02:00

Here is a link to the website Uncertainty in Engineering, with material mostly based on the book Fuzzy randomness by Bernd Möller and Michael Beer. The site is kept by the same Dresden research group.

16. Andrzej Pownuk's fuzzy-probability website

2007-02-28T21:16:00.000+01:00

Andrzej Pownuk's website with many links (up to 2004) to papers, Usenet discussions, etc. on fuzzy sets and probability.

15. New papers on fuzzy p-values

2007-01-30T17:04:00.000+01:00

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.

14. Old paper in Test

2007-01-27T04:32:00.000+01:00

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

2007-01-27T02:24:00.000+01:00

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

2007-01-27T01:47:00.000+01:00

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.

11. Two papers in a forthcoming special issue of FSS

2007-01-10T18:41:00.000+01:00

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.

10. Old paper by Gustave Choquet

2007-01-05T15:29:00.000+01:00

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).

9. New special issue of CSDA

2006-11-10T17:26:00.000+01:00

The special issue of Computational Statistics and Data Analysis on The fuzzy approach to Statistics is no longer "forthcoming".

Volume 51, issue 1 of CSDA contains nothing less than 25 papers. Some of them present overviews of specific aspects of the SPFS interface.

The table of contents is as follows:

The fuzzy approach to statistical analysis
Pages 1-14
Renato Coppi, Maria A. Gil and Henk A.L. Kiers

Generalized theory of uncertainty (GTU)—principal concepts and ideas
Pages 15-46
Lotfi A. Zadeh

Possibility theory and statistical reasoning
Pages 47-69
Didier Dubois

Random and fuzzy sets in coarse data analysis
Pages 70-85
Hung T. Nguyen and Berlin Wu

Practical representations of incomplete probabilistic knowledge
Pages 86-108
C. Baudrit and D. Dubois

Tools for fuzzy random variables: Embeddings and measurabilities
Pages 109-114
Miguel López-Díaz and Dan A. Ralescu

Conditional probability and fuzzy information
Pages 115-132
Giulianella Coletti and Romano Scozzafava

Univariate statistical analysis with fuzzy data
Pages 133-147
Reinhard Viertl

Bootstrap approach to the multi-sample test of means with imprecise data
Pages 148-162
María Ángeles Gil, Manuel Montenegro, Gil González-Rodríguez, Ana Colubi and María Rosa Casals

A fuzzy representation of random variables: An operational tool in exploratory analysis and hypothesis testing
Pages 163-176
Gil González-Rodríguez, Ana Colubi and María Ángeles Gil

A decision support system methodology for forecasting of time series based on soft computing
Pages 177-191
J.D. Bermúdez, J.V. Segura and E. Vercher

Data analysis with fuzzy clustering methods
Pages 192-214
Christian Döring, Marie-Jeanne Lesot and Rudolf Kruse

Extending fuzzy and probabilistic clustering to very large data sets
Pages 215-234
Richard J. Hathaway and James C. Bezdek

Regression with fuzzy random data
Pages 235-252
Wolfgang Näther

Dual models for possibilistic regression analysis
Pages 253-266
Peijun Guo and Hideo Tanaka

Least squares estimation of a linear regression model with LR fuzzy response
Pages 267-286
Renato Coppi, Pierpaolo D’Urso, Paolo Giordani and Adriana Santoro

Fuzzy clusterwise linear regression analysis with symmetrical fuzzy output variable
Pages 287-313
Pierpaolo D’Urso and Adriana Santoro

The coefficient of concordance for vague data
Pages 314-322
Przemysław Grzegorzewski

Goodman–Kruskal γ measure of dependence for fuzzy ordered categorical data
Pages 323-334
Olgierd Hryniewicz

Fuzzy multidimensional scaling
Pages 335-359
Pierre-Alexandre Hébert, Marie-Hélène Masson and Thierry Denœux

I-Scal: Multidimensional scaling of interval dissimilarities
Pages 360-378
P.J.F. Groenen, S. Winsberg, O. Rodríguez and E. Diday

A comparison of three methods for principal component analysis of fuzzy interval data
Pages 379-397
Paolo Giordani and Henk A.L. Kiers

Design of local fuzzy models using evolutionary algorithms
Pages 398-416
Piero P. Bonissone, Anil Varma, Kareem S. Aggour and Feng Xue

Fuzzy modelling and estimation of economic relationships
Pages 417-433
David Shepherd and Francis K.C. Shi

Development of fuzzy process control charts and fuzzy unnatural pattern analyses
Pages 434-451
Murat Gülbay and Cengiz Kahraman

8. Old paper by Lotfi Zadeh

2006-11-09T15:29:00.000+01:00

Toward a Generalized Theory of Uncertainty (GTU)—An Outline is the most up-to-date version of Zadeh's recent ideas available at the BISC website.

This paper appeared in Information Sciences 172 (2005), 1-40. If you have access to this paper via Sciencedirect, this version is a Word document with all the tables and figures at the end.

Additionally, you can download a few selected Zadeh papers here.

7. New edited volume (SMPS'06)

2006-10-16T19:19:00.000+02:00

Springer has published the edited volume Soft Methods for Integrated Uncertainty Modelling containing the proceedings of the SMPS'06 (Soft Methods in Probability and Statistics) conference held at Bristol last month. Editors are J. Lawry, E. Miranda, A. Bugarin, S. Li, M.A. Gil, P. Grzegorzewski and O. Hryniewicz.

The last time I checked, the Springer website offered no TOC for this volume. You can find the titles and authors of the contributions here at the conference website.

Btw, the 4th SMPS will be Toulouse 2008.

6. Old paper by Brian Weatherson

2006-10-16T18:42:00.000+02:00

This paper by philosopher Brian Weatherson is not about fuzzy sets but I find it relevant for foundational discussions with Bayesians. Weatherson presents a Dutch Book argument which works under intuitionistic logic. An obvious implication, good news for open-minded Bayesianism, is that commitment to classical logic is not necessary in order to adhere to De Finetti's view of probability. Another implication is that adherence to the Dutch Book cannot, in and of itself, rule out other logics.

In From classical to intuitionistic probability, a bet on the occurence of A can be settled for A, against A or remain unsettled (cf. a proposition in intuitionistic logic can be true, false or neither- if it hasn't been proved true or proved false).

Accordingly, Weatherson's intuitionistic probabilities allow for the probabilities of an event and its contrary to sum up to less than 1. Thus he presents them as an alternative to belief functions.

This paper appeared in Notre Dame Journal of Formal Logic 44 (2004), 111-123.

5. New paper by Agresti and Gottard

2006-10-16T15:53:00.000+02:00

This paper elaborates on a suggestion made by Alan Agresti and Anna Gottard in their recent discussion of a paper by Geyer and Meeden in Statistical Science.

If you missed a non-fuzzy statistician suggesting a fuzzy p-value and having it discussed in a major Statistics journal, that proves something like this blog is needed.

The paper Reducing Conservatism of Exact Small-Sample Methods of Inference for Discrete Data is available as a Technical Report from the Università di Firenze. Update: To appear in Computational Statistics and Data Analysis.

You may also want to visit Charles Geyer's website.

4. Forthcoming special issue of CSDA

2006-10-16T15:44:00.000+02:00

A special issue of Computational Statistics and Data Analysis is forthcoming on the topic The fuzzy approach to statistical analysis. Guest editors are Renato Coppi, Maria A. Gil and Henk A.L. Kiers.

The papers are already available via Sciencedirect at the journal's site (in the 'Articles in Press' section).

This is the first special issue on Fuzzy Sets ever to appear in a Statistics journal, and I expect this fact to arouse some reaction.