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Dubois and Prade defined an interval-valued expectation of fuzzy numbers, viewing them as consonant random sets. Fullér and Majlender then proposed an weighted possibility mean value, variance and covariance of fuzzy numbers, viewing them as weighted possibility distributions. In this paper, we define a new weighted possibilistic variance and covariance of fuzzy numbers based on Fullér and Majlenders' notations. Some properties of these notations are obtained in a similar manner as in probability theory. We also consider the weighted possibilistic mean-variance model of portfolio selection and introduce the notations of the weighted possibilistic efficient portfolio and efficient frontier. Moreover, a simple example is presented to show the application of our results in security market. [ABSTRACT FROM AUTHOR]