基于偏好信息一致性程度最大的多属性决策方法

研究了方案偏好信息以区间数互反判断矩阵形式给出,属性偏好信息以区间数互补判断矩阵形式给出的不确定多属性决策问题。首先针对属性值以实数形式给出的多属性决策问题,基于区间数判断矩阵一致性的性质,建立了求解属性和方案偏好信息一致性程度最大化的线性规划模型,然后把其推广到属性值以区间数形式给出的多属性决策问题,最后通过一个算例说明了该方法的适用性和有效性。     

区间直觉模糊信息的相容性测度和一致性群决策调整

考虑到区间直觉模糊信息的群决策问题,给出区间直觉模糊判断矩阵相容性及其基于基本相容性调整一致性群决策的过程.首先,提出了基于区间直觉模糊判断矩阵的相容性定义及其一些性质.其次,给出了区间直觉模糊判断矩阵的一个相容性指标及衡量区间直觉模糊判断矩阵的相容性准则.再次,利用临界值给出区间直觉模糊信息的一致性群决策调整的过程.最后,利用实例给出了群决策的整体过程,说明了方法的合理性和有效性.     

区间直觉模糊判断矩阵群决策中的逆判问题

研究了区间直觉模糊判断矩阵的群决策问题.定义了两种区间直觉模糊集相似度公式,给出两种与决策群体意见一致性程度最高的理想区间直觉模糊判断矩阵构造优化方法.利用矩阵对不同专家判断矩阵中相同位置元素的一致性进行分析,并对不同专家的判断信息进行整体相似程度分析,最后通过算例说明了该方法的有效性和实用性.     

基于残缺信息的直觉模糊判断矩阵群决策方法

直觉模糊判断模拟人类的决策过程、反映人类的经验和行为,在处理复杂不确定性决策问题方面具有较高的灵活性和实用性。在实际决策过程中,直觉模糊判断矩阵中的元素会有残缺。本文研究了残缺信息下直觉模糊群组判断矩阵的最优排序方法问题。利用直觉模糊判断的一致性条件,提出了残缺信息下直觉模糊群组判断的最小二乘排序模型,并将此模型推广到完全信息直觉模糊群组判断的情形。算例分析表明,本文的研究是有效可行的。     

一种基于残缺语言判断矩阵的群决策方法

本文针对具有残缺语言判断矩阵形式方案偏好信息的群决策问题,提出了一种决策分析方法.首先,阐述了二元语义的概念,并提出了一种扩展的二元语义有序加权平均(ETOWA)算子;然后,采用ETOWA算子集结具有残缺语言判断矩阵形式的方案偏好信息,可计算出每个方案优于其他方案的总体偏好程度,进而可得到所有方案的排序结果.最后,通过给出一个算例说明了本文提出方法的可行性和实用性.     

基于乘性一致性残缺互补判断矩阵的决策方法

对于满足乘性一致性的残缺互补判断矩阵的决策问题,提出了一种决策方法。首先把互补判断矩阵的乘性一致性定义进行了简化,得到了互补判断矩阵乘性一致性的另外几种表达形式;进一步得到了在已知n-1个特殊元素的条件下,残缺互补判断矩阵中缺失元素的补全方法;然后给出了残缺互补判断矩阵可接受的条件,以及矩阵的一致性检验及调整方法;基于残缺互补判断矩阵,给出了以下决策步骤:残缺互补判断矩阵的一致性检验及调整过程,补全缺失元素的迭代过程和最优方案择优过程。最后给出了一个实例,通过该实例的计算以及本文方法与已有方法的比较,证明了本文方法是简便和有效的。     

三角模糊数互补判断矩阵的一种排序方法

研究决策信息以三角模糊数互补判断矩阵形式给出的多属性决策问题。给出了三角模糊数一致性互补判断矩阵与其权重向量之间的关系，建立了一个目标规划模型。通过求解该模型得到三角模糊数互补判断矩阵的权重向量，并利用已有的三角模糊数排序公式求得决策方案的排序。最后，给出了一个算例。     

一种基于Choquet积分的多属性直觉模糊决策方法

研究了决策者对方案的主观偏好值以及属性值均为直觉模糊数的且属性间存在关联的多属性决策问题.利用Choquet模糊积分作为集结算子,构建了基于属性关联的M OD和SOD模型.通过求解模型获得属性的权重,进而给出了一种新的直觉模糊多属性决策方法.最后通过一个算例说明了该决策方法的有效性和可行性.     

