Moments and semi-moments for fuzzy portfolio selection

The aim of this paper is to consider the moments and the semi-moments for credibilistic portfolio selection with fuzzy risk factors (for example trapezoidal risk factors). In order to measure the leptokurtocity of credibilistic portfolio return, notions of moments (for example Kurtosis) and semi-moments (for example Semi-kurtosis) for credibilistic portfolios are originally introduced in this paper, and their mathematical properties are studied. As an extension of the mean-variance-skewness model for credibilistic portfolio, the mean-variance-skewness-semi-kurtosis is presented and its four corresponding variants are also considered. We display numerical examples for our optimization models.

► We introduce kurtosis and semi-kurtosis for fuzzy variables. ► We derive some properties of fuzzy moments and semi-moments. ► We use fuzzy moments and fuzzy semi-moments for portfolio theory. ► Examples of multi-objective optimization portfolio selection are given.