Journal
IEEE TRANSACTIONS ON FUZZY SYSTEMS
Volume 23, Issue 6, Pages 2135-2143Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TFUZZ.2015.2404340
Keywords
Fuzzy number; mean-variance-skewness model; skewness
Funding
- National Natural Science Foundation of China [71371027, 91224001]
- National Science Fund for Distinguished Young Scholars [71025005]
- Beijing Nova Program [Z14111000180000]
- Fundamental Research Funds for the Central Universities [ZZ1316]
- State Key Laboratory of Rail Traffic Control and Safety [RCS2014K011]
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A fuzzy number is a normal and convex fuzzy subset of the real line. In this paper, based on membership function, we redefine the concepts of mean and variance for fuzzy numbers. Furthermore, we propose the concept of skewness and prove some desirable properties. A fuzzy mean-variance-skewness portfolio selection model is formulated and two variations are given, which are transformed to nonlinear optimization models with polynomial objective and constraint functions such that they can be solved analytically. Finally, we present some numerical examples to demonstrate the effectiveness of the proposed models.
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