Elsevier

Fuzzy Sets and Systems

Volume 122, Issue 2, 1 September 2001, Pages 315-326
Fuzzy Sets and Systems

On possibilistic mean value and variance of fuzzy numbers

https://doi.org/10.1016/S0165-0114(00)00043-9Get rights and content

Abstract

Dubois and Prade introduced the mean value of a fuzzy number as a closed interval bounded by the expectations calculated from its upper and lower distribution functions. In this paper introducing the notations of lower possibilistic and upper possibilistic mean values we define the interval-valued possibilistic mean and investigate its relationship to the interval-valued probabilistic mean. We also introduce the notation of crisp possibilistic mean value and crisp possibilistic variance of continuous possibility distributions, which are consistent with the extension principle. We also show that the variance of linear combination of fuzzy numbers can be computed in a similar manner as in probability theory.

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Supported by the E-MS Bullwhip project TEKES 40965/98.

1

On leave from Department of Operations Research, Eötvös Loránd University, Kecskeméti utca 10-12, H-1053 Budapest, Hungary. Partially supported by FKFP-0157/2000 and OTKA T032412.

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