A class of weighted possibilistic mean-variance portfolio selection problems

Based on the notions of the weighted possibilistic mean proposed by Fuller and Majlender, we develop the notions of the weighted lower and upper possibilistic variances and covariances and also show that the variance of linear combination of fuzzy numbers can be computed on a similar manner as in probability theory. Then the weighted possibilistic portfolio models are present, from which we introduce the conceptions of the weighted lower and upper possibilistic efficient portfolios and efficient frontiers. Moreover, when returns of assets are fuzzy numbers with linear or segmented linear membership functions, the portfolio model that is quadratic programming can be transformed into linear programming problem.