一种基于区间数判断矩阵的加权AIP群决策方法

针对决策过程中区间数更适合表达决策者对候选方案的偏好程度,基于区间数判断矩阵,综合考虑决策者个体权重,扩展“和积法”,应用“相对熵”的概念,提出了一种加权个体方案权重集结的群体决策方法．该方法将中间结果转化为实数型再进行集结,避免了决策者判断信息的丢失．最后,通过算例说明了该方法的可行性和有效性．

     

群决策中两类不确定偏好信息的集结方法研究

研究区间数互反判断矩阵和区间数互补判断矩阵的集结，采用UOWA算子将决策者的偏好信息集结为区间数互反判断矩阵和互补判断矩阵两种形式，结合决策者给出的允许偏差，定义群满意度隶属函数，建立求解群偏好一致程度最大化的权重模型．为解决模型存在多组最优解问题，在第2阶段建立群偏好权重分布范围估计模型，研究模型所具有的性质，最后通过区间数比较的可能度方法排定各方案的最终优劣顺序。     

群决策中两类三端点区间数判断矩阵的集结方法

研究群决策过程中三端点区间数互反判断矩阵和三端点区间数互补判断矩阵的集结. 采用OWA(Ordered weighted averaging) 方法将决策者的偏好信息集结为两个三端点区间数判断矩阵. 基于三端点区间数判断矩阵的完全一致性概念, 建立三端点区间数判断矩阵的权重求解模型. 根据群决策背景下专家群最大一致的目标, 建立求解专家群体偏好权重的模型. 在第二阶段建立群偏好权重分布范围估计模型, 最后通过可能度方法以排定各方案的最终优劣顺序.     

区间值模糊随机多准则决策方法

针对不完全信息的区间值模糊随机多准则决策问题,提出了两种求解方法。第一种方法利用离差最大化构建区间参数线性规划,通过区间数运算法则和定位规划求得最优准则权重向量、状态集结值区间决策矩阵与期望值区间决策矩阵,根据决策者风险偏好水平得到各方案的期望集结值从而确定排序。第二种方法将区间值模糊数决策矩阵转化为直觉模糊数决策矩阵,利用不完全的准则权重,通过规划模型求解,获取各方案在各自然状态下的加权记分函数值与加权精确函数值的区间,利用不完全的状态概率,得到各方案的记分函数期望值与精确函数期望值的区间,根据决策者风险偏好水平,求得各方案的记分函数与精确函数的期望集结值,进而确定方案的排序结果。算例分析验证了两种方法的有效性和可行性。     

区间灰色不确定语言多属性群决策方法

针对属性值为区间灰色不确定语言信息的多属性群决策问题,在定义区间灰色不确定语言变量及其运算规则的基础上,给出了3种几何加权集结算子,由区间灰色不确定语言几何加权算子集结各决策者给出的决策矩阵得到群体决策矩阵。在属性权重已知的情形下,基于该算子集结单个决策者给出的属性权重向量得到群体属性权重向量;在属性权重完全未知的情形下,采用信息熵法确定属性权重向量。采用区间灰色不确定语言混合几何加权算子集结各属性评价信息,得到各方案的综合评价值,基于区间灰色不确定语言变量大小比较的方法得到方案排序结果。算例分析表明了该方法的有效性与可行性。     

专家权重完全未知的区间直觉不确定语言多属性群决策方法

针对专家权重信息完全未知且属性值为区间直觉不确定语言数的模糊多属性群决策问题,提出一种基于混合权重信息及决策者风险态度的群决策分析方法。在定义区间直觉不确定语言数差异度的基础上,分别利用专家在方案评价值上的贴近度以及方案排序上的一致度来计算两类专家权重,并基于均衡度得到专家的客观综合权重。进而通过融合专家客观综合权重以及基于相似度的个体综合评价值权重,提出一种混合加权集结方法,从而得到方案的群体综合评价值,并通过定义带有风险态度因子的期望值与精确函数实现对方案的比较和排序。最后,通过实例分析证明所提方法的有效性和合理性。     

一种基于证据推理的混合型灰色多属性群决策方法

针对方案的属性值为区间灰数与确定语言等级,或在两个连续的语言等级之间权重完全已知的混合型灰色多属性群决策问题,提出一种新的决策方法．该方法可根据决策者的偏好给出定量属性的白化值和定性属性的信用结构,确定了每个决策者和群体的等级信用结构矩阵;提出了求解群体集成权重的新方法,并利用证据推理算法求出各方案在各等级的信任度;最后利用期望效用和区间数排序法对方案进行了排序．实例分析表明了该方法的合理性和有效性．     

