模糊环境下的投资规划研究
|
摘要
投资组合(Portfolio)决策研究的核心问题是研究如何把有限资金合理的分配到不同的资产中,以达到分散风险并确保投资收益的目的。而证券投资规划从本质上来说,就是在不确定性的投资环境中,以现代投资组合理论为研究基础,通过建立模拟实际投资情况的数学规划模型,在综合平衡投资收益和投资风险等相关因素的条件下,构造出投资决策分析框架,求解出最优投资决策的研究方法。Markowitz的均值-方差模型就是利用概率论的相关理论度量证券市场的不确定性,在投资组合理论的基本框架下,构造出既定投资收益条件下,最小化投资风险或者是既定投资风险条件下,最大化投资收益的证券投资规划模型。
然而,证券市场中存在着两种不确定性事件：随机不确定性事件和模糊不确定性事件,这样,证券投资规划可以相应的分为度量随机不确定性事件的证券投资规划模型和度量模糊不确定性事件的证券投资规划模型。建立在概率论基础上的均值-方差模型仅考虑了证券市场的随机不确定性,却忽视了模糊不确定性对证券选择的影响,而证券市场中的不确定性事件更多的表现为模糊不确定性事件,模糊不确定性是证券市场固有的本质特征,构建模糊不确定性环境下的证券投资规划模型更加符合实际的投资情况。
本研究立足于我国的实际情况,充分利用定量和定性的知识相结合的办法,利用专家的知识和经验,在深入挖掘证券市场上模糊特性的基础上,综合利用模糊理论和最优化方法来研究证券投资组合的决策问题,为我国的投资实践提供行之有效的决策意见。本研究主要关注以下几个方面：
(1)模糊环境下投资规划的构建和应用性研究。在模糊不确定环境下,构建出证券投资选择规划,并给出相应地优化求解方法,研究模糊投资规划在投资决策实践中的决策效果,并且在研究单期模糊投资规划构建和优化求解的基础上,研究多期模糊投资规划在证券选择方面的投资决策效果。
(2)模糊环境下投资规划的有效性研究。以模糊AR时间序列预测的投资组合未来的收益状况代替样本期望值来度量投资收益,在模糊决策的理论框架下,将绝对偏差度量的投资风险调整为模糊松弛约束,建立目标函数为梯形模糊数的投资收益,风险约束为模糊松弛约束的模糊投资规划,将模糊环境下所求得的有效性前沿和随机环境下的有效性前沿进行比较分析,研究模糊环境下投资规划的有效性以及模糊投资规划比随机投资规划的优越性。
(3)模糊环境下二目标梯形模糊数投资规划研究。以模糊时间序列预测投资收益为基础,建立证券价格为梯形模糊数的预测模型,以预测值和购买价格的比值衡量投资收益,以预测收益低于期望值的半绝对偏差度量投资风险,建立了二目标投资规划模型,在充分利用证券市场开盘价、收盘价、最高价和最低价四个价格,在模拟出证券价格的梯形模糊数的基础上,采用折衷规划的方法进行优化求解,利用我国上证50指数的真实数据进行实证检验分析,并与概率框架下的均值-绝对偏差模型的投资组合效果进行比较。
(4)模糊环境下二目标区间数投资规划决策研究。采用S型隶属函数描述投资收益为投资者带来的满意度水平,并利用模糊逻辑关系预测未来的满意度水平,构建了模糊目标为区间收益和区间风险的二目标区间数投资规划,利用我国上证180成分指数的真实数据进行实证检验分析。
(5)模糊环境下多期投资组合优化研究。将模糊单期规划拓展为多期投资组合,利用解释变量为三角形模糊数的模糊AR模型预测未来的多期投资收益,三角形模糊数的方差和协方差度量投资风险,构建出多期投资规划模型,利用含遗传交叉变异因子的粒子群智能优化算法优化求解,并利用我国深圳证券市场的真实数据进行实证检验。
(6)基于两步模糊机会规划的多期决策研究。考虑采用模糊变量为对称三角形模糊数的模糊AR模型预测投资收益,以模糊收益中值的协方差度量投资风险,并将市场的流动性因素纳入投资决策框架,利用模糊数的清晰化公式,将预测的模糊收益转化为清晰化的投资收益,在单期两步模糊机会规划的基础上,构建出模糊多期规划寻求投资收益和投资风险的Pareto解,在动态规划分析框架下,采用含遗传交叉变异因子的粒子群算法求解,并利用我国上证50指数的真实数据进行实证检验。
(7)模糊环境下基于情景树多期层次资产配置研究。利用模糊层次分析法,将金融资产中的基本面因素纳入投资分析框架,采用因素变量之间的绝对偏差和相对偏差,构造出模糊判断矩阵,利用所获得的三角形模糊收益综合评价值和模糊风险收益综合评价值,构建出模糊环境下的单期资产配置模型,在情景树的多期框架下,利用市场状态之间的模糊逻辑关系出现的概率,计算相应的贝叶斯概率,将单期模糊投资规划拓展为多期模糊资产配置模型,利用我国沪深300行业指数的真实数据进行实证检验分析。
最后,总结了本文的主要研究内容和结论,并指出了本文研究的局限性和进一步研究的方向。
The core question of the portfolio's decision-making research is to study how to distribute the limiting funds to the different assets in order to achieve the goal which to spread the loss and to ensure the earnings. And in essence, based on the research of the modern portfolio theory, the portfolio investment programming is the research method in the uncertainty environment which to establish the mathematic programming model which can simulate the actual investment complexions, and on the condition of the synthetical balance of the correlative factors, such as, the investment return and the investment risk, to construct the analytic framework of the investment decision, then solve the optimal investment decision. Using the correlative theories of the probability to measure the uncertainty of the security market, and under the basal analytic framework of the modern portfolio theary, Markowitz's mean-variance model is the security programming model which minimize the investment risk on the condition of the certain investment return, or maximize the invesetment retun on the condition of the certain investment risk.
However, there are two uncertainty events in the security market: the stochastic uncertainty events and the fuzzy uncertainty events, then the security investment programming can correspondingly be classified the security investment programming model measuring the stochastic uncertainty events and the security investment programming model measuring the fuzzy uncertainty events. Based on the probability theory, mean-variance model only considers the stochastic uncertainty of the security market, while ignores the impact of the fuzzy uncertainty. The uncertainty of the security market is showed more fuzzy uncertainty. The fuzzy uncertainty is the intrinsic and essence characteristic of the security market, establishing the security portfolio programming under the fuzzy uncertainty environment will be more suitable the actual investment decision.
Based on the actual situation of our country, by making fully use of the approach which to combine the quantitative and qualitative knowledge, and using the knowledge and experience of the expert, and on the basis of the in-depth digging the fuzzy characteristics of the security market, this study is to research the selectable question of the security investment portfolio by synthetically using the fuzzy theory and optimal method in order to give the effective decision-making advice for the investment practice of our country. The main concern of this study is following aspects:
(1) The constructing and applied research of the portfolio in the fuzzy environment. Under the fuzzy uncertainty environment, I have constructed the portfolio programming, and gived the optimal and solving methods correspondingly, then studied the decision-making impact of the fuzzy portfolio programming in the investment decision-making practice, and then based on the construction and the optimal solution of the single-period portfolio programming, I have studied the investment decision-making impact of the multi-period fuzzy portfolio programming for the choices of the securities.
(2) The portfolio validity research in the fuzzy environment. The future return states of the portfolio forecasted by the fuzzy AR model is taken the place of the sample expectation to measure the investment return, and under the framework of the fuzzy decision-making theory, the investment risk measured by the absolute deviation is adjusted by the fuzzy relaxation constraint, and I construct a fuzzy investment programming which the goal function is the investment return of the trapezoidal fuzzy number and the risk constraint is the fuzzy relaxation constraint, compare and analyze the effective frontier of the fuzzy environment and the stochastic environment, and study the validity of the investment programming under the fuzzy environment and the superiority of the compare between the fuzzy portfolio programming and the stochastic portfolio programming.
(3) The investment programming research of the two-goal trapezoid fuzzy number under the fuzzy environment. I establish the predicting model which the security price is the trapezoidal fuzzy numbers based on the prediction of the fuzzy time series, and measuring the investment return by the ratio of the predicting value and measuring the purchasing price and the investment risk by the semi-absolute deviation which the predicting value is below to the expectation, I construct the two-goal programming, and solve the programming to obtain the optimal solution with the method of the compromise programming based on simulating the trapezoid fuzzy number of the security price by fully using the open price, the close price, the highest price and the lowest price of the security market, then empirically analyze the perform of the fuzzy model with the actual data of the SSE50, and then compare the portfolio perform with the mean-absolute deviation model under the probability framework.
(4) The portfolio decision-making research of the two-goal interval number under the fuzzy environment. I use the S-type membership to describe the satisfaction degree level of the investment return, and make use of the fuzzy logic relationship to forecast the future satisfaction degree level, then establish the two-goal interval number investment programming which the fuzzy goal is the interval return and the interval risk, and then empirically analyze this fuzzy programming with the actual data of the SSE180.
(5) The multi-period portfolio optimization research under the fuzzy environment. I spread the fuzzy single programming into the multi-period portfolio, and use the fuzzy AR model that the fuzzy variables are the triangular fuzzy number to predict the future multi-period investment returns, then measure the investment risk with the variance and covariance of the triangular fuzzy number, and then construct the multi-period portfolio model, and solve the optimal solution by using the PSO algorithm with the factor of the genetic cross and the genetic variation, at last, empirically analyze this programming with the actual data of the Shenzhen Security Market.
