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

Download

[15811832 - Organizacija] Fuzzy optimization for portfolio selection based on Embedding Theorem in Fuzzy Normed Linear Spaces.pdf

Date

2014-5-1

Author

Solatikia, Farnaz
Kiliç, Erdem
Weber, Gerhard Wilhelm

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

124
views

57
downloads

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.

Subject Keywords

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

URI

https://hdl.handle.net/11511/51456

Journal

Organizacija

DOI

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

Collections

Graduate School of Applied Mathematics, Article

Suggestions

OpenMETU
Core

Some finite-dimensional backward shift-invariant subspaces in the ball and a related factorization problem Alpay, D; Kaptanoglu, HT (2000-12-15) Beurling's theorem characterizes subspaces of the Hardy space invariant under the forward-shift operator in terms of inner functions. In this Note we consider the case where the ball replaces the open unit desk and the reproducing kernel Hilbert space with reproducing kernel 1/(1-Sigma (N)(1) a(j)w(j)*) replaces the Hardy space. We give explicit formulas which generalize Blaschke products in the case of spaces of finite codimension. (C) 2000 Academie des sciences/Editions scientifiques et medicales Elsevier...
Linear Canonical Domains and Degrees of Freedom of Signals and Systems Öktem, Sevinç Figen (2016-01-01) We discuss the relationships between linear canonical transform (LCT) domains, fractional Fourier transform (FRT) domains, and the space-frequency plane. In particular, we show that LCT domains correspond to scaled fractional Fourier domains and thus to scaled oblique axes in the space-frequency plane. This allows LCT domains to be labeled and monotonically ordered by the corresponding fractional order parameter and provides a more transparent view of the evolution of light through an optical system modeled...
Temporal neuro-fuzzy MAR Algorithm for time series data in rule-based systems Sisman, NA; Alpaslan, Ferda Nur (1998-04-23) This paper introduces a new neuro-fuzzy model for constructing a knowledge-base of temporal fuzzy rules obtained by MAR (Multivariate Autoregressive) Algorithm. The model described contains two main parts which are fuzzy-rule extraction and storage of them. The fuzzy rules are obtained from time series data using MAR Algorithm. Fuzzy linear function with fuzzy number coefficients are used. The extracted rules are fed into the temporal fuzzy multilayer feedforward neural network.
Parallel Approximation, and Integer Programming Reformulation Patakı, Gabor; Tural, Mustafa Kemal (null; 2008-03-14) We show that in a knapsack feasibility problem an integral vectorp, which is short, and nearparallel to the constraint vector gives a branching direction with small integer width.We use this result to analyze two computationally efficient reformulation techniques on lowdensity knapsack problems. Both reformulations have a constraint matrix with columns reducedin the sense of Lenstra, Lenstra, and Lov ́asz. We prove an upper bound on the integer widthalong the last variable, which becomes 1,when the density ...
On endomorphisms of surface mapping class groups Korkmaz, Mustafa (Elsevier BV, 2001-05-01) In this paper, we prove that every endomorphism of the mapping class group of an orientable surface onto a subgroup of finite index is in fact an automorphism.

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, pp. 90–97, 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/51456.