On weighted possibilistic mean and variance of fuzzy numbers

Dubois and Prade defined an interval-valued expectation of fuzzy numbers, viewing them as consonant random sets. Carlsson and Fullér defined an interval-valued mean value of fuzzy numbers, viewing them as possibility distributions. In this paper we shall introduce the notation of weighted interval-valued possibilistic mean value of fuzzy numbers and investigate its relationship to the interval-valued probabilistic mean. We shall also introduce the notations of crisp weighted possibilistic mean value, variance and covariance of fuzzy numbers, which are consistent with the extension principle. Furthermore, we show that the weighted variance of linear combination of fuzzy numbers can be computed in a similar manner as in probability theory.