(6) The multi-period decision-making research based on the two-step fuzzy chance programming. I predict the investment return by using the fuzzy AR model which the fuzzy variables are the symmetric triangular fuzzy number, and measure the investment risk by the covariance of the fuzzy return middle-value, then introduce the market liquidity into the investment decision-making framework, and then change the predictive fuzzy return to the clear investment return by using the clear formula of the fuzzy number, and based on the establishment the single two-step fuzzy chance programming, I establish a two-stage chance programming in order to obtain the Pareto solution of the investment return and the investment risk, then use the PSO algorithm with the factor of the genetic cross and the genetic variation to solve the optimal solution under the framework of the dynamic programming, and then empirically analyze this programming with the actual data of the SSE.50.
(7) The multi-period fuzzy AHP asset allocation research based on the scenarios tree under the fuzzy environment. Using the fuzzy AHP method, I introduce the fundamental factors of the financial asset into the framework of the investment analysis, and use the absolute deviation and the relative deviation between the factor variables, then construct the fuzzy judgment matrix, then based on the synthetic evaluate value of the triangular fuzzy return and the synthetic evaluate value of the triangular fuzzy risk, establish the single asset allocation under fuzzy environment, and then with the multi-period framework of the scenarios tree model and the probability appeared the fuzzy logic relationship between the market states, calculate the corresponding Bayesian probability, then extend the single fuzzy investment programming into the multi-period fuzzy asset allocation model, and then empirically analyze the programming with the actual data of the SHSZ300Industry Index.
Finally, the main contents and results of our research in this dissertation are summarized as well as future research directions.
然而,证券市场中存在着两种不确定性事件：随机不确定性事件和模糊不确定性事件,这样,证券投资规划可以相应的分为度量随机不确定性事件的证券投资规划模型和度量模糊不确定性事件的证券投资规划模型。建立在概率论基础上的均值-方差模型仅考虑了证券市场的随机不确定性,却忽视了模糊不确定性对证券选择的影响,而证券市场中的不确定性事件更多的表现为模糊不确定性事件,模糊不确定性是证券市场固有的本质特征,构建模糊不确定性环境下的证券投资规划模型更加符合实际的投资情况。
本研究立足于我国的实际情况,充分利用定量和定性的知识相结合的办法,利用专家的知识和经验,在深入挖掘证券市场上模糊特性的基础上,综合利用模糊理论和最优化方法来研究证券投资组合的决策问题,为我国的投资实践提供行之有效的决策意见。本研究主要关注以下几个方面：
(1)模糊环境下投资规划的构建和应用性研究。在模糊不确定环境下,构建出证券投资选择规划,并给出相应地优化求解方法,研究模糊投资规划在投资决策实践中的决策效果,并且在研究单期模糊投资规划构建和优化求解的基础上,研究多期模糊投资规划在证券选择方面的投资决策效果。
(2)模糊环境下投资规划的有效性研究。以模糊AR时间序列预测的投资组合未来的收益状况代替样本期望值来度量投资收益,在模糊决策的理论框架下,将绝对偏差度量的投资风险调整为模糊松弛约束,建立目标函数为梯形模糊数的投资收益,风险约束为模糊松弛约束的模糊投资规划,将模糊环境下所求得的有效性前沿和随机环境下的有效性前沿进行比较分析,研究模糊环境下投资规划的有效性以及模糊投资规划比随机投资规划的优越性。
(3)模糊环境下二目标梯形模糊数投资规划研究。以模糊时间序列预测投资收益为基础,建立证券价格为梯形模糊数的预测模型,以预测值和购买价格的比值衡量投资收益,以预测收益低于期望值的半绝对偏差度量投资风险,建立了二目标投资规划模型,在充分利用证券市场开盘价、收盘价、最高价和最低价四个价格,在模拟出证券价格的梯形模糊数的基础上,采用折衷规划的方法进行优化求解,利用我国上证50指数的真实数据进行实证检验分析,并与概率框架下的均值-绝对偏差模型的投资组合效果进行比较。
(4)模糊环境下二目标区间数投资规划决策研究。采用S型隶属函数描述投资收益为投资者带来的满意度水平,并利用模糊逻辑关系预测未来的满意度水平,构建了模糊目标为区间收益和区间风险的二目标区间数投资规划,利用我国上证180成分指数的真实数据进行实证检验分析。
(5)模糊环境下多期投资组合优化研究。将模糊单期规划拓展为多期投资组合,利用解释变量为三角形模糊数的模糊AR模型预测未来的多期投资收益,三角形模糊数的方差和协方差度量投资风险,构建出多期投资规划模型,利用含遗传交叉变异因子的粒子群智能优化算法优化求解,并利用我国深圳证券市场的真实数据进行实证检验。
(6)基于两步模糊机会规划的多期决策研究。考虑采用模糊变量为对称三角形模糊数的模糊AR模型预测投资收益,以模糊收益中值的协方差度量投资风险,并将市场的流动性因素纳入投资决策框架,利用模糊数的清晰化公式,将预测的模糊收益转化为清晰化的投资收益,在单期两步模糊机会规划的基础上,构建出模糊多期规划寻求投资收益和投资风险的Pareto解,在动态规划分析框架下,采用含遗传交叉变异因子的粒子群算法求解,并利用我国上证50指数的真实数据进行实证检验。
(7)模糊环境下基于情景树多期层次资产配置研究。利用模糊层次分析法,将金融资产中的基本面因素纳入投资分析框架,采用因素变量之间的绝对偏差和相对偏差,构造出模糊判断矩阵,利用所获得的三角形模糊收益综合评价值和模糊风险收益综合评价值,构建出模糊环境下的单期资产配置模型,在情景树的多期框架下,利用市场状态之间的模糊逻辑关系出现的概率,计算相应的贝叶斯概率,将单期模糊投资规划拓展为多期模糊资产配置模型,利用我国沪深300行业指数的真实数据进行实证检验分析。
最后,总结了本文的主要研究内容和结论,并指出了本文研究的局限性和进一步研究的方向。
The core question of the portfolio's decision-making research is to study how to distribute the limiting funds to the different assets in order to achieve the goal which to spread the loss and to ensure the earnings. And in essence, based on the research of the modern portfolio theory, the portfolio investment programming is the research method in the uncertainty environment which to establish the mathematic programming model which can simulate the actual investment complexions, and on the condition of the synthetical balance of the correlative factors, such as, the investment return and the investment risk, to construct the analytic framework of the investment decision, then solve the optimal investment decision. Using the correlative theories of the probability to measure the uncertainty of the security market, and under the basal analytic framework of the modern portfolio theary, Markowitz's mean-variance model is the security programming model which minimize the investment risk on the condition of the certain investment return, or maximize the invesetment retun on the condition of the certain investment risk.
However, there are two uncertainty events in the security market: the stochastic uncertainty events and the fuzzy uncertainty events, then the security investment programming can correspondingly be classified the security investment programming model measuring the stochastic uncertainty events and the security investment programming model measuring the fuzzy uncertainty events. Based on the probability theory, mean-variance model only considers the stochastic uncertainty of the security market, while ignores the impact of the fuzzy uncertainty. The uncertainty of the security market is showed more fuzzy uncertainty. The fuzzy uncertainty is the intrinsic and essence characteristic of the security market, establishing the security portfolio programming under the fuzzy uncertainty environment will be more suitable the actual investment decision.
Based on the actual situation of our country, by making fully use of the approach which to combine the quantitative and qualitative knowledge, and using the knowledge and experience of the expert, and on the basis of the in-depth digging the fuzzy characteristics of the security market, this study is to research the selectable question of the security investment portfolio by synthetically using the fuzzy theory and optimal method in order to give the effective decision-making advice for the investment practice of our country. The main concern of this study is following aspects:
(1) The constructing and applied research of the portfolio in the fuzzy environment. Under the fuzzy uncertainty environment, I have constructed the portfolio programming, and gived the optimal and solving methods correspondingly, then studied the decision-making impact of the fuzzy portfolio programming in the investment decision-making practice, and then based on the construction and the optimal solution of the single-period portfolio programming, I have studied the investment decision-making impact of the multi-period fuzzy portfolio programming for the choices of the securities.
(2) The portfolio validity research in the fuzzy environment. The future return states of the portfolio forecasted by the fuzzy AR model is taken the place of the sample expectation to measure the investment return, and under the framework of the fuzzy decision-making theory, the investment risk measured by the absolute deviation is adjusted by the fuzzy relaxation constraint, and I construct a fuzzy investment programming which the goal function is the investment return of the trapezoidal fuzzy number and the risk constraint is the fuzzy relaxation constraint, compare and analyze the effective frontier of the fuzzy environment and the stochastic environment, and study the validity of the investment programming under the fuzzy environment and the superiority of the compare between the fuzzy portfolio programming and the stochastic portfolio programming.
(3) The investment programming research of the two-goal trapezoid fuzzy number under the fuzzy environment. I establish the predicting model which the security price is the trapezoidal fuzzy numbers based on the prediction of the fuzzy time series, and measuring the investment return by the ratio of the predicting value and measuring the purchasing price and the investment risk by the semi-absolute deviation which the predicting value is below to the expectation, I construct the two-goal programming, and solve the programming to obtain the optimal solution with the method of the compromise programming based on simulating the trapezoid fuzzy number of the security price by fully using the open price, the close price, the highest price and the lowest price of the security market, then empirically analyze the perform of the fuzzy model with the actual data of the SSE50, and then compare the portfolio perform with the mean-absolute deviation model under the probability framework.
(4) The portfolio decision-making research of the two-goal interval number under the fuzzy environment. I use the S-type membership to describe the satisfaction degree level of the investment return, and make use of the fuzzy logic relationship to forecast the future satisfaction degree level, then establish the two-goal interval number investment programming which the fuzzy goal is the interval return and the interval risk, and then empirically analyze this fuzzy programming with the actual data of the SSE180.
