Centroid of a type-2 fuzzy set
Information Sciences: an International Journal
Pattern recognition using type-II fuzzy sets
Information Sciences—Informatics and Computer Science: An International Journal
A review of credibilistic portfolio selection
Fuzzy Optimization and Decision Making
Type-2 fuzzy variables and their arithmetic
Soft Computing - A Fusion of Foundations, Methodologies and Applications
Methods of critical value reduction for type-2 fuzzy variables and their applications
Journal of Computational and Applied Mathematics
Modeling fuzzy data envelopment analysis by parametric programming method
Expert Systems with Applications: An International Journal
A portfolio selection model using fuzzy returns
Fuzzy Optimization and Decision Making
IEEE Transactions on Fuzzy Systems
Expected value of fuzzy variable and fuzzy expected value models
IEEE Transactions on Fuzzy Systems
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This paper develops a robust method to describe fuzzy returns by employing parametric possibility distributions. The parametric possibility distributions are obtained by equivalent value (EV) reduction methods. For common type-2 triangular and trapezoidal fuzzy variables, their reduced fuzzy variables are studied in the current development. The parametric possibility distributions of reduced fuzzy variables are first derived, then the second moment formulas for the reduced fuzzy variables are established. Taking the second moment as a new risk measure, the reward-risk and risk-reward models are developed to optimize fuzzy portfolio selection problems. The mathematical properties of the proposed optimization models are analyzed, including the analytical representations for the second moments of linear combinations of reduced fuzzy variables as well as the convexity of second moments with respect to decision vectors. On the basis of the analytical representations for the second moments, the reward-risk and risk-reward models can be turned into their equivalent parametric quadratic convex programming problems, which can be solved by conventional solution methods or general-purpose software. Finally, some numerical experiments are performed to demonstrate the new modeling ideas and the efficiency of solution method.