基于集成算子的多属性决策与时间序列预测方法
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摘要
集成算子作为一种信息融合的工具，在决策分析、组合预测、军事运筹等领域都有着重要的应用。本文主要针对多属性群决策和非线性时间序列预测中存在的问题，结合集成算子理论，提出了相应的多属性决策和时间序列预测方法。论文的主要工作和创新如下：
（1）将Quasi-OWA算子推广到输入变量为连续区间数的情况，提出连续QOWA（C-QOWA）算子的概念，该算子将C-OWA、C-OWG、C-OWH和C-GOWA等算子都进行了拓展。其次，定义了C-QOWA算子的orness测度，证明该测度可以反映集成算子的乐观程度，并且证明了C-QOWA算子及其orness测度的相关性质。进而为了集成多个连续区间数，将C-QOWA算子进行推广，得到加权C-QOWA(WC-QOWA）算子、有序加权C-QOWA(OWC-QOWA）算子和组合C-QOWA(CC-QOWA）算子。针对决策信息为连续区间数的多属性群决策问题，提出一种基于CC-QOWA算子的多属性群决策方法。
（2）为了集成三角模糊数，定义了模糊Bonferroni平均(FBM）算子，讨论它的几种特殊情形。在此基础上，提出模糊加权Bonferroni平均（FWBM）算子和组合FWBM（C-FWBM）算子，同时研究它们的一些性质。针对决策信息以三角模糊数给出的决策问题，给出一种基于FWBM算子和C-FWBM算子的多属性群决策方法，该方法的优点是考虑到了决策属性之间的相互影响。实证分析的结果表明该方法是切实可行的。
（3）针对语言环境下的多属性决策，将Bonferroni平均算子推广到语言环境中，提出了二元语义Bonferroni平均（2TLBA）算子、加权2TLBA（W2TLBA）算子和组合W2TLBA（C-W2TLBA）算子的概念，研究它们的相关性质。给出一种语言环境下基于W2TLBA算子和C-W2TLBA算子的多属性群决策方法，并通过实证分析说明了该方法的有效性。
（4）针对具有非线性和不稳定性的时间序列，提出一种结合小波分解、基于OWA算子滑动平均离散差分方程预测模型（OWA-SDDEPM）和马尔可夫方法的动态预测模型。该模型利用小波多尺度分解将原时间序列分解到不同频率通道上，然后对分解出的低频近似小波系数利用OWA-SDDEPM进行预测，并利用马尔可夫方法对时间序列的高频细节小波系数进行预测，再将低频和高频的预测结果进行小波重构得到时间序列的实际预测值。利用此模型对WTI原油（周度）价格进行实证预测分析，分别预测WTI原油价格的整体变化趋势和周度实际原油价格。研究结果表明，此模型不但可以有效地预测时间序列的整体变化趋势，能从细节上对其进行有效的刻画，而且比其他基于小波的预测模型具有更高的预测精度。
上述研究成果不仅丰富了集成算子的理论内容，给出了相应多属性群决策与时间序列预测的新方法，而且为我们利用这些方法解决实际问题提供了充分的科学依据。
Aggregation operators as indispensable tools, which are used for informationfusion, have been disseminated throughout various fields including decision analysis,combination forecasting, military operations, and so on. In view of the existingproblems of multi-attribute group decision making and nonlinear time series forecast,we propose the correspongding solving methods, which are based on the aggregationoperators. The main work and innovations of the dissertation are summarized asfollows:
(1) We extend the Quasi-OWA operator to the case in which the input argumentis a continuous valued interval and present the continuous Quasi-OWA (C-QOWA)operator, which generalizes a wide range of continuous operators such as the C-OWAoperator, the C-OWH operator and the C-GOWA operator. Then an orness measure toreflect the optimistic degree of the C-QOWA operator is proposed. Moreover, somedesirable properties of the C-QOWA operator associated with its orness measure areinvestigated. In addition, we apply the C-QOWA operator to the aggregation ofmultiple interval arguments and obtain the weighted C-QOWA operator, the orderedweighted C-QOWA (OWC-QOWA) operator, the combined C-QOWA (CC-QOWA)operator. We present an approach to multi-attribute group decision making based onthe CC-QOWA operator, when the decision information are continuous valuesinterval.
