Score-hesitation trade-off and portfolio selection under intuitionistic fuzzy environment

Qualitative portfolio selection approach is a suitable technique for obtaining an optimal portfolio when quantitative data are unavailable and traditional portfolio models are ineffective. However, few studies focus on this issue. This study addresses the lack of research by defining the score-hesitation trade-off rule and introducing the intuitionistic fuzzy set (IFS), based on which an intuitionistic fuzzy portfolio selection (IFPS) model is proposed. The IFS is introduced because of its comprehensive consideration of preference and nonpreference, and is used to represent qualitatively evaluated information from investors and experts. Furthermore, an intuitionistic fuzzy investment scenario is established and a trisection approach is designed to distinguish three types of risk investors, based on which three corresponding IFPS models are constructed. After this, a portfolio selection process under the intuitionistic fuzzy environment is provided, and a simple example is given to show the application of the process. In addition, the investment opportunities and efficient frontier of the IFPS model are investigated to demonstrate the effectiveness of the proposed portfolio selection model. Finally, an example of calculating optimal investment ratios and selecting an optimal portfolio for four newly listed stocks in China is provided to demonstrate the feasibility and practicability of the proposed approaches.     

Random fuzzy mean-absolute deviation models for portfolio optimization problem with hybrid uncertainty

Absolute deviation is a commonly used risk measure, which has attracted more attentions in portfolio optimization. The existing mean-absolute deviation models are devoted to either stochastic portfolio optimization or fuzzy one. However, practical investment decision problems often involve the mixture of randomness and fuzziness such as stochastic returns with fuzzy information. Thus it is necessary to model portfolio selection problem in such a hybrid uncertain environment. In this paper, we employ random fuzzy variable to describe the stochastic return on individual security with ambiguous information. We first define the absolute deviation of random fuzzy variable and then employ it as risk measure to formulate mean-absolute deviation portfolio optimization models. To find the optimal portfolio, we design random fuzzy simulation and simulation-based genetic algorithm to solve the proposed models. Finally, a numerical example for synthetic data is presented to illustrate the validity of the method.     

基于MIC架构稳健投资组合并行算法及实现

投资组合选择是数量化投资管理领域中的一项关键技术,目前其在应用中亟需高性能算法与实现研究。本论文针对现实投资场景下的稳健投资组合选择最优化模型,设计出高效的并行算法,利用并行计算技术多层级优化性能,实现对稳健投资组合计算的快速响应。该稳健投资组合将模糊集理论与投资组合理论相结合,建立基于可能性理论和机会测度的投资组合模型,用BP神经网络算法和遗传算法对模型进行求解,并在最新的高性能计算集成众核(Many Integrated Core,MIC)架构上实现并行。文章选取上证50指数成份股近两年的交易数据,对并行算法及其性能进行分析。结果显示,该算法计算得到的投资组合收益率优于经典模型收益率和上证50指数同期收益率,基于MIC架构的并行求解性能优于传统的CPU架构,平均并行效率达到80%。     

Hesitant fuzzy linguistic portfolio model with variable risk appetite and its application in the investment ratio calculation

Qualitative evaluation information is important for financial decision-making and investment when quantitative data are unavailable. Although an alternative ranking is available, specific portfolio and optimal investment ratios cannot be obtained by using the qualitative decision-making methods. To address this issue, this paper proposes a hesitant fuzzy linguistic portfolio model based on the max-score rule and the hesitant fuzzy linguistic element with variable risk appetite (HFLE-RA). The HFLE-RA is able to express qualitative evaluation information by using the hesitant fuzzy linguistic term set and describe the variable investor risk appetites by introducing the asymmetric sigmoid semantics. Thus, different investors can be distinguished by the risk appetite parameters according to the asymmetric sigmoid semantics, and the optimal investment ratios can be obtained by applying the proposed portfolio model. Moreover, the investment opportunities and efficient frontiers of the hesitant fuzzy linguistic portfolio model are investigated. Also, a value-at-risk fitting approach is introduced to calculate the risk appetite parameters. Based on these works, a qualitative investment ratio calculation process is provided in the HFLE-RA environment. Lastly, a real example of calculating the optimal investment ratios for four newly listed stocks in the Growth Enterprises Market board of the Shenzhen Stock Exchange is provided to demonstrate the proposed approaches.     

