假设各决策时段的时间权重、各决策时段下的属性权重以及决策者权重均已知,各决策者针对各决策时段给出的属性值以直觉模糊数形式给出的动态多属性群决策问题,提出了一种基于导出直觉模糊混合平均（I-IFHA）算子动态直觉模糊多属性群决策方法.该方法利用动态直觉模糊加权平均（DIFWA）算子和动态加权平均（DWA）算子集结动态决策信息分别得到各决策者的综合直觉模糊决策矩阵和综合属性权重向量,并在此基础上利用直觉模糊加权平均（IFWA）算子计算得到各决策者下各方案的直觉模糊评价值;利用I-IFHA算子集结决策者群体决策信息得到各方案的综合直觉模糊评价值;利用直觉模糊数的得分函数及精确函数对决策方案进行排序和择优.最后,通过投资银行对企业进行投资的实例说明了该方法的应用.

This paper presents an induced intuitionistic fuzzy hybrid averaging( I-IFHA)operator-based method with respect to dynamic multiple attribute group decision making(DMAGDM)problem,in which period weights,attribute weights of each period and decision makers(DMs)weights are given and attribute values provided by each DM at different periods are expressed in intuitionistic fuzzy numbers. With dy-namic intuitionistic fuzzy weighted averaging(DIFWA)operator and dynamic weighted averaging(DWA) operator,the proposed method aggregates the intuitionistic fuzzy decision making matrices for each DM and weights of attributes at different periods into the collective intuitionistic fuzzy decision making matrix for each DM and weights of attributes,and then uses intuitionistic fuzzy weighted averaging(IFWA)opera-tor to derive the individual intuitionistic fuzzy evaluation values of the given alternatives for each DM. It also employs the I-IFHA operator to get the overall intuitionistic fuzzy values of

为了合理安排各个目标的打击顺序和强度,给指挥员提供客观、可靠的目标攻击顺序建议,提出一种基于双重模糊决策的炮兵战场目标价值排序方法。通过应用模糊决策理论,对个体决策者应用"多因素模糊决策法"进行排序,对最高决策者根据个体决策情况运用"模糊群体决策法"决定最终排序结果,通过以上双重模糊决策的方式,得出最合理的战场目标价值排序结果,并进行实例仿真。分析结果证明:该方法能避免主观臆断,对我军炮兵尤其是远程炮兵作战的辅助决策有一定的指导作用。

In order to determine the target value and provide the best attacked targets sequence, a target value analysis method based on double fuzzy decision-making is proposed. According to the fuzzy decision-making theory, this paper applies the method of“multi-factor fuzzy decision-making”for the individual decision-maker;the method of“fuzzy group decision-making”is applied for the top decision maker. Draw a result of the reasonable target value sequencing result based on double fuzzy decision-making. The simulation result is proved that the method can avoid the subjective judgment, which is helpful to provide the assistant decision-making for our army artillery especially long-rang artillery combat.

研究了属性值为三角直觉模糊数的多属性决策问题，提出了一种基于权重函数的决策方法。给出了三角直觉模糊数的定义、运算法则和截集；定义了三角直觉模糊数关于隶属函数和非隶属函数的精确值和模糊度，以及精确值的指标和模糊度的指标，给出了三角直觉模糊数的排序方法，并将其应用到属性值为三角直觉模糊数的多属性决策问题中；给出了属性值为三角直觉模糊数的多属性决策的步骤；通过数值算例分析和验证了该方法的有效性。

This paper studies the multi-attribute group decision making problems where the attribute values are triangular intuitionistic fuzzy numbers (TIFNs), and proposes a new decision making method on the basis of weight function. Firstly, this paper introduces the concept, arithmetic operations and cut sets of TIFNs. Secondly, this paper defines the crisp value and ambiguities of the membership function and the non-membership function for TIFNs as well as the crisp value-index and ambiguity-index, then develops a crisp value and ambiguity based ranking method and uses the method to solve multi-attribute decision making problems. Thirdly, this paper gives the steps of triangular intuitionistic multiple attribute decision making. Finally, an illustrative example shows the effectiveness of the proposed method.

研究了时序模糊软集的群决策问题，针对实际问题中模糊软集的信息随时间动态变化对最终决策的影响不同，将这类影响量化为时间权重，根据各对象保持前一时刻状态的能力不同，造成对象集整体在不同时刻状态有所差异，得到权重值；并利用集成思想，通过时序模糊几何加权平均算子将时序模糊软集集成为综合模糊软集；再利用水平软集等工具计算各对象的机会值，得出最优决策。最后，给出具体的时序模糊软集的群决策步骤，并通过实例验证了决策方法的合理性及可行性。

Group decision-making problems based on times-series fuzzy soft set have been investiga-ted. For the situation that fuzzy soft sets information dynamic change as time has different effect on fi-nal decision,there have been quantified these effects to time weights and obtained them by optimiza-tion programming model. With aggregating thought,the time-series fuzzy soft sets have been aggrega-ted into collective fuzzy soft by time-series fuzzy weighted geometric average operator. The optimal de-cision can be obtained by calculating choice value of objects with the level soft set. Finally,the group decision making approach based on time-series fuzzy soft sets has been proposed and a practical exam-ple has been analyzed to verify the reasonability and feasibility of the approach.

研究了决策信息为区间直觉梯形模糊数且属性间存在相互关联的多属性群决策问题，提出一种基于区间直觉梯形模糊几何加权 Bonferroni 平均算子的决策方法。基于区间梯形直觉模糊数的运算法则和几何 Bonferroni 平均算子，定义了区间直觉梯形模糊几何 Bonferroni 平均算子及其加权算子。给出了这些算子的一些性质，建立基于区间直觉梯形模糊几何加权 Bonferroni 平均算子的多属性群决策模型。最后，将该方法应用在供应商选择的群决策问题中，结果表明了该方法的有效性与可行性。

For solving multiple attributes group decision-making (MAGDM)problems where attribute values are in the form of interval-valued intuitionistic trapezoidal fuzzy numbers and attributes are associated with each other,an approach was proposed based on interval-valued intuitionistic trapezoidal fuzzy geometric weighted Bonferroni means (IVITFGWBM)operator.The concepts of interval-valued intuitionistic trapezoidal fuzzy numbers were introduced,and interval-valued intuitionistic trapezoidal fuzzy geometric Bonferroni means (IVITFGBM)operator and IVITFGWBM operator were defined based on operational laws and Bonferroni means operator. Meanwhile,the related properties were analysed,then a model of multi-attribute group decision making was constructed based on IVITFGWBM operator,which was for making decisions combined with sort methods.The approach was further applied in group decision-making problems of supplier selection,and the results show that the developed approach is feasible an