A fuzzy goal programming approach to portfolio selection
01 Jan 2001-European Journal of Operational Research (EUROPEAN JOURNAL OF OPERATIONAL RESEARCH)-Vol. 133, Iss: 2, pp 287-297
TL;DR: A fuzzy G.P. approach is applied to the optimum portfolio for a private investor, taking into account three criteria: return, risk and liquidity, where the goals and the constraints are fuzzy.
About: This article is published in European Journal of Operational Research.The article was published on 2001-01-01. It has received 272 citations till now. The article focuses on the topics: Fuzzy set operations & Fuzzy number.
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TL;DR: This paper reviews theory and methodology that have been developed to cope with the complexity of optimization problems under uncertainty and discusses and contrast the classical recourse-based stochastic programming, robust stochastics programming, probabilistic (chance-constraint) programming, fuzzy programming, and stochastically dynamic programming.
1,145 citations
TL;DR: In this paper, the authors provide an in-depth presentation of the contributions of Multi-Criteria Decision Aid (MCDA) in the field of finance, focusing on the methods used and their real-world applications.
Abstract: Over the past decades the complexity of financial decisions has increased rapidly, thus highlighting the importance of developing and implementing sophisticated and efficient quantitative analysis techniques for supporting and aiding financial decision making. Multi-criteria decision aid (MCDA), an advanced field of operations research, provides financial decision makers (DMs) and analysts a wide range of methodologies, which are well suited to the complexity of financial decision problems. The aim of this paper is to provide an in-depth presentation of the contributions of MCDA in the field of finance, focusing on the methods used and their real-world applications. Copyright © 2003 John Wiley & Sons, Ltd.
283 citations
Additional excerpts
...Arenas Parra et al. (2001)...
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TL;DR: A mean-variance-skewness model is presented and the corresponding variations are also considered, and a genetic algorithm integrating fuzzy simulation is designed to solve the models.
280 citations
TL;DR: A fuzzy goal programming (FGP) approach that integrates activity-based costing (ABC) and performance evaluation in a value-chain structure for optimal GSC supplier selection and flow allocation is proposed.
Abstract: Supply chain operation with sustainable consideration has become an increasingly important issue in recent years. However, the decision framework with integrated costing and performance evaluation for green supply chain (GSC) has not been well developed so far in the literature. For this reason, this paper is aimed to propose a fuzzy goal programming (FGP) approach that integrates activity-based costing (ABC) and performance evaluation in a value-chain structure for optimal GSC supplier selection and flow allocation. The FGP approach is particularly suitable for such a decision model which includes flexible goals, financial and non-financial measures, quantitative and qualitative methods, multi-layer structure, multiple criteria, multiple objectives, and multiple strategies. An activity-based example of structural GSC with relevant costs and performances is presented for computing the composite performance indices of the GSC suppliers. A green supply chain of a mobile phone is used as an illustrative case...
258 citations
TL;DR: The results of the empirical study show that the portfolios obtained using the proposed algorithms are very close to the efficient frontier, indicating that the proposed method can obtain near optimal and also practically feasible solutions to the portfolio selection problem in an acceptable short time.
231 citations
References
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TL;DR: In this paper, the authors present a body of positive microeconomic theory dealing with conditions of risk, which can be used to predict the behavior of capital marcets under certain conditions.
Abstract: One of the problems which has plagued thouse attempting to predict the behavior of capital marcets is the absence of a body of positive of microeconomic theory dealing with conditions of risk/ Althuogh many usefull insights can be obtaine from the traditional model of investment under conditions of certainty, the pervasive influense of risk in finansial transactions has forced those working in this area to adobt models of price behavior which are little more than assertions. A typical classroom explanation of the determinationof capital asset prices, for example, usually begins with a carefull and relatively rigorous description of the process through which individuals preferences and phisical relationship to determine an equilibrium pure interest rate. This is generally followed by the assertion that somehow a market risk-premium is also determined, with the prices of asset adjusting accordingly to account for differences of their risk.
17,922 citations
TL;DR: In this article, the problem of selecting optimal security portfolios by risk-averse investors who have the alternative of investing in risk-free securities with a positive return or borrowing at the same rate of interest and who can sell short if they wish is discussed.
Abstract: Publisher Summary This chapter discusses the problem of selecting optimal security portfolios by risk-averse investors who have the alternative of investing in risk-free securities with a positive return or borrowing at the same rate of interest and who can sell short if they wish. It presents alternative and more transparent proofs under these more general market conditions for Tobin's important separation theorem that “ … the proportionate composition of the non-cash assets is independent of their aggregate share of the investment balance … and for risk avertere in purely competitive markets when utility functions are quadratic or rates of return are multivariate normal. The chapter focuses on the set of risk assets held in risk averters' portfolios. It discusses various significant equilibrium properties within the risk asset portfolio. The chapter considers a few implications of the results for the normative aspects of the capital budgeting decisions of a company whose stock is traded in the market. It explores the complications introduced by institutional limits on amounts that either individuals or corporations may borrow at given rates, by rising costs of borrowed funds, and certain other real world complications.