面向不同利益相关者的IT投资决策模型

为了响应不同利益相关者在IT投资决策过程中的不同需求,把备选项目看作一个组合,综合IT项目的战略对应和财务收益为目标,权衡其成本、收益和风险,构建基于模糊多目标规划的IT投资决策模型,其中模糊数用来刻画不确定的项目信息。通过改变各临界值和求解过程中产生的参数,模型支持各种假设分析。最后用案例说明模型的用法和功能。     

Expected model for portfolio selection with random fuzzy returns

This paper researches portfolio selection problem in combined uncertain environment of randomness and fuzziness. Due to the complexity of the security market, expected values of the security returns may not be predicted accurately. In the paper, expected returns of securities are assumed to be given by fuzzy variables. Security returns are regarded as random fuzzy variables, i.e. random returns with fuzzy expected values. Following Markowitz's idea of quantifying investment return by the expected value of the portfolio and risk by the variance, a new type of mean–variance model is proposed. In addition, a hybrid intelligent algorithm is provided to solve the new model problem. A numeral example is also presented to illustrate the optimization idea and the effectiveness of the proposed algorithm.     

A group decision-making model based on incomplete comparative expressions with hesitant linguistic terms

As a result of uncertainty and complexity for environments of decision-making, it is more suitable for decision makers to use hesitant fuzzy linguistic information. In this paper, a novel group decision making (GDM) model based on fuzzy linear programming is proposed for incomplete comparative expressions with hesitant fuzzy linguistic term set (HFLTSs). We establish an equivalence theorem of additive consistency between 2-tuple fuzzy linguistic preference relation (FLPR) and corresponding fuzzy preference relation. Based on this framework, a fuzzy linear programming is established to address incomplete comparative expressions with HFLTSs. It is more important that the proposed fuzzy linear programming has a double action, finding the highest consistent incomplete 2-tuple FLPR and increasing inconsistent 2-tuple FLPR to the additive consistent 2-tuple FLPR based on given incomplete comparative expressions with HFLTSs. By this means, a novel GDM model is constructed based on importance induced ordered weighted averaging operator. Finally, an investment decision-making in real-world is solved by the proposed model, which shows the result of GDM is effectiveness.     

基于战略对应的IT项目组合选择模型

把信息技术项目当作组合来管理可以通过平衡风险和收益来促进企业目标和IT应用的结合,但由于决策信息的不确定性和IT项目目标与企业战略的难以对应,企业面临IT项目组合选择的挑战。构建基于战略对应的IT项目组合选择模型,其中模糊集和模糊层次分析法用来刻画不确定信息和评估IT项目风险、成本及收益,关键成功因素法用来提高IT项目与企业战略的对应,并建立模糊0－1整数规划。利用定性可能性理论把模糊组合选择模型转化为一般可求解的整数规划形式,最后用一个案例说明模型的用法。     

Fuzzy portfolio selection using fuzzy analytic hierarchy process

Financial problems have been the subject of much research. A widely used approach in recent work on these problems is the use of fuzzy set theory, where fuzzy terms are used to model the uncertain environments. The purpose of this work is to combine the fuzzy analytic hierarchy process (AHP) with the portfolio selection problem. More specifically, the decision-making problem is to decide which stocks are to be chosen for investment and in what proportions they will be bought. To do this, we first dealt with two constrained fuzzy AHP methods given by Enea and Piazza [M. Enea, T. Piazza, Project selection by constrained fuzzy AHP, Fuzzy Optimization and Decision Making 3 (2004) 39–62]. We revised the first of these methods, addressing some of its fallacies, and called it revised constrained fuzzy AHP method (RCFAHP). Then we applied these two methods, namely, RCFAHP and the second- method of Enea and Piazza (2004), to the problem of choosing stocks on the Istanbul Stock Exchange (ISE). The methodology used for the hierarchy construction is based on the paper of Satty et al. [T.L. Saaty, P.C. Rogers, R. Bell, Portfolio selection through hierarchies, The Journal of Portfolio Management (1980) 16–21].In this paper, we show that both of the models provide both ranking and weighting information, via fuzzy AHP, to the investors in this financial scenario. Finally, we discuss the relative advantages and disadvantages of these methods in comparison to existing methods in the literature.     

Evaluating methods of investment project and optimizing models of portfolio selection in fuzzy uncertainty

This paper deals with the problems of both project valuation and portfolio selection under the assumption that the investment capitals and the net cash flows of the projects are fuzzy variables. Using the credibilistic expected value and the credibilistic lower semivariance of fuzzy variables, this paper proposes both the credibilistic return index and the credibilistic risk index, which are measures of investment return and investment risk with annuity form for evaluating single project. Moreover, a composite risk-return index for selecting the optimal investment strategy is also presented. Then, we set up a general project portfolio optimization model with fuzzy returns and two specific models: triangle and interval fuzzy returns. Furthermore, we provide two algorithms: the improved heuristic rules based on genetic algorithm and the traversal algorithm. Finally, two numerical examples are presented to illustrate the efficiency and the effectiveness of these proposed optimization methods.     

