Marginal impacts of assets on portfolio higher moments are characterized by triangular fuzzy numbers and then evaluated by fuzzy ranking procedures in order to assemble fuzzy reciprocal matrices that are needed for the constrained fuzzy analytic hierarchy process (AHP) methods. The proposed methodology increases the scope for emphasizing objective quantitative measures, thus alleviating the influence of subjective qualitative factors. Employing constrained fuzzy arithmetic during fuzzy AHP application produces greater precision and reliability compared with applications of the standard fuzzy arithmetic. By reference to higher moments, the investor is able to strategize portfolios so that there is a reduction not only in exposure to normal risk (i.e., volatility) but also to risk of asymmetry (skewness) and the risk of fat tails (kurtosis). The efficiency of the proposed approach is highlighted in the ability to handle investor preferences regarding higher moment risks. More optimal values for a particular risk can be obtained if that risk is of more concern. Moreover, in terms of obtaining portfolio diversification, the method is shown to be more useful than conventional optimization models.
Nguyen, T. T., & Gordon-Brown, L. N. (2012). Constrained fuzzy hierarchical analysis for portfolio selection under higher moments. IEEE Transactions on Fuzzy Systems, 20(4), 666 - 682. https://doi.org/10.1109/TFUZZ.2011.2181520