Evaluate fuzzy optimization problems based on biobjective programming problems

Wu, Hsien-Chung

doi:10.1016/s0898-1221(04)90073-9

Cited by 29 publications

(6 citation statements)

References 24 publications

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“…Optimization problems with fuzzy-valued objective functions were studied by many researchers. For instance, see [5,8,23,20,[30][31][32][33][34][35][36][37]39]. In particular, in [5,9,33,37] Karush-Kuhn-Tucker type optimality conditions for this class of fuzzy optimization problems were obtained.…”

Section: Introductionmentioning

confidence: 99%

On the Newton method for solving fuzzy optimization problems

Chalco-Cano

Silva

Rufián-Lizana

2015

Fuzzy Sets and Systems

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 AbstractIn this article we consider optimization problems where the objectives are fuzzy functions (fuzzy-valued functions). For this class of fuzzy optimization problems we discuss the Newton method to find a non-dominated solution. For this purpose, we use the generalized Hukuhara differentiability notion, which is the most general concept of existing differentiability for fuzzy functions. This work improves and correct the Newton Method previously proposed in the literature.

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Section: Introductionmentioning

confidence: 99%

On the Newton method for solving fuzzy optimization problems

Chalco-Cano

Silva

Rufián-Lizana

2015

Fuzzy Sets and Systems

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“…The model includes return, transaction cost, risk and skewness of the portfolio as decision parameters. Wu (2004) develops models with fuzzy space and special spaces such as Banach spaces. In particular, Wu and Ma (1991) provide a specific Banach space that the set of all fuzzy real numbers, which was introduced by Zadeh (1965) and plays the most fundamental role in the theory of fuzzy analysis, can be embedded into a Banach space…”

Section: Introductionmentioning

confidence: 99%

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

Kılıç

Weber

2014

Organizacija

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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.

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“…To do so, the fuzzy optimization problem is transformed into a bi-objective programming problem by applying the embedding theorem. Wu [5] shows that the optimal solution of the crisp optimization problem obtained from the fuzzy optimization problem by using embedding theorem is also an optimal solution of the original fuzzy optimization problem under the set of core values of fuzzy numbers.…”

Section: Introductionmentioning

confidence: 99%

Uncertainty Theory Based Novel Multi-Objective Optimization Technique Using Embedding Theorem with Application to R & D Project Portfolio Selection

Bhattacharyya¹,

Chatterjee²,

Kar³

2010

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This paper introduces a novice solution methodology for multi-objective optimization problems having the coefficients in the form of uncertain variables. The embedding theorem, which establishes that the set of uncertain variables can be embedded into the Banach space C[0, 1] × C[0, 1] isometrically and isomorphically, is developed. Based on this embedding theorem, each objective with uncertain coefficients can be transformed into two objectives with crisp coefficients. The solution of the original m-objectives optimization problem with uncertain coefficients will be obtained by solving the corresponding 2 m-objectives crisp optimization problem. The R & D project portfolio decision deals with future events and opportunities, much of the information required to make portfolio decisions is uncertain. Here parameters like outcome, risk, and cost are considered as uncertain variables and an uncertain bi-objective optimization problem with some useful constraints is developed. The corresponding crisp tetra-objective optimization model is then developed by embedding theorem. The feasibility and effectiveness of the proposed method is verified by a real case study with the consideration that the uncertain variables are triangular in nature.

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Evaluate fuzzy optimization problems based on biobjective programming problems

Cited by 29 publications

References 24 publications

On the Newton method for solving fuzzy optimization problems

On the Newton method for solving fuzzy optimization problems

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

Uncertainty Theory Based Novel Multi-Objective Optimization Technique Using Embedding Theorem with Application to R & D Project Portfolio Selection

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Evaluate fuzzy optimization problems based on biobjective programming problems

Cited by 29 publications

References 24 publications

On the Newton method for solving fuzzy optimization problems

On the Newton method for solving fuzzy optimization problems

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

Uncertainty Theory Based Novel Multi-Objective Optimization Technique Using Embedding Theorem with Application to R &amp; D Project Portfolio Selection

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Product

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Uncertainty Theory Based Novel Multi-Objective Optimization Technique Using Embedding Theorem with Application to R & D Project Portfolio Selection