Title :
Skewness of Fuzzy Numbers and Its Applications in Portfolio Selection
Author :
Xiang Li ; Sini Guo ; Lean Yu
Author_Institution :
Sch. of Econ. & Manage., Beijing Univ. of Chem. Technol., Beijing, China
Abstract :
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.
Keywords :
fuzzy set theory; investment; optimisation; polynomials; constraint functions; convex fuzzy subset; fuzzy mean-variance-skewness portfolio selection model; fuzzy number skewness; membership function; nonlinear optimization models; polynomial objective; Analytical models; Computational modeling; Investment; Level set; Numerical models; Optimization; Portfolios; Fuzzy number; Mean-varianceskewness model; Skewness; mean-variance-skewness model; skewness;
Journal_Title :
Fuzzy Systems, IEEE Transactions on
DOI :
10.1109/TFUZZ.2015.2404340