9,970 citations
TL;DR: The theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable.
8,918 citations
Book•
01 Mar 1981
TL;DR: In this paper, the authors present a classification of MADM methods by data type and propose a ranking method based on the degree of similarity of the MADM method to the original MADM algorithm.
Abstract: I. Introduction.- II. Multiple Attribute Decision Making - An Overview.- 2.1 Basics and Concepts.- 2.2 Classifications of MADM Methods.- 2.2.1 Classification by Information.- 2.2.2 Classification by Solution Aimed At.- 2.2.3 Classification by Data Type.- 2.3 Description of MADM Methods.- Method (1): DOMINANCE.- Method (2): MAXIMIN.- Method (3): MAXIMAX.- Method (4): CONJUNCTIVE METHOD.- Method (5): DISJUNCTIVE METHOD.- Method (6): LEXICOGRAPHIC METHOD.- Method (7): LEXICOGRAPHIC SEMIORDER METHOD.- Method (8): ELIMINATION BY ASPECTS (EBA).- Method (9): LINEAR ASSIGNMENT METHOD (LAM).- Method (10): SIMPLE ADDITIVE WEIGHTING METHOD (SAW).- Method (11): ELECTRE (Elimination et Choice Translating Reality).- Method (12): TOPSIS (Technique for Order Preference by Similarity to Ideal Solution).- Method (13): WEIGHTED PRODUCT METHOD.- Method (14): DISTANCE FROM TARGET METHOD.- III. Fuzzy Sets and their Operations.- 3.1 Introduction.- 3.2 Basics of Fuzzy Sets.- 3.2.1 Definition of a Fuzzy Set.- 3.2.2 Basic Concepts of Fuzzy Sets.- 3.2.2.1 Complement of a Fuzzy Set.- 3.2.2.2 Support of a Fuzzy Set.- 3.2.2.3 ?-cut of a Fuzzy Set.- 3.2.2.4 Convexity of a Fuzzy Set.- 3.2.2.5 Normality of a Fuzzy Set.- 3.2.2.6 Cardinality of a Fuzzy Set.- 3.2.2.7 The mth Power of a Fuzzy Set.- 3.3 Set-Theoretic Operations with Fuzzy Sets.- 3.3.1 No Compensation Operators.- 3.3.1.1 The Min Operator.- 3.3.2 Compensation-Min Operators.- 3.3.2.1 Algebraic Product.- 3.3.2.2 Bounded Product.- 3.3.2.3 Hamacher's Min Operator.- 3.3.2.4 Yager's Min Operator.- 3.3.2.5 Dubois and Prade's Min Operator.- 3.3.3 Full Compensation Operators.- 3.3.3.1 The Max Operator.- 3.3.4 Compensation-Max Operators.- 3.3.4.1 Algebraic Sum.- 3.3.4.2 Bounded Sum.- 3.3.4.3 Hamacher's Max Operator.- 3.3.4.4 Yager's Max Operator.- 3.3.4.5 Dubois and Prade's Max Operator.- 3.3.5 General Compensation Operators.- 3.3.5.1 Zimmermann and Zysno's ? Operator.- 3.3.6 Selecting Appropriate Operators.- 3.4 The Extension Principle and Fuzzy Arithmetics.- 3.4.1 The Extension Principle.- 3.4.2 Fuzzy Arithmetics.- 3.4.2.1 Fuzzy Number.- 3.4.2.2 Addition of Fuzzy Numbers.- 3.4.2.3 Subtraction of Fuzzy Numbers.- 3.4.2.4 Multiplication of Fuzzy Numbers.- 3.4.2.5 Division of Fuzzy Numbers.- 3.4.2.6 Fuzzy Max and Fuzzy Min.- 3.4.3 Special Fuzzy Numbers.- 3.4.3.1 L-R Fuzzy Number.- 3.4.3.2 Triangular (or Trapezoidal) Fuzzy Number.- 3.4.3.3 Proof of Formulas.- 3.4.3.3.1 The Image of Fuzzy Number N.- 3.4.3.3.2 The Inverse of Fuzzy Number N.- 3.4.3.3.3 Addition and Subtraction.- 3.4.3.3.4 Multiplication and Division.- 3.5 Conclusions.- IV. Fuzzy Ranking Methods.- 4.1 Introduction.- 4.2 Ranking Using Degree of Optimality.- 4.2.1 Baas and Kwakernaak's Approach.- 4.2.2 Watson et al.'s Approach.- 4.2.3 Baldwin and Guild's Approach.