基于云模型具有语言评价信息的多属性群决策研究

针对多属性群决策中具有语言评价信息偏好的表示与集结的关键问题．研究了基于云模型的决策专家个体偏好表示、偏好集结和方案优选方法．首先采用云模型表示决策者给出的自然语言评价信息，而属性和决策者权重大小则用云的语气运算表示；然后用浮动云进行偏好集结，根据云模型的相对距离进行方案的排序和优选．此方法可充分表达评价语言的模糊性和随机性，具有较大的客观性．     

基于累积前景理论的动态风险灰靶决策方法

研究信息值为区间灰数, 指标权重未知的动态风险决策问题, 提出一种基于累积前景理论和灰靶思想的决策方法. 该方法定义了区间灰数的距离测度和排序方法; 以各指标值的平均值作为参照点计算各时段的前景矩阵; 通过WAA算子将动态前景矩阵集结为静态前景矩阵; 在此基础上求解基于极大熵思想的规划模型得出各指标权重. 构造正负椭球灰靶模型, 根据各方案的正负靶心综合距对方案进行排序. 最后, 通过算例分析结果验证了该方法更加符合决策者的心理行为.

     

基于模糊多属性决策的目标威胁估计方法

针对目标威胁估计的功能及特点，提出一种属性为区间数且属性权重完全未知，决策者对方案有偏好的多属性决策（MADM）方法．首先给出方案偏好度的计算公式，在综合考虑客观优化排序和决策者对方案有主观偏好的基础上，建立了一种主客观综合属性权重获取模型，使得属性权重信息更加合理地反映实际情况，模型具有较强的泛化能力．最后，通过防空目标威胁估计实例说明了该方法的实用性和有效性．     

基于熵和风险态度的二型模糊多属性决策方法

针对属性权重信息完全未知的二型模糊多属性决策问题,提出了一种基于二型模糊熵和决策者风险态度的决策方法。首先,为了准确测度二型模糊集（T2FS）的不确定性,通过引入模糊因子和犹豫因子建立了二型模糊熵的公理化准则,并基于距离测度给出了对应的计算公式。其次,为了减少整体不确定信息对决策结果的影响,结合二型模糊熵构建非线性规划模型来确定属性权重。同时,将决策者的风险态度引入二型模糊信息的得分函数中并给出具体的决策步骤。最后,通过实例分析验证了该决策方法的可行性,并与现有文献对比发现该决策方法更具有灵活性。     

Fuzzy analytic hierarchy process and analytic network process: An integrated fuzzy logarithmic preference programming

This paper proposes a two-stage fuzzy logarithmic preference programming with multi-criteria decision-making, in order to derive the priorities of comparison matrices in the analytic hierarchy pprocess (AHP) and the analytic network process (ANP). The Fuzzy Preference Programming (FPP) proposed by Mikhailov and Singh [L. Mikhailov, M.G. Singh, Fuzzy assessment of priorities with application to competitive bidding, Journal of Decision Systems 8 (1999) 11–28] is suitable for deriving weights in interval or fuzzy comparison matrices, especially those displaying inconsistencies. However, the weakness of the FPP is that it obtains priorities of comparison matrices by additive constraints, and generates different priorities by processing upper and lower triangular judgments. In addition, the FPP solves the comparison matrix individually. By using multiplicative constraints, the method proposed in this paper can generate the same priorities from upper and lower triangular judgments with crisp, interval or fuzzy values. Our proposed method can solve all of the matrices simultaneously by multiple objective programming. Finally, five examples are demonstrated to show the proposed method in more detail.     

Nonlinear fusion method for multistage product design decision-making using plant growth simulation algorithm

Design decision-making is a vital activity for selecting an optimal scheme for product development. Owing to the uncertainty and ambiguity of design requirements and constraints, several product design phases are often deployed for concept refinement, which makes multistage product design decision-making (MPDDM) and the effective fusion of MPDDM data indispensable. However, few existing methods have considered the nonlinear relationships among the MPDDM information. Therefore, a nonlinear fusion method for MPDDM was proposed in this study. This method applies a three-parameter interval grey number to depict decision-makers’ judgement about product design schemes. Based on converting linguistic judgements into interval scales, an interval analytic hierarchy process (AHP) method was employed to calculate the weights of the design criteria, decision-makers, and decision-making stages. Considering the advantage of integrating multiple matrices without requiring external control parameters, a multistage decision-making fusion process using a plant growth simulation algorithm (PGSA) was proposed to aggregate multistage decision-making data for product design. A case study was conducted to collect multistage decision-making data, and the PGSA was developed. Through comparison with the extant method, the effectiveness and feasibility of the fusion of MPDDM was verified. The results indicate that (1) uncertainty perceived by decision-makers at three stages accounted for 96.7%, 95%, and 97.2%, respectively. The “center of gravity” of a three-parameter interval grey number, which reflects the largest possibility of decision-makers’ preferences, is not always equally distant from its maximum or minimum value (73.9%). (2) The optimization model using interval AHP to calculate the weights of decision-making indicators and stages is conducive to reducing the decision-maker’s uncertainty. (3) The global search mechanism of the PGSA can effectively realize the nonlinear fusion of MPDDM.     

