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

Naimeh Sadeghi (2009).

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).

Cédric Baudrit, Dominique Guyonnet, Didier Dubois, Hélène Fargier (2005).

Cédric Baudrit, Didier Dubois, Dominique Guyonnet (2006).

**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.
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