(2) In order to aggregate triangular fuzzy numbers, the fuzzy Bonferroni mean(FBM) operator is developed and its some special cases are discussed. Based on this,the fuzzy weighted Bonferroni mean (FWBM) operator and combined fuzzy weightedBonferroni mean (C-FWBM) operator are proposed. Meanwhile, some desirableproperties of these operators are investigated. With respect to multi-criteria groupdecision making in which the decision making information is given by triangularfuzzy numbers, a new decision making method is proposed based on FWBM operatorand C-FWBM operator. The advantage of the proposed method is its capability tocapture the interrelationship between attributes. The results of an empirical analysisshow that the developed method is feasible.
(3) In view of multi-attribute decision making in linguistic environment, weextend the Bonferroni mean operators to the situation where the inputs are linguisticarguments and proposed2-tuple linguistic Bonferroni averaging (2TLBA) operator, weighted2TLBA (W2TLBA) operator and combined W2TLBA (C-W2TLBA)operator. Moreover, some desirable properties and special cases of these aggregationoperators are investigated. Then a decision-making approach is presented based onW2TLBA operator and C-W2TLBA operator. Meanwhile, a numerical experiment isgiven to prove the feasibility of the developed approach.
(4) In view of unstable and nonlinear time series, a dynamic forecasting model isproposed in this paper, which integrate wavelet decomposition, OWA operator basedSlip Discrete Difference Equation Prediction Model (OWA-SDDEPM) and Markovmethods. In this model, the original time series are decomposed into differentfrequency channels by multi-scale wavelet. Then we predict the wavelet coefficientsof the low-frequency approximation with the SDDEPM and predict the waveletcoefficients of high frequency details by Markov method, respectively. Therefore,forecasting value of the original time series is obtained by wavelet reconstruction ofthe low and high frequency foresting results. The model is applied to forecasting WTIweekly crude oil prices. The research result shows that the proposed forecastingmodel could not only forecast holistic fluctuation frequency of time series effectivelybut also characterize the details of the time series. The forecasting accuracy of thismodel is much higher than any other wavelet-based models.
The above research results not only enrich the content of aggregation operatortheory, develop the corresponding new methods for multi-attribute group decisionmaking and time series forecasting, and provide more sufficient scientific evidencefor applying these methods to solve practical problems.
（1）将Quasi-OWA算子推广到输入变量为连续区间数的情况，提出连续QOWA（C-QOWA）算子的概念，该算子将C-OWA、C-OWG、C-OWH和C-GOWA等算子都进行了拓展。其次，定义了C-QOWA算子的orness测度，证明该测度可以反映集成算子的乐观程度，并且证明了C-QOWA算子及其orness测度的相关性质。进而为了集成多个连续区间数，将C-QOWA算子进行推广，得到加权C-QOWA(WC-QOWA）算子、有序加权C-QOWA(OWC-QOWA）算子和组合C-QOWA(CC-QOWA）算子。针对决策信息为连续区间数的多属性群决策问题，提出一种基于CC-QOWA算子的多属性群决策方法。
（2）为了集成三角模糊数，定义了模糊Bonferroni平均(FBM）算子，讨论它的几种特殊情形。在此基础上，提出模糊加权Bonferroni平均（FWBM）算子和组合FWBM（C-FWBM）算子，同时研究它们的一些性质。针对决策信息以三角模糊数给出的决策问题，给出一种基于FWBM算子和C-FWBM算子的多属性群决策方法，该方法的优点是考虑到了决策属性之间的相互影响。实证分析的结果表明该方法是切实可行的。
（3）针对语言环境下的多属性决策，将Bonferroni平均算子推广到语言环境中，提出了二元语义Bonferroni平均（2TLBA）算子、加权2TLBA（W2TLBA）算子和组合W2TLBA（C-W2TLBA）算子的概念，研究它们的相关性质。给出一种语言环境下基于W2TLBA算子和C-W2TLBA算子的多属性群决策方法，并通过实证分析说明了该方法的有效性。
（4）针对具有非线性和不稳定性的时间序列，提出一种结合小波分解、基于OWA算子滑动平均离散差分方程预测模型（OWA-SDDEPM）和马尔可夫方法的动态预测模型。该模型利用小波多尺度分解将原时间序列分解到不同频率通道上，然后对分解出的低频近似小波系数利用OWA-SDDEPM进行预测，并利用马尔可夫方法对时间序列的高频细节小波系数进行预测，再将低频和高频的预测结果进行小波重构得到时间序列的实际预测值。利用此模型对WTI原油（周度）价格进行实证预测分析，分别预测WTI原油价格的整体变化趋势和周度实际原油价格。研究结果表明，此模型不但可以有效地预测时间序列的整体变化趋势，能从细节上对其进行有效的刻画，而且比其他基于小波的预测模型具有更高的预测精度。
上述研究成果不仅丰富了集成算子的理论内容，给出了相应多属性群决策与时间序列预测的新方法，而且为我们利用这些方法解决实际问题提供了充分的科学依据。
