# Fuzzy optimization for portfolio selection based on Embedding Theorem in Fuzzy Normed Linear Spaces

2014-5-1
Solatikia, Farnaz
Kiliç, Erdem
Weber, Gerhard Wilhelm
<jats:title>Abstract</jats:title> <jats:p>Background: This paper generalizes the results of Embedding problem of Fuzzy Number Space and its extension into a Fuzzy Banach Space C(Ω) × C(Ω), where C(Ω) is the set of all real-valued continuous functions on an open set Ω. </jats:p> <jats:p>Objectives: The main idea behind our approach consists of taking advantage of interplays between fuzzy normed spaces and normed spaces in a way to get an equivalent stochastic program. This helps avoiding pitfalls due to severe oversimplification of the reality. </jats:p> <jats:p>Method: The embedding theorem shows that the set of all fuzzy numbers can be embedded into a Fuzzy Banach space. Inspired by this embedding theorem, we propose a solution concept of fuzzy optimization problem which is obtained by applying the embedding function to the original fuzzy optimization problem. </jats:p> <jats:p>Results: The proposed method is used to extend the classical Mean-Variance portfolio selection model into Mean Variance-Skewness model in fuzzy environment under the criteria on short and long term returns, liquidity and dividends. </jats:p> <jats:p>Conclusion: A fuzzy optimization problem can be transformed into a multiobjective optimization problem which can be solved by using interactive fuzzy decision making procedure. Investor preferences determine the optimal multiobjective solution according to alternative scenarios.</jats:p>

Citation Formats
F. Solatikia, E. Kiliç, and G. W. Weber, “Fuzzy optimization for portfolio selection based on Embedding Theorem in Fuzzy Normed Linear Spaces,” Organizacija, vol. 47, no. 2, pp. 90–97, 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/51456. 