(5) The multi-period portfolio optimization research under the fuzzy environment. I spread the fuzzy single programming into the multi-period portfolio, and use the fuzzy AR model that the fuzzy variables are the triangular fuzzy number to predict the future multi-period investment returns, then measure the investment risk with the variance and covariance of the triangular fuzzy number, and then construct the multi-period portfolio model, and solve the optimal solution by using the PSO algorithm with the factor of the genetic cross and the genetic variation, at last, empirically analyze this programming with the actual data of the Shenzhen Security Market.
(6) The multi-period decision-making research based on the two-step fuzzy chance programming. I predict the investment return by using the fuzzy AR model which the fuzzy variables are the symmetric triangular fuzzy number, and measure the investment risk by the covariance of the fuzzy return middle-value, then introduce the market liquidity into the investment decision-making framework, and then change the predictive fuzzy return to the clear investment return by using the clear formula of the fuzzy number, and based on the establishment the single two-step fuzzy chance programming, I establish a two-stage chance programming in order to obtain the Pareto solution of the investment return and the investment risk, then use the PSO algorithm with the factor of the genetic cross and the genetic variation to solve the optimal solution under the framework of the dynamic programming, and then empirically analyze this programming with the actual data of the SSE.50.
(7) The multi-period fuzzy AHP asset allocation research based on the scenarios tree under the fuzzy environment. Using the fuzzy AHP method, I introduce the fundamental factors of the financial asset into the framework of the investment analysis, and use the absolute deviation and the relative deviation between the factor variables, then construct the fuzzy judgment matrix, then based on the synthetic evaluate value of the triangular fuzzy return and the synthetic evaluate value of the triangular fuzzy risk, establish the single asset allocation under fuzzy environment, and then with the multi-period framework of the scenarios tree model and the probability appeared the fuzzy logic relationship between the market states, calculate the corresponding Bayesian probability, then extend the single fuzzy investment programming into the multi-period fuzzy asset allocation model, and then empirically analyze the programming with the actual data of the SHSZ300Industry Index.
Finally, the main contents and results of our research in this dissertation are summarized as well as future research directions.
引文
1. Zadeh LA. Fuzzy Sets[J], Information and Control,1965,8 (3):338-353.
2. Bellman R, Zadeh L A. Decision making in a fuzzy environment[J], Management Science,1970,17 (4):141-164.
3. Ramaseamy S. Portfolio selection using fuzzy decision theory[R], Working Paper, Bank for International Settlements,1998,59.
4. Leon T, Liern V and Vercher E. Viability of infeasible portfolio selection problems: a fuzzy approach[J], European Journal of Operational Research,2002,139 (4):178-189.
5. Watada J. Fuzzy portfolio model for decision making in investment [M], Heidelberg: Physica-Verlag,2001,141-162.
6. Lai K K, Fang Y and Wang S Y. Portfolio rebalancing model with transaction costs based on fuzzy decision theory[J], European Journal of Operational Research,2006,175(2):879-893.
7.庄新田,黄小原,卢新.证券组合的模糊优化[J],东北大学学报(自然科学版),2001,22(2)：165-168.
8.曾建华,汪寿阳.一个基于模糊决策理论的投资组合模型[J],系统工程理论与实践,2003,16(1)：99-104
9.庄新路,庄新田,黄小原.基于VAR风险指标的投资组合模糊优化[J],数学的实践与认识,2003,33(3)：3540.
10.黄小原,赵光华,庄新田.企业投融资组合饿模糊模型与优化[J],控制与决策,2004,19(7)：756-763.
11.肖冬荣,黄静.基于均值、方差和偏度的投资组合模糊优化模型[J],统计与决策,2006,(14)：3940.
12.姚天祥,刘思峰.基于预测收益率的模糊投资组合优化模型[J],统计与决策,2007,(19)：47-48.
13. Watada J. Fuzzy portfolio selection and its applications to decision making[M], Tatra Mountains:Mathematical Publication,1997,219-248.
14. Yang Fang, K.K.Lai and Shou-Yang Wang. Portfolio rebalancing model with transaction costs based on fuzzy decision theory[J], European Journal of Operational Research,2006,175(2): 879-893.
15. Huang Xiaoxia. Portfolio selection with fuzzy returns[J], Journal of Intelligent & Fuzzy Systems,2007,18 (4):383-390.
16.吕昌会,何湘藩,黄德斌,严碧清.证券投资决策的模糊多目标规划方法[J],系统工程理论方法应用,1998,7(2)：14-18.
17.郭存芝,郑垂勇.一种证券组合投资的模糊多目标规划方法[J],系统工程理论与实践,2001,(1)：21-30.
18.徐维军,徐寅峰,王迅,张卫国.收益率为模糊数的加权证券组合选择模型[J],系统工程学报,2005,20(1)：6-11.
19.李建新,胡刚.风险厌恶型的证券投资数学模型[J],数量经济技术经济研究,2005,22(3)：97-106.
20.陈国华,陈收,房勇,汪寿阳.基于模糊收益率的组合投资模型[J],经济数学,2006,23(1)：19-25.
21.李建新,胡刚.基于模糊数分析的时机捕捉型的证券投资模型[J],模糊系统与数学,2006,20(4)：141-150.
22.程巧华,张博侃.模糊数在投资组合中的应用[J],苏州科技学院学报(自然科学版),2006,23(3)：21-26.
23.何树红,乐晓梅,毛娟芳.带交易费用的证券组合投资的模糊多目标优化模型[J],云南民族大学学报(自然科学版),2007,16(1)：25-28.
24.岳伟,贺兴时,刘宣会.模糊数在证券投资组合选择模型中的运用[J],统计与决策,2007,(8)：125-127.
25.王庆,李政.证券市场的模糊投资组合模型[J],江苏工业学院学报,2007,8(3)：48-50.
26.严维真,宁玉富,郭长友.具有模糊收益率的贷款组合优化决策[J],系统工程学报,2008,23(2)：168-173.
27. Bitran G R. Linear multiple objective problems with interval coefficients[J], Management Science,1980,26 (3):694-706.
28. Steuer R E. Algorithm for linear programming problems with interval objective function coefficients[J], Mathematics of Operational Research,1980,6(2):333-348.
29. Ishibuchi H, Tanaka H. Formulation and analysis of linear programming with interval coefficients [J], Journal of Japan Industrial Management Association,1989,40(3):320-329.
30. Ishibuchi H, Tanaka H. Multiobjective programming in optimization of the interval objective function[J], European Journal of Operational Research,1990,48 (2):219-225.
31. Nakahara Y, Sasaki M and Gen M. On the linear programming with interval coefficients [J], international Journal of Computers and Engineering,1992,23(2):301-304.
32. Chanas S, Kuchta D. Multiobjective programming in optimization of interval objective functions-a generalized approach[J], European Journal of Operational Research, 1996,94(4):594-598.
33. Tong S. Interval number and fuzzy number linear programming [J], Fuzzy Sets and Systems, 1994,66(3):301-306.
34.刘新旺,达庆利.一种区间数线性规划的满意解[J],系统工程学报,1999,14(2)：123-128.
35. Chinneck J W, Ramadan K. Linear programming with interval coefficients [J], Journal of the Operational Research Society,2000.51(2):209-220.
36. Lai K K, Wang S Y, Xu J P and Fang Y. A class of linear interval programming problems and Its applications to portfolio selection[J]. IEEE Transaction on Fuzzy Systems,2002, 10:698-704.
37.房勇,汪寿阳.模糊投资组合优化：理论与方法[M],北京：高等教育出版社,2005：73-108.
38. Arenas M P, Bilbao A T and Rodriguez M V. A fuzzy goal programming approach to portfolio selection[J]. European of Operational Research,2001,133 (2):287-297.
39. Liu Y K, Zhang W G and Wang Y L. On admissible efficient portfolio selection: Models and algorithms [J], Applied Mathematics and Computation,2006,176 (1):208-218.
40. Zhang W G, Nie Z K. On admissible efficient portfolio selection problem[J], Applied Mathematics and Computation,2004,159(2):357-371.
41. Zhang W G, Nie Z K. On admissible efficient portfolio selection policy [J], Applied Mathematics and Computation,2005,169(1):608-623.
42. Giove S, Funari S and Nardelli C. An interval portfolio selection problem based on regret function[J], European Journal of Operational Research,2006,170 (1):253-264.
43.路应金,唐小我,周宗放.证券组合投资的区间数线性规划方法[J],系统工程学报,2004,19(1)：33-37.
44.赵玉梅,陈华友.证券组合投资的多目标区间数线性规划模型[J],运筹与管理,2006, 15(2)：124-127.
45.陈国华,陈收,汪寿阳.区间数模糊投资组合模型[J],系统工程,2007,25(8)：34-37.
46. Zadeh L A. Fuzzy sets as a basis for a theory of possibility[J], Fuzzy Sets and Systems, 1978,1(1):3-28.
47. Tanaka H, Guo P and Turksen I B. Portfolio selection based on fuzzy probabilities and possibility distributions[J], Fuzzy Sets and Systems,2000,111 (3):387-397.
48. Tanaka H, Guo P. Portfolio selection based on upper and lower exponential possibility distributions [J], European Journal of Operational Research,1999,114(2):115-126.
49. Inuiguchi M, Ramik J. Possibilistic linear programming: A brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem [J]. Fuzzy Sets and Systems,2000,111 (1):3-28.
50. Inuiguchi M, Tanina T. Portfolio selection under independent possibilistic information[J], Fuzzy Sets and Systems,2000,115(1):83-92.
51. Carlsson C, Fuller R and Majlender P. A possibilistic approach to selecting portfolio with highest utility score[J], Fuzzy Sets and Systems,2002,131 (1):13-21.
52.洪雁,邵全,吴祈宗.模糊机会约束规划下的投资组合模型研究[J],数量经济技术经济研究,2005,(9)：112-118.