- 4.3 Ranking Using Hamming Distance.- 4.3.1 Yager's Approach.- 4.3.2 Kerre's Approach.- 4.3.3 Nakamura's Approach.- 4.3.4 Kolodziejczyk's Approach.- 4.4 Ranking Using ?-Cuts.- 4.4.1 Adamo's Approach.- 4.4.2 Buckley and Chanas' Approach.- 4.4.3 Mabuchi's Approach.- 4.5 Ranking Using Comparison Function.- 4.5.1 Dubois and Prade's Approach.- 4.5.2 Tsukamoto et al.'s Approach.- 4.5.3 Delgado et al.'s Approach.- 4.6 Ranking Using Fuzzy Mean and Spread.- 4.6.1 Lee and Li's Approach.- 4.7 Ranking Using Proportion to The Ideal.- 4.7.1 McCahone's Approach.- 4.8 Ranking Using Left and Right Scores.- 4.8.1 Jain's Approach.- 4.8.2 Chen's Approach.- 4.8.3 Chen and Hwang's Approach.- 4.9 Ranking with Centroid Index.- 4.9.1 Yager's Centroid Index.- 4.9.2 Murakami et al.'s Approach.- 4.10 Ranking Using Area Measurement.- 4.10.1 Yager's Approach.- 4.11 Linguistic Ranking Methods.- 4.11.1 Efstathiou and Tong's Approach.- 4.11.2 Tong and Bonissone's Approach.- V. Fuzzy Multiple Attribute Decision Making Methods.- 5.1 Introduction.- 5.2 Fuzzy Simple Additive Weighting Methods.- 5.2.1 Baas and Kwakernaak's Approach.- 5.2.2 Kwakernaak's Approach.- 5.2.3 Dubois and Prade's Approach.- 5.2.4 Cheng and McInnis's Approach.- 5.2.5 Bonissone's Approach.- 5.3 Analytic Hierarchical Process (AHP) Methods.- 5.3.1 Saaty's AHP Approach.- 5.3.2 Laarhoven and Pedrycz's Approach.- 5.3.3 Buckley's Approach.- 5.4 Fuzzy Conjunctive/Disjunctive Method.- 5.4.1 Dubois, Prade, and Testemale's Approach.- 5.5 Heuristic MAUF Approach.- 5.6 Negi's Approach.- 5.7 Fuzzy Outranking Methods.- 5.7.1 Roy's Approach.- 5.7.2 Siskos et al.'s Approach.- 5.7.3 Brans et al.'s Approach.- 5.7.4 Takeda's Approach.- 5.8 Maximin Methods.- 5.8.1 Gellman and Zadeh's Approach.- 5.8.2 Yager's Approach.- 5.9 A New Approach to Fuzzy MADM Problems.- 5.9.1 Converting Linguistic Terms to Fuzzy Numbers.- 5.9.2 Converting Fuzzy Numbers to Crisp Scores.- 5.9.3 The Algorithm.- VI. Concluding Remarks.- 6.1 MADM Problems and Fuzzy Sets.- 6.2 On Existing MADM Solution Methods.- 6.2.1 Classical Methods for MADM Problems.- 6.2.2 Fuzzy Methods for MADM Problems.- 6.2.2.1 Fuzzy Ranking Methods.- 6.2.2.2 Fuzzy MADM Methods.- 6.3 Critiques of the Existing Fuzzy Methods.- 6.3.1 Size of Problem.- 6.3.2 Fuzzy vs. Crisp Data.- 6.4 A New Approach to Fuzzy MADM Problem Solving.- 6.4.1 Semantic Modeling of Linguistic Terms.- 6.4.2 Fuzzy Scoring System.- 6.4.3 The Solution.- 6.4.4 The Advantages of the New Approach.- 6.5 Other Multiple Criteria Decision Making Methods.- 6.5.1 Multiple Objective Decision Making Methods.- 6.5.2 Methods of Group Decision Making under Multiple Criteria.- 6.5.2.1 Social Choice Theory.- 6.5.2.2 Experts Judgement/Group Participation.- 6.5.2.3 Game Theory.- 6.6 On Future Studies.- 6.6.1 Semantics of Linguistic Terms.- 6.6.2 Fuzzy Ranking Methods.- 6.6.3 Fuzzy MADM Methods.- 6.6.4 MADM Expert Decision Support Systems.- VII. Bibliography.
8,629 citations
TL;DR: Ebsco as mentioned in this paper examines the arbitrage model of capital asset pricing as an alternative to the mean variance pricing model introduced by Sharpe, Lintner and Treynor.
6,763 citations