Skewness of Fuzzy Numbers and Its Applications in Portfolio Selection

Xiang Li, Sini Guo, Lean Yu

Research output: Contribution to journalArticlepeer-review

48 Citations (SciVal)


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.
Original languageEnglish
Pages (from-to)2135-2143
Number of pages9
JournalIEEE Transactions on Fuzzy Systems
Issue number6
Early online date16 Feb 2015
Publication statusPublished - 25 Nov 2015
Externally publishedYes


  • fuzzy number
  • mean-variance-skewness model
  • skewness


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