53.乔峰,黄培清,顾锋.可能性投资组合模型[J],上海交通大学学报,2005,39(10)：1606-1610.
54. Chen Y J, Liu Y K. Portfolio selection in fuzzy environment[C], In Proceedings of the Fourth International Conference on Machine Learning and Cybernetics, Guangzhou,2005, 2694-2699.
55. Henry M, Mok K, Peng J and Tse W M. Credibility programming approach to fuzzy portfolio selection problems [C], In Proceedings of the Fourth International Conference on Machine Learning and Cybernetics, Guangzhou,2005,2523-2528.
56. Wang Y Q, Tang W S. Research on intelligent algorithm for portfolio selection with credibility criterion[C], Proceedings of the Fourth International Conference on Machine Learning and Cybernetics, Guangzhou,2005,3517-3522.
57. Zhang J P, Li S M. Portfolio selection with quadratic utility under fuzzy environment[C], Proceedings of the Fourth International Conference on Machine Learning and Cybernetics, Guangzhou,2005,2529-2533.
58. Zhang W G, Zhang Q M and Nie Z K. A class of fuzzy portfolio selection problems[C], Proceedings of the Second International Conferenece on Machine Learing and Cybernetics, 2003,2654-2658.
59. Huang J J, Tzeng G H and Ong C S. A novel algorithm for uncertain portfolio selection[J], Applied Mathematics and Computation,2006,173(1):350-359.
60. Ong C S, Huang J J and Tzeng G H. A novel hybrid model for portfolio selection[J], Applied Mathematics and Computation,2005,169 (2):1195-1210.
61. Ammar E, Khalifa H A. Fuzzy portfolio optimization a quadratic programming approach[J], Chaos, Solitons and Fractals,2003,18(5):1045-1054.
62. Ida M. Solutions for the portfolio selection problem with interval and fuzzy coefficients[J], Reliable Computering,2004,10(3):389-400.
63. Leon T, Liern V and Vercher E. Viability of infeasible portfolio selection problems:a fuzzy approach[J], European Journal of Operational Research,2002,139(2):178-189.
64. Tiryaki F, Ahlatcioglu M. Fuzzy stock selection using a new fuzzy ranking and weighting algorithm[J], Applied Mathematics and Computation,2005,170(1):144-157.
65. YAN Yan-mei, WANG Dabuxilatu. A note on portfolio selection based on weighted possibilistic mean and variance[J], Journal of Guangzhou University(Natural Science Edition),2007,6(4):15-18.
66. Song Q, Chissom BS. Forecasting enrollments with fuzzy time series--Part Ⅰ[J]. Fuzzy Sets and system,1993,54(1):1-9.
67. Song Q, Chissom BS. Forecasting enrollments with fuzzy time series--Part Ⅱ[J]. Fuzzy Sets and system,1994,62(1):1-8.
68. Chen S M. Forecasting enrollments based on fuzzy time-series[J], Fuzzy Sets and Systems, 1996,81(3):311-319.
69. Chen S M. Forecasting enrollments based on high-order fuzzy time series[J], Cybernetics and Systems,2002,33(1):1-16.
70. Chen S M, Hsu C C. A new method to forecast enrollments using fuzzy time series[J], Applied Science and Eng,2004,2(3):234-244.
71. Chen S M, Chung N Y. Forecasting enrollments using high-order fuzzy time series and genetic algorithms[J], International Journal of Intelligent Systems,2006,21(4):485-501.
72. Chen S M. Temperature Prediction Using Fuzzy Time-series[J], IEEE Trans CYBERNETICS, 2000,30:263-275.
73. Huarng K. Heuristic models of fuzzy time series for forecasting[J]. Fuzzy Sets and System, 2001,123(3):369-386.
74. Huarng K. Effective lengths of intervals to improve forecasting in fuzzy time series[J] Fuzzy Sets and Systems,2001,123(2):155-162.
75. Huarng K, Yu H K. An N-th order heuristic fuzzy time series model for TAIEX forecasting[J], International Journal of Fuzzy Systems,2003,5(4):247-253.
76. Huarng K, Yu H K. A type-2 fuzzy time-series model for stock index forecasting[J], Physica A, 2005,353(4):445-462.
77. Huarng K, Yu T H K. The application of neural networks to forecast fuzzy time series[J], Physica A,2006,336(4):481-491.
78. Yu H K.Weighted fuzzy time-series models for TAIEX forecasting[J], Physica A, 2005,349(6):609-624.
79. Yu H K. A refined fuzzy time-series model for forecasting[J], Physica A,2005,346(6): 657-681.
80. Cheng C H, Chen T L and Chiang C H. Trend-Weighted Fuzzy Time-Series Model for TAIEX Forecasting[J], Lecture Notes in Computer Science,2006,4234(4):469-477.
81. Chen T L, Cheng C H and Hia J T. Fuzzy Time-series Based on Fibonacci Sequence for Stock Price Forecasting[J], Physica A,2007,380(7):377-390.
82. Cheng C H, Chen T L, Teoh H J and Chiang C H. Fuzzy time-series based on adaptive expectation model for TAIEX forecasting[J], Expert Systems with Applications,2008, 34(2):1126-1132.
83. Sun, Li. Average-Based Fuzzy time series models for forecasting Shanghai Compound Index[J], International Journal of Applied Science and Engineering,2005,3(2):234-244.
84. Tsai Chaochih, Wu Shunjy. A study for second-order modeling of fuzzy time series[C].1999 IEEE International Fuzzy Systems conference proceedings. Seoul, Korea, August 22-25,199,219-725.
85. Ozawa K Niimura T. Fuzzy time series of electric power consumption[C]. Proceedings of the 1999 IEEE Canadian Conference electrical and computer engineering. Shaw Conference center, Edmonton, Alberta, Canada,1999.1195-1198.
86.郑文瑞,张国良.模糊时间序列分析方法在铜资源消费预测中的应用[J],世界地质,1999,18(3)：88-91.
87. Chen T L, Cheng C H, Teoh H J. High order fuzzy time-series based on multi-period model for forecasting stock markets[J]. Physica A,2007, doi:10.1016/j.physa.2007.10.004.
88.宋明军.基于模糊时间序列的时变动态系统模糊建模[J],现代防御技术,2003,31(5)：2842.
89.吴铭峰,蒋勋.基于模糊时间序列的预测模型—以上阵指数为例[J],无锡南洋学院学报,2008,7(3)：57-63.
90.何云峰,杨燕.基于模糊时间序列—股票走势的建模与应用[J],微计算机信息,2006,22(11)：253-255.
91. Tanaka H, Uejima S, Asai K. Linear Regression Analysis with Fuzzy Model[J], IEEE Trans.Systems Man Cybernet,1982,12:903-907.
92. Heshmaty B, Kandel A. Fuzzy linear Regression and Its Applications to Forecasting in Uncertain Environment[J], Fuzzy Sets and Systems,1985,15(2):159-191.
93. Yang M S, Liu H H. Fuzzy Least-squares Algorithms for Interactive Fuzzy Linear Regression Models[J], Fuzzy Sets and Systems,2003,135(2):305-316.
94. Nasrabadi M M, Nasrabadi E. A Mathematical-programming Approach to Fuzzy Linear Regression Analysis[J], Applied Mathematics and Computation,2004,155(3):873-881.
95. Hong D H, Hwang C, Ahn C.Ridge Estimation for Regression Models with Crisp Inputs and Gaussian Fuzzy Output[J], Fuzzy Sets and Systems,2004,142(2):307-319.
96. Chang P T. Fuzzy Seasonality Forecasting[J], Fuzzy Sets and Systems,1997,90 (1):1-10.
97. Chen T, Wang M J J. Forecasting Methods Using Fuzzy Concepts[J], Fuzzy Sets and Systems, 1997,105(3):339-352.
98. Fang Mei Tseng, Gwo Hshiung Tzeng. A fuzzy seasonal ARIMA model for forecasting[J], Fuzzy Sets and Systems,2002,126(3):267-376.
99.石岩,胡昌振,马宝华,谭惠民.模糊时间序列的最优预测方法[J],探测与控制学报,1999,21(3)：53-56.
100.哈明虎,王丽敏,胡运权.一种新的模糊时间序列预测模型[J],预测,2000,(3)：63-65.
101.吴今培.模糊时间序列建模及应用[J],系统工程,2002,20(4)：72-76.
102.常娜娜,石永全,苏莉.模糊时间序列预测在动态经济系统预测中的应用[J],山东科技大学学报(自然科学版),2007,26(5)：72-74.
103. Tsaur R C, Wang H F, Yang J. Fuzzy Regression for Seasonal Time Series Analysis[J], International Journal of Information Technology and Decision Making,2002,1(1):165-175.
104.游仕洪,程浩忠,谢宏.应用模糊线性回归模型预测中长期电力负荷[J],电力自动化设备,2006,26(3)：51-53.
104.李竹渝,刘威仪,王泰积.金融资产收益率的模糊双线性回归[J],统计研究,2009,26(2)：68-73.
105.刘金禄.水库水温结构划分的模糊回归预测模型及其应用[J],水资源与水工程学报,2004,15(3)：56-58.
106.张喆.股票价格的模糊预测方法[J],现代经济信息,2008,(10)：32-34.
107.张文修.模糊数学基础[M],西安：西安交通大学出版社,1989.
108. Dubois D, Prade H. Fuzzy Sets and Systems: Theory and Applications[M], New York: Academic Press,1980.
109. Carlsson C, Fuller R. On possibilistic mean value and variance of fuzzy numbers[J], Fuzzy Sets and Systems,2001,122(2):315-326.