Engaging multiple perspectives: A value-based decision-making model

In some decision contexts, such as a crisis or when confronted by a new or novel set of circumstances, people may be forced to make decisions with limited information or time available for analysis. In such contexts, the set of alternative solutions developed may be greatly affected by the personal values and the perspective those values precipitate. Being able to view the decision environment from multiple perspectives enhances the decision-maker's ability to make better-informed choices. This article introduces the value-based decision-making model that suggests that multiple perspectives may be achieved by considering a foundation of individual values. Empirical testing indicates that this model provides a viable framework that decision-makers and researchers can use to better understand and facilitate multiple perspectives in decision-making.     

Consolidating SWOT analysis with nonhomogeneous uncertain preference information

SWOT analysis is an important support tool for decision-making, and is commonly used to systematically analyze organizations’ internal and external environments. However, one of its deficiencies is in the measurement and evaluation of prioritization of the factors and strategies. This paper is aimed to present a novel quantified SWOT analytical method based multiple criteria group decision-making (MCGDM) concept, in which the priorities of SWOT factors and groups are derived by multiple decision makers (DMs) with nonhomogeneous uncertain preference information (NUPI), such as interval multiplicative preference relations, interval fuzzy preference relations, and uncertain linguistic preference relations. In this method, the SWOT analysis provides a basic frame within which to perform analyses of decision situations, in turn, MCGDM methods assist in carrying out SWOT more analytically and in elaborating the results of the analyses so that SWOT factors and groups can be prioritized with respect to the entire SWOT. The uniform and aggregation of the NUPI and the derivation of priorities for SWOT groups and factors are investigated in detail. Finally, an example is to validate the procedure of the proposed method.     

Generating consensus priority point vectors: a logarithmic goal programming approach

The analytic hierarchy process (Saaty, The Analytic Hierarchy Process: Planning, Priority Setting, Resource Allocation, NewYork: McGraw-Hill 1980) is a popular technique for addressing multiple-criteria decision-making problems (MCDMs). Various techniques have been proposed for using the AHP in group situations. Fundamental to the AHP is the generation of priority point vectors from matrices of pairwise comparison data. In this paper, we present a logarithmic goal programming model for generating the ‘consensus’ priority point vector from the set of individual priority point vectors.Scope and purposeWithin modern organizations, multiple-criteria decision-making problems (MCDMs) often occur within a group context, and individual priorities for decision alternatives must be synthesized into a single set of priorities which represents the consensus opinion for the group. This requires a process for aggregating individual priorities into a set of group priorities. In this paper, we examine the use of the analytic hierarchy process (AHP) MCDM technique for the group situation, and present an approach for aggregating individual priorities into a set of group ‘consensus’ priorities.     

基于幂均算子的区间型多属性决策方法

针对决策矩阵元素为区间数的不确定多属性决策问题,提出一种新的决策方法．定义了区间数幂均算子和区间数的相似度,利用一致度矩阵获得每个属性与其他属性的相对一致度．通过区间数幂均算子集成得到方案的综合属性值,进而给出了方案的排序结果．该方法不需要求解属性的权重．应用实例表明了所提出方法的有效性和实用性．     

人才选择的决策问题研究

采用能表现人的主观模糊性的尺度，即用含有模糊元素的模糊关系逆问题法描述人才选择等决策问题，利用可观测量推断出无法观测（或短期间内无法观测）但在决策问题中极为重要的评价量，从而使评价具有更高的可信度和合理性。     

INGIOWGA算子的多属性决策方法及其应用

研究了方案的属性评估信息以模糊语言形式给出的多属性群决策问题，在导出的有序加权几何平均（IOWGA）算子理论的基础上，给出了一种区间数广义导出有序加权几何平均（INGIOWGA）算子，利用广义的导出有序加权平均（GIOWA）算子，对专家所给出的对应于各方案的属性评估信息进行了集结，并提出了一种基于模糊语言评估和GIOWA算子的多属性群决策方法。利用该算法对X射线实时成像检测系统方案选择中的判断信息进行集结，并且通过算例说明了该方法的有效性和实用性。     

基于两参照点的动态混合多属性群决策算法

针对方案属性值为三参数区间灰数与三角模糊数相混合的动态多属性群决策问题,提出一种基于前景理论和两参照点的动态解决方案.针对灰数与模糊数混合的状况,提出混合靶心模型;设置时间参照点,通过均值和平均发展速度,考察各方案之间动态发展情况;利用向量之间的夹角,考察专家个体决策与群决策之间的相似度,建立相应的专家权重调整模型;考虑决策问题发展过程中的未来多个阶段,采用熵权法确定时间权重,并通过算例验证所提出方法的可行性和实用性.