Fuzzy portfolio selection using genetic algorithm

This paper presents the development of fuzzy portfolio selection model in investment. Fuzzy logic is utilized in the estimation of expected return and risk. Using fuzzy logic, managers can extract useful information and estimate expected return by using not only statistical data, but also economical and financial behaviors of the companies and their business strategies. In the formulated fuzzy portfolio model, fuzzy set theory provides the possibility of trade-off between risk and return. This is obtained by assigning a satisfaction degree between criteria and constraints. Using the formulated fuzzy portfolio model, a Genetic Algorithm (GA) is applied to find optimal values of risky securities. Numerical examples are given to demonstrate the effectiveness of proposed method.     

Knowledge acquisition in incomplete fuzzy information systems via the rough set approach

Abstract: Machine learning can extract desired knowledge from training examples and ease the development bottleneck in building expert systems. Most learning approaches derive rules from complete and incomplete data sets. If attribute values are known as possibility distributions on the domain of the attributes, the system is called an incomplete fuzzy information system. Learning from incomplete fuzzy data sets is usually more difficult than learning from complete data sets and incomplete data sets. In this paper, we deal with the problem of producing a set of certain and possible rules from incomplete fuzzy data sets based on rough sets. The notions of lower and upper generalized fuzzy rough approximations are introduced. By using the fuzzy rough upper approximation operator, we transform each fuzzy subset of the domain of every attribute in an incomplete fuzzy information system into a fuzzy subset of the universe, from which fuzzy similarity neighbourhoods of objects in the system are derived. The fuzzy lower and upper approximations for any subset of the universe are then calculated and the knowledge hidden in the information system is unravelled and expressed in the form of decision rules.     

Credibilistic multi-period portfolio optimization model with bankruptcy control and affine recourse

Avoiding the possibility of bankruptcy during the investment horizon is very important to multi-period portfolio management. This paper considers a multi-period fuzzy portfolio selection problem with bankruptcy control. A multi-period portfolio optimization model imposed by a bankruptcy control constraint in fuzzy environment is proposed on the basis of credibility theory. In the proposed model, a linearly recourse policy is used to reflect the influence of historical predication basis on current portfolio decision. Three optimization objectives, viz., maximizing the terminal wealth and minimizing the cumulative risk and the cumulative uncertainty of the returns of portfolios over the whole investment horizon, are taken into consideration. For solving the proposed model, a fuzzy programming approach is applied to transform it into a single objective programming model. Then, a hybrid particle swarm optimization algorithm is designed for solution. Finally, an empirical example is presented to illustrate the application of the proposed model and solution comparisons are also given to demonstrate the effectiveness of the designed algorithm.     

考虑投资者心理特征的模糊投资组合优化模型

投资者在实际金融市场中的决策行为往往会受到主观心理认知的影响.考虑参照依赖、敏感性递减和损失厌恶等影响投资决策的心理特征,研究模糊环境下的投资组合选择问题.首先,假设资产的收益为梯形模糊数,依据前景理论中的价值函数,将组合收益转化为体现投资者心理特征的感知价值;然后,以感知价值的可能性均值最大化和可能性下半方差最小化为目标,建立考虑心理特征的模糊投资组合优化模型;接着,为了有效地求解模型,设计一个多种群遗传算法;最后,通过实例分析表明模型和算法的有效性.结果表明,与传统的遗传算法相比,所设计的多种群遗传算法可更有效地求解模型,考虑心理特征的模糊投资组合优化模型能够提升投资者的满意程度,可为实际的投资活动提供决策支持.     

A Consensus Model for Group Decision Making With Incomplete Fuzzy Preference Relations

Two processes are necessary to solve group decision making problems: A consensus process and a selection process. The consensus reaching process is necessary to obtain a final solution with a certain level of agreement between the experts; and the selection process is necessary to obtain such a final solution. In a previous paper, we present a selection process to deal with group decision making problems with incomplete fuzzy preference relations, which uses consistency measures to estimate the incomplete fuzzy preference relations. In this paper we present a consensus model. The main novelty of this consensus model is that of being guided by both consensus and consistency measures. Also, the consensus reaching process is guided automatically, without moderator, through both consensus and consistency criteria. To do that, a feedback mechanism is developed to generate advice on how experts should change or complete their preferences in order to reach a solution with high consensus and consistency degrees. In each consensus round, experts are given information on how to change their preferences, and to estimate missing values if their corresponding preference relation is incomplete. Additionally, a consensus and consistency based induced ordered weighted averaging operator to aggregate the experts' preferences is introduced, which can be used in consensus models as well as in selection processes. The main improvement of this consensus model is that it supports the management of incomplete information and it allows to achieve consistent solutions with a great level of agreement.     