110. Alefeld G, Herzberger J. Introduction to Interval Computations[M], New York: Academic Press,1983.
111. Hansen E. Global Optimization Using Interval Analysis[M], New York: Marcel Dekker, 1992.
112.杨纶标,高英仪.模糊数学原理及应用[M],广州：华南理工大学出版社,2003,203-207.
113.胡宝清.模糊理论基础[M],武汉：武汉大学出版社,2006,340-375.
114. Markowitz H M. Portfolio selection[J], Journal of Finance,1952,7(3):77-91.
115. Sharpe W. Capital asset price: a theory of market equilibrium under conditions of risk[J], The Journal of Finance,1964,19(1):425-442.
116. Sharpe W. A simplified model for portfolio analysis[J], Management Science,1963,9(2): 277-293.
117. Sharpe W, Alexander G F, Bailey J V. Investments[M], London: Prentice Hall,1995.
118. Mao J. Models of capital budgeting, E-V vs E-S[J], Journal of Financial and Quantitative Analysis,1970,5(5):657-675.
119. Swalm R O. Utility theory-insights into risk taking[J], Harvard Business Review,1966,44(1): 123-136.
120.攀登,吴冲锋.用遗传算法直接搜索证券组合投资的有效边界[J],系统工程学报,2002,17(4)：364-367.
121. Faff R W, Brooks R D, Ho Y K. New evidence on the impact of financial leverage on beta risk:a time-series approach[J], North American Journal of Economics and Finance,2002, 13(1):1-20.
122. Yu H K. Weighted fuzzy times-series models for TAIEX forecasting[J], Physica A: Statistical and Theoretical Physics,2004,349(3-4):609-624.
123. Leon Lee C h, Liu A, Chen W S. Pattern discovery of fuzzy time series for financial prediction[J], IEEE Trans Knowledge. Date Eng,2006,18(5):613-625.
124. Huarng K, Yu H. A type-2 fuzzy time-series model for stock index forecasting[J], Physica A: Statistical and Theoretical Physics,2005,353(1):445-462.
125. Speranza M G. Linear programming models for decision analysis[J], Management Science, 1993,14(1):107-123.
126. Rommelfanger H, Hanuschek R, Wolf J. Linear programming with fuzzy objective[J], Fuzzy Sets and Systems,1989,29(1):31-48.
127. Zimmermann H J. Fuzzy Sets Theory and Its Applications[M], Dordrecht: Kluwer Academic Publshers,1991.
128. Yu P L. A class of solutions for group decisions problems[J], Management Science,1973, 19(8):936-946.
129. Zeleny M. Compromise programming[C]//Cochrane J L, Zeleny M. Multiple Criteria Decision Making, Columbia, South Carolina: University of South Carolina Press,1973: 262-301.
130. Arenas M P, Bilbao A T, Perez B G, Rodriguez M V. Solving a multiobjective possibilistic problem through compromise programming[J], European Journal of Operational Research, 2005,164(3):748-759.
131. Amelia Bilbao-Terol, Perez B P, Arenas M P, Rodri guez M V. Fuzzy compromise programming for portfolio selection[J], Applied Mathematics and Computation,2006,173 (1):251-264.
132. Bilbao A T, Perez B G, Antomil J. Selecting the optimum portfolio using fuzzy compromise programming and Sharpe's-index model[J], Applied Mathematics and Computation,2006, 182(1):644-664.
133. Jimenez M. Ranking fuzzy numbers through the comparison of their expected intervals. International Journal of Uncertainty [J], Fuzziness and knowledge-Based Systems,1996, 4(4):379-388.
134. Arenas M P, Bilbao A T, Rodriguez M V. Solving the multiobjective possibilistic linear programming problem[J], European Journal of Operational Research,1999,117(1): 175-182.
135. Watada J. Fuzzy Portfolio model for decision making in investment, in Yoshida, Y(eds.), Dynamical Aspects in Fuzzy Decision Making[M], Heidelberg: Physica-Verlag,2001,141-162.
136. Chen Shyi-Ming. Forecasting enrollments based on fuzzy time series[J], Fuzzy Sets and Systems,1996,81(3):311-319.
137. Chen Tai-Liang, Cheng Ching-Hsue, Teoh Hia-Jong. High order fuzzy time-series based on multi-period model for forecasting stock markets[J], Physica A,2007, doi:10.1016/j.physa.2007.10.004.
138. Mossin J. Optimal multi-period portfolio policies[J], Journal of Business,1968,41(4): 215-229.
139. Samuelson P A. Lifetime portfolio selection by dynamic stochastic programming[J], The Review of Economics and Statistics,1969,51(3):239-246.
140. Hakansson N H. Multi-period mean-variance analysis:toward a general theory of portfolio choice[J], Journal of Finance,1971,26(4):857-884.
141. Grauer R R, Hakansson N H. On the use of mean-variance and quadratic approximations in implementing dynamic investment strategies: a comparison of returns and investment policies[J], Management Science,1993,39(7):856-871.
142. Li D, Ng W K. Optimal dynamic portfolio selection: multi-period mean-variance formulation[J], Mathematical Finance,2000,10(3):387-406.
143. Wei Yan, Rong Miao, Shurong Li. Multi-period semi-variance portfolio selection: Model and numerical solution[J], Applied Mathematics and Computation,2007,194(1):128-134.
144. Shu-zhi Wei, Zhong-xing Ye. Multi-period optimization portfolio with bankruptcy control in stochastic market[J], Applied Mathematics and Computation,2007,186(3):414-425.
145. Dimitris Bertsimas, Dessislava Pachamanova. Robust Multi-period portfolio management in the presence of transaction costs[J], Computers & Operations Research,2008,35(1):3-17.
146.宿洁,刘家壮.多阶段资产投资的动态规划决策模型[J],中国管理科学,2001,9(3)：55-61.
147. Yang Miin-Shen, Liu Hsien-Hsiung. Fuzzy Least-squares Algorithms for Interactive Fuzzy Linear Regression Models[J], Fuzzy Set and Systems,2003,135(2):305-316.
148. Kim Byungjoon, Ram Bishu R. Evaluation of Fuzzy Linear Regression Models by Comparison Membership Function[J], Fuzzy Sets and Systems,1998,100(3):343-352.
149. Kennedy J, Eberhart R C. Particle swarm optimization[C], In: Proceedings of IEEE Conference on Neural Network, IV, Poscataway, NJ,1995,1942-1948.
150. Krohling R A. Gaussian Swarm: A Novel Particle Swarm Optimization Algorithm[C], In: Proceedings of the 2004 IEEE Conference on Cybernetics and Intelligent Systems, Singapore,2004,1-3.
151. Angeline P J. Evolutionary optimization versus particle swarm optimization:philosophy and performance differences [C], Proceedings of the 7th Annual Conference on Evolutionary Programming.1998,601-610.
152.高尚,杨静宇.群智能算法及其应用[M],北京：中国水利水电出版社,2006,85-89.
153. Tseng Fang-Mei, Tzeng Gwo-Hshiung, Yu Hsiao-Cheng, Yuan Benjamin J C. Fuzzy ARIMA model for forecasting the foreign exchange market[J], Fuzzy Sets and Systems, 2001,118(1):9-19.
154. Ishibuchi H, Tanaka H. Interval regression analysis based on mixed 0-1 integer programming problem [J], J. Japan Soc. Ind. Eng,1998,40(5):312-319.
155. Tanaka H, Hayashi I, Watada J. Possibilistic linear Regression Analysis for Fuzzy Data[J], European Journal of Operational Research,1989,40(l):389-396.
156.刘宝碇,赵瑞清,王纲.不确定规划及应用[M],北京：清华大学出版社,2003：84-87.
157. Saaty T L. The Analytic Hierarchy Process[M], McGraw-Hill, New York,1980.
158. Saaty T L. Rogers P C, Bell B. Portfolio selection through hierarchies[J], The Journal of Portfolio Management,1980,6(3):16-21.
159. Chen M.-F., Tzeng G.-H., Ding C.G.. Combining fuzzy AHP with MDS in identifying the preference similarity of alternatives[J], Applied Soft Computing,2008,8(1):110-117.
160. Fatma Tiryaki, Beyza Ahlatcioglu. Fuzzy portfolio selection using fuzzy analytic hierarchy process[J], Inform.Sci.(2008), doi:10.1016/j.ins.2008.07.023.
161. Enea M., Piazza T. Project selection by constrained fuzzy AHP[J], Fuzzy Optimization and Decision Making,2004,3 (1):39-62.
162. Dupacov aJ, Consigli G, Wallace S W. Scenarios for multistage stochastic programs[J], Annals of Operations Research,2000,29(100):25-33.
163. Hoyland K, Wallace S W. Generating scenario trees for multistage decision problem[J], Management science,2001,47(2):295-307.
164. Klaassen P. Comment on "Generating Scenario Trees for Multistage Decision Problems" [J], Management Science,2002,48(11):1512-1516.
165. Gulplnar N, Rustem B, Settergren R.Simulation and optimization approaches to scenario tree generation[J], Journal of Economic Dynamics & Control,2004,28(7):1291-1315.
166.金秀,黄小原.资产负债管理模型及在辽宁养老金问题中的应用[J],系统工程理论与实践,2005,25(9)：42-48.
167.金秀,李冰冰,黄小原.多阶段金融资产配置情景生成与实证研究[J],系统工程理论与实践,2008,1(1)：78-83.
168.宋光兴,杨德礼.模糊判断矩阵的一致性检验及一致性改进方法[J].系统工程,2003,21(1)：110-116.
169.张吉军.模糊层次分析法(FAHP) [J],模糊系统与数学,2000,14(2)：80-88.
170. Chang D.-Y. Applications of the extent analysis method on fuzzy AHP[J], European Journal of Operational Research,1996,95(3):649-655.
