Abstract

This paper presents two fuzzy portfolio selection models where the objective is to minimize the downside risk constrained so that a given expected return should be achieved. We assume that the rates of returns on securities are approximated as LR-fuzzy numbers of the same shape, and that the expected return and risk are evaluated by interval-valued means. We establish the relationship between those mean-interval definitions for a given fuzzy portfolio by using suitable ordering relations. And then we compare those with a given not fuzzy portfolio one. Finally, we formulate the portfolio selection problem as a linear program when the returns on the assets are of trapezoidal form.

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