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

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

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

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

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.