171. Lai. L J, Huang C L. Fuzzy Mathematical Programming[M], Berlin: Springer-Verlag,1992.
172. Chen T.-L, Cheng C.-H, Teoh H.-J. High order fuzzy time-series based on multi-period adaptation model for forecasting stock markets[J], Physica A (2007), dot:10.1016/j.physa.2007.10.004.
173.刘宝碇,赵瑞清,王纲.不确定规划及应用[M],北京：清华大学出版社,2003.
174.刘宝碇,彭锦.不确定理论教程[M],北京：清华大学出版社,2005.
175.郝燕玲,徐耀群,罗跃生,沈继红.最优化方法[M],哈尔滨：哈尔滨工业大学出版社, 2001.
176.刘宝碇,赵瑞清.随机规划与模糊规划[M],北京：清华大学出版社,1998.
177.方述城,汪定伟.模糊数学与模糊优化[M],北京：科学出版社,1997.
178.余湄,董洪斌,汪寿阳.摩擦市场下的投资组合与无套利分析[M],北京：科学出版社,2005.
179.姚远.投资组合保险及策略研究[M],北京：中国经济出版社,2007.
2. Bellman R, Zadeh L A. Decision making in a fuzzy environment[J], Management Science,1970,17 (4):141-164.
3. Ramaseamy S. Portfolio selection using fuzzy decision theory[R], Working Paper, Bank for International Settlements,1998,59.
4. Leon T, Liern V and Vercher E. Viability of infeasible portfolio selection problems: a fuzzy approach[J], European Journal of Operational Research,2002,139 (4):178-189.
5. Watada J. Fuzzy portfolio model for decision making in investment [M], Heidelberg: Physica-Verlag,2001,141-162.
6. Lai K K, Fang Y and Wang S Y. Portfolio rebalancing model with transaction costs based on fuzzy decision theory[J], European Journal of Operational Research,2006,175(2):879-893.
7.庄新田,黄小原,卢新.证券组合的模糊优化[J],东北大学学报(自然科学版),2001,22(2)：165-168.
8.曾建华,汪寿阳.一个基于模糊决策理论的投资组合模型[J],系统工程理论与实践,2003,16(1)：99-104
9.庄新路,庄新田,黄小原.基于VAR风险指标的投资组合模糊优化[J],数学的实践与认识,2003,33(3)：3540.
10.黄小原,赵光华,庄新田.企业投融资组合饿模糊模型与优化[J],控制与决策,2004,19(7)：756-763.
11.肖冬荣,黄静.基于均值、方差和偏度的投资组合模糊优化模型[J],统计与决策,2006,(14)：3940.
12.姚天祥,刘思峰.基于预测收益率的模糊投资组合优化模型[J],统计与决策,2007,(19)：47-48.
13. Watada J. Fuzzy portfolio selection and its applications to decision making[M], Tatra Mountains:Mathematical Publication,1997,219-248.
14. Yang Fang, K.K.Lai and Shou-Yang Wang. Portfolio rebalancing model with transaction costs based on fuzzy decision theory[J], European Journal of Operational Research,2006,175(2): 879-893.
15. Huang Xiaoxia. Portfolio selection with fuzzy returns[J], Journal of Intelligent & Fuzzy Systems,2007,18 (4):383-390.
16.吕昌会,何湘藩,黄德斌,严碧清.证券投资决策的模糊多目标规划方法[J],系统工程理论方法应用,1998,7(2)：14-18.
17.郭存芝,郑垂勇.一种证券组合投资的模糊多目标规划方法[J],系统工程理论与实践,2001,(1)：21-30.
18.徐维军,徐寅峰,王迅,张卫国.收益率为模糊数的加权证券组合选择模型[J],系统工程学报,2005,20(1)：6-11.
19.李建新,胡刚.风险厌恶型的证券投资数学模型[J],数量经济技术经济研究,2005,22(3)：97-106.
20.陈国华,陈收,房勇,汪寿阳.基于模糊收益率的组合投资模型[J],经济数学,2006,23(1)：19-25.
21.李建新,胡刚.基于模糊数分析的时机捕捉型的证券投资模型[J],模糊系统与数学,2006,20(4)：141-150.
22.程巧华,张博侃.模糊数在投资组合中的应用[J],苏州科技学院学报(自然科学版),2006,23(3)：21-26.
23.何树红,乐晓梅,毛娟芳.带交易费用的证券组合投资的模糊多目标优化模型[J],云南民族大学学报(自然科学版),2007,16(1)：25-28.
24.岳伟,贺兴时,刘宣会.模糊数在证券投资组合选择模型中的运用[J],统计与决策,2007,(8)：125-127.
25.王庆,李政.证券市场的模糊投资组合模型[J],江苏工业学院学报,2007,8(3)：48-50.
26.严维真,宁玉富,郭长友.具有模糊收益率的贷款组合优化决策[J],系统工程学报,2008,23(2)：168-173.
27. Bitran G R. Linear multiple objective problems with interval coefficients[J], Management Science,1980,26 (3):694-706.
28. Steuer R E. Algorithm for linear programming problems with interval objective function coefficients[J], Mathematics of Operational Research,1980,6(2):333-348.
29. Ishibuchi H, Tanaka H. Formulation and analysis of linear programming with interval coefficients [J], Journal of Japan Industrial Management Association,1989,40(3):320-329.
30. Ishibuchi H, Tanaka H. Multiobjective programming in optimization of the interval objective function[J], European Journal of Operational Research,1990,48 (2):219-225.
31. Nakahara Y, Sasaki M and Gen M. On the linear programming with interval coefficients [J], international Journal of Computers and Engineering,1992,23(2):301-304.
32. Chanas S, Kuchta D. Multiobjective programming in optimization of interval objective functions-a generalized approach[J], European Journal of Operational Research, 1996,94(4):594-598.
33. Tong S. Interval number and fuzzy number linear programming [J], Fuzzy Sets and Systems, 1994,66(3):301-306.
34.刘新旺,达庆利.一种区间数线性规划的满意解[J],系统工程学报,1999,14(2)：123-128.
35. Chinneck J W, Ramadan K. Linear programming with interval coefficients [J], Journal of the Operational Research Society,2000.51(2):209-220.
36. Lai K K, Wang S Y, Xu J P and Fang Y. A class of linear interval programming problems and Its applications to portfolio selection[J]. IEEE Transaction on Fuzzy Systems,2002, 10:698-704.
37.房勇,汪寿阳.模糊投资组合优化：理论与方法[M],北京：高等教育出版社,2005：73-108.
38. Arenas M P, Bilbao A T and Rodriguez M V. A fuzzy goal programming approach to portfolio selection[J]. European of Operational Research,2001,133 (2):287-297.
39. Liu Y K, Zhang W G and Wang Y L. On admissible efficient portfolio selection: Models and algorithms [J], Applied Mathematics and Computation,2006,176 (1):208-218.
40. Zhang W G, Nie Z K. On admissible efficient portfolio selection problem[J], Applied Mathematics and Computation,2004,159(2):357-371.
41. Zhang W G, Nie Z K. On admissible efficient portfolio selection policy [J], Applied Mathematics and Computation,2005,169(1):608-623.
42. Giove S, Funari S and Nardelli C. An interval portfolio selection problem based on regret function[J], European Journal of Operational Research,2006,170 (1):253-264.
43.路应金,唐小我,周宗放.证券组合投资的区间数线性规划方法[J],系统工程学报,2004,19(1)：33-37.
44.赵玉梅,陈华友.证券组合投资的多目标区间数线性规划模型[J],运筹与管理,2006, 15(2)：124-127.
45.陈国华,陈收,汪寿阳.区间数模糊投资组合模型[J],系统工程,2007,25(8)：34-37.
46. Zadeh L A. Fuzzy sets as a basis for a theory of possibility[J], Fuzzy Sets and Systems, 1978,1(1):3-28.
47. Tanaka H, Guo P and Turksen I B. Portfolio selection based on fuzzy probabilities and possibility distributions[J], Fuzzy Sets and Systems,2000,111 (3):387-397.
48. Tanaka H, Guo P. Portfolio selection based on upper and lower exponential possibility distributions [J], European Journal of Operational Research,1999,114(2):115-126.
49. Inuiguchi M, Ramik J. Possibilistic linear programming: A brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem [J]. Fuzzy Sets and Systems,2000,111 (1):3-28.
50. Inuiguchi M, Tanina T. Portfolio selection under independent possibilistic information[J], Fuzzy Sets and Systems,2000,115(1):83-92.
51. Carlsson C, Fuller R and Majlender P. A possibilistic approach to selecting portfolio with highest utility score[J], Fuzzy Sets and Systems,2002,131 (1):13-21.
52.洪雁,邵全,吴祈宗.模糊机会约束规划下的投资组合模型研究[J],数量经济技术经济研究,2005,(9)：112-118.
53.乔峰,黄培清,顾锋.可能性投资组合模型[J],上海交通大学学报,2005,39(10)：1606-1610.
54. Chen Y J, Liu Y K. Portfolio selection in fuzzy environment[C], In Proceedings of the Fourth International Conference on Machine Learning and Cybernetics, Guangzhou,2005, 2694-2699.
55. Henry M, Mok K, Peng J and Tse W M. Credibility programming approach to fuzzy portfolio selection problems [C], In Proceedings of the Fourth International Conference on Machine Learning and Cybernetics, Guangzhou,2005,2523-2528.
56. Wang Y Q, Tang W S. Research on intelligent algorithm for portfolio selection with credibility criterion[C], Proceedings of the Fourth International Conference on Machine Learning and Cybernetics, Guangzhou,2005,3517-3522.
57. Zhang J P, Li S M. Portfolio selection with quadratic utility under fuzzy environment[C], Proceedings of the Fourth International Conference on Machine Learning and Cybernetics, Guangzhou,2005,2529-2533.
