Résumé
The aim of this paper is to consider the moments and the semi-moments (i.e semi-kurtosis) for portfolio selection with fuzzy risk factors (i.e. trapezoidal risk factors). In order to measure the leptokurtocity of fuzzy portfolio return, notions of moments (i.e. Kurtosis) kurtosis and semi-moments(i.e. Semi-kurtosis) for fuzzy port- folios are originally introduced in this paper, and their mathematical properties are studied. As an extension of the mean-semivariance-skewness model for fuzzy portfolio, the mean-semivariance-skewness- semikurtosis is presented and its four corresponding variants are also considered. We briefly designed the genetic algorithm integrating fuzzy simulation for our optimization models.