基于概率不确定犹豫模糊偏好关系的决策模型

针对犹豫模糊信息在现实决策中难以准确和充分的提供决策者评价信息的问题,引入了概率不确定犹豫模糊偏好关系（PUHFPR）的概念,其能够有效处理概率不确定犹豫模糊元（PUHFE）中元素发生概率信息部分已知和完全未知的决策问题;给出了PUHFPR的期望加行一致性、满意加性期望一致性定义,并以偏差最小化为目标函数构建最优化模型确定PUHFPR元素的发生概率;建立基于一致性调整算法的概率不确定犹豫模糊偏决策模型,得到方案的排序权重向量,从而选择最佳的方案;通过遴选上市公司进行投资的实例说明决策模型的有效性。     

基于信息测度的勾股模糊决策模型及其应用

相对于直觉模糊集，勾股模糊集能够更为全面和有效地表达描述复杂问题中的不确定和非一致信息，使其受到了广泛研究。对于属性评价值为勾股模糊数并且属性指标权重信息数据完全未知的多属性决策问题，以提出的勾股模糊信息测度为基础，设计了新的多属性决策模型。该模型运用对数函数设计了一种新的勾股模糊数信息熵计算方法；引入了勾股模糊相似度概念，并结合对数行数提出勾股模糊数相似度的衡量方法，随后挖掘出勾股模糊数的信息熵和相似度之间的内在联系；运用提出的勾股模糊熵和相似度计算方法，构建新的多属性决策模型，并进行应用研究。实验结果表明，提出的模型合理有效，同时拓展了模型的使用范围。     

Incomplete interval-valued intuitionistic fuzzy preference relations

The aim of this paper is to investigate decision making problems with interval-valued intuitionistic fuzzy preference information, in which the preferences provided by the decision maker over alternatives are incomplete or uncertain. We define some new preference relations, including additive consistent incomplete interval-valued intuitionistic fuzzy preference relation, multiplicative consistent incomplete interval-valued intuitionistic fuzzy preference relation and acceptable incomplete interval-valued intuitionistic fuzzy preference relation. Based on the arithmetic average and the geometric mean, respectively, we give two procedures for extending the acceptable incomplete interval-valued intuitionistic fuzzy preference relations to the complete interval-valued intuitionistic fuzzy preference relations. Then, by using the interval-valued intuitionistic fuzzy averaging operator or the interval-valued intuitionistic fuzzy geometric operator, an approach is given to decision making based on the incomplete interval-valued intuitionistic fuzzy preference relation, and the developed approach is applied to a practical problem. It is worth pointing out that if the interval-valued intuitionistic fuzzy preference relation is reduced to the real-valued intuitionistic fuzzy preference relation, then all the above results are also reduced to the counterparts, which can be applied to solve the decision making problems with incomplete intuitionistic fuzzy preference information.     

基于模糊粗集的不完备信息表属性约简新算法

模糊粗糙集结合了粗集和模糊集的优点,是一种有效的数据处理理论,尤其在不完备信息表数据处理中。论文对Krysckiewcz容差关系模型加以改进,充分考虑信息表中属性取值的规律,构造模糊的二元不可分辨关系,运用模糊粗糙集理论,推广属性依赖性度量概念,给出了属性约简算法,并通过一个实例验证了它的有效性,为不完备信息表的数据处理提供了一些解决问题的思路。     

Application of VPRS model with enhanced threshold parameter selection mechanism to automatic stock market forecasting and portfolio selection

This study proposes a technique based upon Fuzzy C-Means (FCM) classification theory and related fuzzy theories for choosing an appropriate value of the Variable Precision Rough Set (VPRS) threshold parameter (β) when applied to the classification of continuous information systems. The VPRS model is then combined with a moving Average Autoregressive Exogenous (ARX) prediction model and Grey Systems theory to create an automatic stock market forecasting and portfolio selection mechanism. In the proposed mechanism, financial data are collected automatically every quarter and are input to an ARX prediction model to forecast the future trends of the collected data over the next quarter or half-year period. The forecast data are then reduced using a GM(1, N) model, classified using a FCM clustering algorithm, and then supplied to a VPRS classification module which selects appropriate investment stocks in accordance with a pre-determined set of decision-making rules. Finally, a grey relational analysis technique is employed to weight the selected stocks in such a way as to maximize the rate of return of the stock portfolio. The validity of the proposed approach is demonstrated using electronic stock data extracted from the financial database maintained by the Taiwan Economic Journal (TEJ). The portfolio results obtained using the proposed hybrid model are compared with those obtained using a Rough Set (RS) selection model. The effects of the number of attributes of the RS lower approximation set and VPRS β-lower approximation set on the classification are systematically examined and compared. Overall, the results show that the proposed stock forecasting and stock selection mechanism not only yields a greater number of selected stocks in the β-lower approximation set than in the RS approximation set, but also yields a greater rate of return.