58. Zhang W G, Zhang Q M and Nie Z K. A class of fuzzy portfolio selection problems[C], Proceedings of the Second International Conferenece on Machine Learing and Cybernetics, 2003,2654-2658.
59. Huang J J, Tzeng G H and Ong C S. A novel algorithm for uncertain portfolio selection[J], Applied Mathematics and Computation,2006,173(1):350-359.
60. Ong C S, Huang J J and Tzeng G H. A novel hybrid model for portfolio selection[J], Applied Mathematics and Computation,2005,169 (2):1195-1210.
61. Ammar E, Khalifa H A. Fuzzy portfolio optimization a quadratic programming approach[J], Chaos, Solitons and Fractals,2003,18(5):1045-1054.
62. Ida M. Solutions for the portfolio selection problem with interval and fuzzy coefficients[J], Reliable Computering,2004,10(3):389-400.
63. Leon T, Liern V and Vercher E. Viability of infeasible portfolio selection problems:a fuzzy approach[J], European Journal of Operational Research,2002,139(2):178-189.
64. Tiryaki F, Ahlatcioglu M. Fuzzy stock selection using a new fuzzy ranking and weighting algorithm[J], Applied Mathematics and Computation,2005,170(1):144-157.
65. YAN Yan-mei, WANG Dabuxilatu. A note on portfolio selection based on weighted possibilistic mean and variance[J], Journal of Guangzhou University(Natural Science Edition),2007,6(4):15-18.
66. Song Q, Chissom BS. Forecasting enrollments with fuzzy time series--Part Ⅰ[J]. Fuzzy Sets and system,1993,54(1):1-9.
67. Song Q, Chissom BS. Forecasting enrollments with fuzzy time series--Part Ⅱ[J]. Fuzzy Sets and system,1994,62(1):1-8.
68. Chen S M. Forecasting enrollments based on fuzzy time-series[J], Fuzzy Sets and Systems, 1996,81(3):311-319.
69. Chen S M. Forecasting enrollments based on high-order fuzzy time series[J], Cybernetics and Systems,2002,33(1):1-16.
70. Chen S M, Hsu C C. A new method to forecast enrollments using fuzzy time series[J], Applied Science and Eng,2004,2(3):234-244.
71. Chen S M, Chung N Y. Forecasting enrollments using high-order fuzzy time series and genetic algorithms[J], International Journal of Intelligent Systems,2006,21(4):485-501.
72. Chen S M. Temperature Prediction Using Fuzzy Time-series[J], IEEE Trans CYBERNETICS, 2000,30:263-275.
73. Huarng K. Heuristic models of fuzzy time series for forecasting[J]. Fuzzy Sets and System, 2001,123(3):369-386.
74. Huarng K. Effective lengths of intervals to improve forecasting in fuzzy time series[J] Fuzzy Sets and Systems,2001,123(2):155-162.
75. Huarng K, Yu H K. An N-th order heuristic fuzzy time series model for TAIEX forecasting[J], International Journal of Fuzzy Systems,2003,5(4):247-253.
76. Huarng K, Yu H K. A type-2 fuzzy time-series model for stock index forecasting[J], Physica A, 2005,353(4):445-462.
77. Huarng K, Yu T H K. The application of neural networks to forecast fuzzy time series[J], Physica A,2006,336(4):481-491.
78. Yu H K.Weighted fuzzy time-series models for TAIEX forecasting[J], Physica A, 2005,349(6):609-624.
79. Yu H K. A refined fuzzy time-series model for forecasting[J], Physica A,2005,346(6): 657-681.
80. Cheng C H, Chen T L and Chiang C H. Trend-Weighted Fuzzy Time-Series Model for TAIEX Forecasting[J], Lecture Notes in Computer Science,2006,4234(4):469-477.
81. Chen T L, Cheng C H and Hia J T. Fuzzy Time-series Based on Fibonacci Sequence for Stock Price Forecasting[J], Physica A,2007,380(7):377-390.
82. Cheng C H, Chen T L, Teoh H J and Chiang C H. Fuzzy time-series based on adaptive expectation model for TAIEX forecasting[J], Expert Systems with Applications,2008, 34(2):1126-1132.
83. Sun, Li. Average-Based Fuzzy time series models for forecasting Shanghai Compound Index[J], International Journal of Applied Science and Engineering,2005,3(2):234-244.
84. Tsai Chaochih, Wu Shunjy. A study for second-order modeling of fuzzy time series[C].1999 IEEE International Fuzzy Systems conference proceedings. Seoul, Korea, August 22-25,199,219-725.
85. Ozawa K Niimura T. Fuzzy time series of electric power consumption[C]. Proceedings of the 1999 IEEE Canadian Conference electrical and computer engineering. Shaw Conference center, Edmonton, Alberta, Canada,1999.1195-1198.
86.郑文瑞,张国良.模糊时间序列分析方法在铜资源消费预测中的应用[J],世界地质,1999,18(3)：88-91.
87. Chen T L, Cheng C H, Teoh H J. High order fuzzy time-series based on multi-period model for forecasting stock markets[J]. Physica A,2007, doi:10.1016/j.physa.2007.10.004.
88.宋明军.基于模糊时间序列的时变动态系统模糊建模[J],现代防御技术,2003,31(5)：2842.
89.吴铭峰,蒋勋.基于模糊时间序列的预测模型—以上阵指数为例[J],无锡南洋学院学报,2008,7(3)：57-63.
90.何云峰,杨燕.基于模糊时间序列—股票走势的建模与应用[J],微计算机信息,2006,22(11)：253-255.
91. Tanaka H, Uejima S, Asai K. Linear Regression Analysis with Fuzzy Model[J], IEEE Trans.Systems Man Cybernet,1982,12:903-907.
92. Heshmaty B, Kandel A. Fuzzy linear Regression and Its Applications to Forecasting in Uncertain Environment[J], Fuzzy Sets and Systems,1985,15(2):159-191.
93. Yang M S, Liu H H. Fuzzy Least-squares Algorithms for Interactive Fuzzy Linear Regression Models[J], Fuzzy Sets and Systems,2003,135(2):305-316.
94. Nasrabadi M M, Nasrabadi E. A Mathematical-programming Approach to Fuzzy Linear Regression Analysis[J], Applied Mathematics and Computation,2004,155(3):873-881.
95. Hong D H, Hwang C, Ahn C.Ridge Estimation for Regression Models with Crisp Inputs and Gaussian Fuzzy Output[J], Fuzzy Sets and Systems,2004,142(2):307-319.
96. Chang P T. Fuzzy Seasonality Forecasting[J], Fuzzy Sets and Systems,1997,90 (1):1-10.
97. Chen T, Wang M J J. Forecasting Methods Using Fuzzy Concepts[J], Fuzzy Sets and Systems, 1997,105(3):339-352.
98. Fang Mei Tseng, Gwo Hshiung Tzeng. A fuzzy seasonal ARIMA model for forecasting[J], Fuzzy Sets and Systems,2002,126(3):267-376.
99.石岩,胡昌振,马宝华,谭惠民.模糊时间序列的最优预测方法[J],探测与控制学报,1999,21(3)：53-56.
100.哈明虎,王丽敏,胡运权.一种新的模糊时间序列预测模型[J],预测,2000,(3)：63-65.
101.吴今培.模糊时间序列建模及应用[J],系统工程,2002,20(4)：72-76.
102.常娜娜,石永全,苏莉.模糊时间序列预测在动态经济系统预测中的应用[J],山东科技大学学报(自然科学版),2007,26(5)：72-74.
103. Tsaur R C, Wang H F, Yang J. Fuzzy Regression for Seasonal Time Series Analysis[J], International Journal of Information Technology and Decision Making,2002,1(1):165-175.
104.游仕洪,程浩忠,谢宏.应用模糊线性回归模型预测中长期电力负荷[J],电力自动化设备,2006,26(3)：51-53.
104.李竹渝,刘威仪,王泰积.金融资产收益率的模糊双线性回归[J],统计研究,2009,26(2)：68-73.
105.刘金禄.水库水温结构划分的模糊回归预测模型及其应用[J],水资源与水工程学报,2004,15(3)：56-58.
106.张喆.股票价格的模糊预测方法[J],现代经济信息,2008,(10)：32-34.
107.张文修.模糊数学基础[M],西安：西安交通大学出版社,1989.
108. Dubois D, Prade H. Fuzzy Sets and Systems: Theory and Applications[M], New York: Academic Press,1980.
109. Carlsson C, Fuller R. On possibilistic mean value and variance of fuzzy numbers[J], Fuzzy Sets and Systems,2001,122(2):315-326.
110. Alefeld G, Herzberger J. Introduction to Interval Computations[M], New York: Academic Press,1983.
111. Hansen E. Global Optimization Using Interval Analysis[M], New York: Marcel Dekker, 1992.
112.杨纶标,高英仪.模糊数学原理及应用[M],广州：华南理工大学出版社,2003,203-207.
113.胡宝清.模糊理论基础[M],武汉：武汉大学出版社,2006,340-375.
114. Markowitz H M. Portfolio selection[J], Journal of Finance,1952,7(3):77-91.
115. Sharpe W. Capital asset price: a theory of market equilibrium under conditions of risk[J], The Journal of Finance,1964,19(1):425-442.
116. Sharpe W. A simplified model for portfolio analysis[J], Management Science,1963,9(2): 277-293.
117. Sharpe W, Alexander G F, Bailey J V. Investments[M], London: Prentice Hall,1995.
118. Mao J. Models of capital budgeting, E-V vs E-S[J], Journal of Financial and Quantitative Analysis,1970,5(5):657-675.
119. Swalm R O. Utility theory-insights into risk taking[J], Harvard Business Review,1966,44(1): 123-136.
120.攀登,吴冲锋.用遗传算法直接搜索证券组合投资的有效边界[J],系统工程学报,2002,17(4)：364-367.
