<abstract xmlns="http://www.w3.org/1999/xhtml">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. 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. 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. 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. 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.</abstract>

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. 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. 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. 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. 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.

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

Department of Engineering Science, Middle East Technical University, Ankara, Turkey,

Department of Economics, MEF University, Istanbul, Turkey

Institute of Applied Mathematics, Middle East Technical University, Ankara, Turkey

Organizacija

This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

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)...

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

Published Online: May 17, 2014

Page range: 90 - 97

Received: Jan 15, 2014

Accepted: Mar 24, 2014

DOI: https://doi.org/10.2478/orga-2014-0010

Keywords
Embedding problem, Fuzzy optimization, Fuzzy Banach Space, Portfolio selection

© by Farnaz Solatikia

This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

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

Published Online: May 17, 2014

Page range: 90 - 97

Received: Jan 15, 2014

Accepted: Mar 24, 2014

DOI: https://doi.org/10.2478/orga-2014-0010

KeywordsEmbedding problem, Fuzzy optimization, Fuzzy Banach Space, Portfolio selection

© by Farnaz Solatikia

This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Keywords
Embedding problem, Fuzzy optimization, Fuzzy Banach Space, Portfolio selection