Aggregation operators as indispensable tools, which are used for informationfusion, have been disseminated throughout various fields including decision analysis,combination forecasting, military operations, and so on. In view of the existingproblems of multi-attribute group decision making and nonlinear time series forecast,we propose the correspongding solving methods, which are based on the aggregationoperators. The main work and innovations of the dissertation are summarized asfollows:
(1) We extend the Quasi-OWA operator to the case in which the input argumentis a continuous valued interval and present the continuous Quasi-OWA (C-QOWA)operator, which generalizes a wide range of continuous operators such as the C-OWAoperator, the C-OWH operator and the C-GOWA operator. Then an orness measure toreflect the optimistic degree of the C-QOWA operator is proposed. Moreover, somedesirable properties of the C-QOWA operator associated with its orness measure areinvestigated. In addition, we apply the C-QOWA operator to the aggregation ofmultiple interval arguments and obtain the weighted C-QOWA operator, the orderedweighted C-QOWA (OWC-QOWA) operator, the combined C-QOWA (CC-QOWA)operator. We present an approach to multi-attribute group decision making based onthe CC-QOWA operator, when the decision information are continuous valuesinterval.
(2) In order to aggregate triangular fuzzy numbers, the fuzzy Bonferroni mean(FBM) operator is developed and its some special cases are discussed. Based on this,the fuzzy weighted Bonferroni mean (FWBM) operator and combined fuzzy weightedBonferroni mean (C-FWBM) operator are proposed. Meanwhile, some desirableproperties of these operators are investigated. With respect to multi-criteria groupdecision making in which the decision making information is given by triangularfuzzy numbers, a new decision making method is proposed based on FWBM operatorand C-FWBM operator. The advantage of the proposed method is its capability tocapture the interrelationship between attributes. The results of an empirical analysisshow that the developed method is feasible.
(3) In view of multi-attribute decision making in linguistic environment, weextend the Bonferroni mean operators to the situation where the inputs are linguisticarguments and proposed2-tuple linguistic Bonferroni averaging (2TLBA) operator, weighted2TLBA (W2TLBA) operator and combined W2TLBA (C-W2TLBA)operator. Moreover, some desirable properties and special cases of these aggregationoperators are investigated. Then a decision-making approach is presented based onW2TLBA operator and C-W2TLBA operator. Meanwhile, a numerical experiment isgiven to prove the feasibility of the developed approach.
(4) In view of unstable and nonlinear time series, a dynamic forecasting model isproposed in this paper, which integrate wavelet decomposition, OWA operator basedSlip Discrete Difference Equation Prediction Model (OWA-SDDEPM) and Markovmethods. In this model, the original time series are decomposed into differentfrequency channels by multi-scale wavelet. Then we predict the wavelet coefficientsof the low-frequency approximation with the SDDEPM and predict the waveletcoefficients of high frequency details by Markov method, respectively. Therefore,forecasting value of the original time series is obtained by wavelet reconstruction ofthe low and high frequency foresting results. The model is applied to forecasting WTIweekly crude oil prices. The research result shows that the proposed forecastingmodel could not only forecast holistic fluctuation frequency of time series effectivelybut also characterize the details of the time series. The forecasting accuracy of thismodel is much higher than any other wavelet-based models.
The above research results not only enrich the content of aggregation operatortheory, develop the corresponding new methods for multi-attribute group decisionmaking and time series forecasting, and provide more sufficient scientific evidencefor applying these methods to solve practical problems.
引文
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