121. Faff R W, Brooks R D, Ho Y K. New evidence on the impact of financial leverage on beta risk:a time-series approach[J], North American Journal of Economics and Finance,2002, 13(1):1-20.
122. Yu H K. Weighted fuzzy times-series models for TAIEX forecasting[J], Physica A: Statistical and Theoretical Physics,2004,349(3-4):609-624.
123. Leon Lee C h, Liu A, Chen W S. Pattern discovery of fuzzy time series for financial prediction[J], IEEE Trans Knowledge. Date Eng,2006,18(5):613-625.
124. Huarng K, Yu H. A type-2 fuzzy time-series model for stock index forecasting[J], Physica A: Statistical and Theoretical Physics,2005,353(1):445-462.
125. Speranza M G. Linear programming models for decision analysis[J], Management Science, 1993,14(1):107-123.
126. Rommelfanger H, Hanuschek R, Wolf J. Linear programming with fuzzy objective[J], Fuzzy Sets and Systems,1989,29(1):31-48.
127. Zimmermann H J. Fuzzy Sets Theory and Its Applications[M], Dordrecht: Kluwer Academic Publshers,1991.
128. Yu P L. A class of solutions for group decisions problems[J], Management Science,1973, 19(8):936-946.
129. Zeleny M. Compromise programming[C]//Cochrane J L, Zeleny M. Multiple Criteria Decision Making, Columbia, South Carolina: University of South Carolina Press,1973: 262-301.
130. Arenas M P, Bilbao A T, Perez B G, Rodriguez M V. Solving a multiobjective possibilistic problem through compromise programming[J], European Journal of Operational Research, 2005,164(3):748-759.
131. Amelia Bilbao-Terol, Perez B P, Arenas M P, Rodri guez M V. Fuzzy compromise programming for portfolio selection[J], Applied Mathematics and Computation,2006,173 (1):251-264.
132. Bilbao A T, Perez B G, Antomil J. Selecting the optimum portfolio using fuzzy compromise programming and Sharpe's-index model[J], Applied Mathematics and Computation,2006, 182(1):644-664.
133. Jimenez M. Ranking fuzzy numbers through the comparison of their expected intervals. International Journal of Uncertainty [J], Fuzziness and knowledge-Based Systems,1996, 4(4):379-388.
134. Arenas M P, Bilbao A T, Rodriguez M V. Solving the multiobjective possibilistic linear programming problem[J], European Journal of Operational Research,1999,117(1): 175-182.
135. Watada J. Fuzzy Portfolio model for decision making in investment, in Yoshida, Y(eds.), Dynamical Aspects in Fuzzy Decision Making[M], Heidelberg: Physica-Verlag,2001,141-162.
136. Chen Shyi-Ming. Forecasting enrollments based on fuzzy time series[J], Fuzzy Sets and Systems,1996,81(3):311-319.
137. Chen Tai-Liang, Cheng Ching-Hsue, Teoh Hia-Jong. High order fuzzy time-series based on multi-period model for forecasting stock markets[J], Physica A,2007, doi:10.1016/j.physa.2007.10.004.
138. Mossin J. Optimal multi-period portfolio policies[J], Journal of Business,1968,41(4): 215-229.
139. Samuelson P A. Lifetime portfolio selection by dynamic stochastic programming[J], The Review of Economics and Statistics,1969,51(3):239-246.
140. Hakansson N H. Multi-period mean-variance analysis:toward a general theory of portfolio choice[J], Journal of Finance,1971,26(4):857-884.
141. Grauer R R, Hakansson N H. On the use of mean-variance and quadratic approximations in implementing dynamic investment strategies: a comparison of returns and investment policies[J], Management Science,1993,39(7):856-871.
142. Li D, Ng W K. Optimal dynamic portfolio selection: multi-period mean-variance formulation[J], Mathematical Finance,2000,10(3):387-406.
143. Wei Yan, Rong Miao, Shurong Li. Multi-period semi-variance portfolio selection: Model and numerical solution[J], Applied Mathematics and Computation,2007,194(1):128-134.
144. Shu-zhi Wei, Zhong-xing Ye. Multi-period optimization portfolio with bankruptcy control in stochastic market[J], Applied Mathematics and Computation,2007,186(3):414-425.
145. Dimitris Bertsimas, Dessislava Pachamanova. Robust Multi-period portfolio management in the presence of transaction costs[J], Computers & Operations Research,2008,35(1):3-17.
146.宿洁,刘家壮.多阶段资产投资的动态规划决策模型[J],中国管理科学,2001,9(3)：55-61.
147. Yang Miin-Shen, Liu Hsien-Hsiung. Fuzzy Least-squares Algorithms for Interactive Fuzzy Linear Regression Models[J], Fuzzy Set and Systems,2003,135(2):305-316.
148. Kim Byungjoon, Ram Bishu R. Evaluation of Fuzzy Linear Regression Models by Comparison Membership Function[J], Fuzzy Sets and Systems,1998,100(3):343-352.
149. Kennedy J, Eberhart R C. Particle swarm optimization[C], In: Proceedings of IEEE Conference on Neural Network, IV, Poscataway, NJ,1995,1942-1948.
150. Krohling R A. Gaussian Swarm: A Novel Particle Swarm Optimization Algorithm[C], In: Proceedings of the 2004 IEEE Conference on Cybernetics and Intelligent Systems, Singapore,2004,1-3.
151. Angeline P J. Evolutionary optimization versus particle swarm optimization:philosophy and performance differences [C], Proceedings of the 7th Annual Conference on Evolutionary Programming.1998,601-610.
152.高尚,杨静宇.群智能算法及其应用[M],北京：中国水利水电出版社,2006,85-89.
153. Tseng Fang-Mei, Tzeng Gwo-Hshiung, Yu Hsiao-Cheng, Yuan Benjamin J C. Fuzzy ARIMA model for forecasting the foreign exchange market[J], Fuzzy Sets and Systems, 2001,118(1):9-19.
154. Ishibuchi H, Tanaka H. Interval regression analysis based on mixed 0-1 integer programming problem [J], J. Japan Soc. Ind. Eng,1998,40(5):312-319.
155. Tanaka H, Hayashi I, Watada J. Possibilistic linear Regression Analysis for Fuzzy Data[J], European Journal of Operational Research,1989,40(l):389-396.
156.刘宝碇,赵瑞清,王纲.不确定规划及应用[M],北京：清华大学出版社,2003：84-87.
157. Saaty T L. The Analytic Hierarchy Process[M], McGraw-Hill, New York,1980.
158. Saaty T L. Rogers P C, Bell B. Portfolio selection through hierarchies[J], The Journal of Portfolio Management,1980,6(3):16-21.
159. Chen M.-F., Tzeng G.-H., Ding C.G.. Combining fuzzy AHP with MDS in identifying the preference similarity of alternatives[J], Applied Soft Computing,2008,8(1):110-117.
160. Fatma Tiryaki, Beyza Ahlatcioglu. Fuzzy portfolio selection using fuzzy analytic hierarchy process[J], Inform.Sci.(2008), doi:10.1016/j.ins.2008.07.023.
161. Enea M., Piazza T. Project selection by constrained fuzzy AHP[J], Fuzzy Optimization and Decision Making,2004,3 (1):39-62.
162. Dupacov aJ, Consigli G, Wallace S W. Scenarios for multistage stochastic programs[J], Annals of Operations Research,2000,29(100):25-33.
163. Hoyland K, Wallace S W. Generating scenario trees for multistage decision problem[J], Management science,2001,47(2):295-307.
164. Klaassen P. Comment on "Generating Scenario Trees for Multistage Decision Problems" [J], Management Science,2002,48(11):1512-1516.
165. Gulplnar N, Rustem B, Settergren R.Simulation and optimization approaches to scenario tree generation[J], Journal of Economic Dynamics & Control,2004,28(7):1291-1315.
166.金秀,黄小原.资产负债管理模型及在辽宁养老金问题中的应用[J],系统工程理论与实践,2005,25(9)：42-48.
167.金秀,李冰冰,黄小原.多阶段金融资产配置情景生成与实证研究[J],系统工程理论与实践,2008,1(1)：78-83.
168.宋光兴,杨德礼.模糊判断矩阵的一致性检验及一致性改进方法[J].系统工程,2003,21(1)：110-116.
169.张吉军.模糊层次分析法(FAHP) [J],模糊系统与数学,2000,14(2)：80-88.
170. Chang D.-Y. Applications of the extent analysis method on fuzzy AHP[J], European Journal of Operational Research,1996,95(3):649-655.
171. Lai. L J, Huang C L. Fuzzy Mathematical Programming[M], Berlin: Springer-Verlag,1992.
172. Chen T.-L, Cheng C.-H, Teoh H.-J. High order fuzzy time-series based on multi-period adaptation model for forecasting stock markets[J], Physica A (2007), dot:10.1016/j.physa.2007.10.004.
173.刘宝碇,赵瑞清,王纲.不确定规划及应用[M],北京：清华大学出版社,2003.
174.刘宝碇,彭锦.不确定理论教程[M],北京：清华大学出版社,2005.
175.郝燕玲,徐耀群,罗跃生,沈继红.最优化方法[M],哈尔滨：哈尔滨工业大学出版社, 2001.
176.刘宝碇,赵瑞清.随机规划与模糊规划[M],北京：清华大学出版社,1998.
177.方述城,汪定伟.模糊数学与模糊优化[M],北京：科学出版社,1997.
178.余湄,董洪斌,汪寿阳.摩擦市场下的投资组合与无套利分析[M],北京：科学出版社,2005.
179.姚远.投资组合保险及策略研究[M],北京：中国经济出版社,2007.