On the complexity of approximating the maximal inscribed ellipsoid for a polytope
Mathematical Programming: Series A and B
Defuzzification: criteria and classification
Fuzzy Sets and Systems
Fuzzy Sets and Systems - Fuzzy mathematical programming
Portfolio selection based on fuzzy probabilities and possibility distributions
Fuzzy Sets and Systems
A class of possibilistic portfolio selection model with interval coefficients and its application
Fuzzy Optimization and Decision Making
On Khachiyan's algorithm for the computation of minimum-volume enclosing ellipsoids
Discrete Applied Mathematics
A review of credibilistic portfolio selection
Fuzzy Optimization and Decision Making
A class of linear interval programming problems and its application to portfolio selection
IEEE Transactions on Fuzzy Systems
Optimizing fuzzy portfolio selection problems by parametric quadratic programming
Fuzzy Optimization and Decision Making
Robust-based interactive portfolio selection problems with an uncertainty set of returns
Fuzzy Optimization and Decision Making
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We study a static portfolio selection problem, in which future returns of securities are given as fuzzy sets. In contrast to traditional analysis, we assume that investment decisions are not based on statistical expectation values, but rather on maximal and minimal potential returns resulting from the so-called α-cuts of these fuzzy sets. By aggregating over all α-cuts and assigning weights for both best and worst possible cases we get a new objective function to derive an optimal portfolio. Allowing for short sales and modelling α-cuts in ellipsoidal shape, we obtain the optimal portfolio as the unique solution of a simple optimization problem. Since our model does not include any stochastic assumptions, we present a procedure, which turns the data of observable returns as well as experts' expectations into fuzzy sets in order to quantify the potential future returns and the investment risk.