基于相对熵的多粒度语言判断矩阵的群决策方法

针对多粒度语言判断矩阵的群决策问题提出基于相对熵的最优化模型的排序方法.在多粒度语言偏好信息的导出函数基础上定义了语言判断矩阵对应的导出模糊互补判断矩阵,并给出其排序向量的计算式;同时采用语言判断矩阵的一致性指标来确定专家重要性程度的权向量;在相对熵的意义下构建了群决策排序向量的最优化模型,探讨了模型的求解方法.实例分析表明该模型是可行和有效的.     

模糊残缺判断矩阵的修补

模糊判断矩阵是决策者在决策中所提供的一种重要的偏好信息,然而专家所给出的判断矩阵可能是带有残缺的.给出了模糊残缺判断矩阵中残存元素的极大一致独立组、残存元素组导出图、残缺矩阵的可接受性概念,并讨论了模糊残缺判断矩阵的极大一致独立组的导出图是树的条件,进而说明n阶模糊残缺矩阵中n-1个元素所导出的图是n阶树的话,模糊残缺判断矩阵即为可接受的.最后给出了一个可接受的残缺判断矩阵修补的算例.     

Extension of the TOPSIS method for decision making problems under interval-valued intuitionistic fuzzy environment

TOPSIS is one of the well-known methods for multiple attribute decision making (MADM). In this paper, we extend the TOPSIS method to solve multiple attribute group decision making (MAGDM) problems in interval-valued intuitionistic fuzzy environment in which all the preference information provided by the decision-makers is presented as interval-valued intuitionistic fuzzy decision matrices where each of the elements is characterized by interval-valued intuitionistic fuzzy number (IVIFNs), and the information about attribute weights is partially known. First, we use the interval-valued intuitionistic fuzzy hybrid geometric (IIFHG) operator to aggregate all individual interval-valued intuitionistic fuzzy decision matrices provided by the decision-makers into the collective interval-valued intuitionistic fuzzy decision matrix, and then we use the score function to calculate the score of each attribute value and construct the score matrix of the collective interval-valued intuitionistic fuzzy decision matrix. From the score matrix and the given attribute weight information, we establish an optimization model to determine the weights of attributes, and construct the weighted collective interval-valued intuitionistic fuzzy decision matrix, and then determine the interval-valued intuitionistic positive-ideal solution and interval-valued intuitionistic negative-ideal solution. Based on different distance definitions, we calculate the relative closeness of each alternative to the interval-valued intuitionistic positive-ideal solution and rank the alternatives according to the relative closeness to the interval-valued intuitionistic positive-ideal solution and select the most desirable one(s). Finally, an example is used to illustrate the applicability of the proposed approach.     

An integrated model-based interactive approach to FMAGDM with incomplete preference information

Incomplete fuzzy preference relations, incomplete multiplicative preference relations, and incomplete linguistic preference relations are very useful to express decision makers’ incomplete preferences over attributes or alternatives in the process of decision making under fuzzy environments. The aim of this paper is to investigate fuzzy multiple attribute group decision making problems where the attribute values are represented in intuitionistic fuzzy numbers and the information on attribute weights is provided by decision makers by means of one or some of the different preference structures, including weak ranking, strict ranking, difference ranking, multiple ranking, interval numbers, incomplete fuzzy preference relations, incomplete multiplicative preference relations, and incomplete linguistic preference relations. We transform all individual intuitionistic fuzzy decision matrices into the interval decision matrices and construct their expected decision matrices, and then aggregate all these expected decision matrices into a collective one. We establish an integrated model by unifying the collective decision matrix and all the given different structures of incomplete weight preference information, and develop an integrated model-based approach to interacting with the decision makers so as to adjust all the inconsistent incomplete fuzzy preference relations, inconsistent incomplete linguistic preference relations and inconsistent incomplete multiplicative preference relations into the ones with acceptable consistency. The developed approach can derive the attribute weights and the ranking of the alternatives directly from the integrated model, and thus it has the following prominent characteristics: (1) it does not need to construct the complete fuzzy preference relations, complete linguistic preference relations and complete multiplicative preference relations from the incomplete fuzzy preference relations, incomplete linguistic preference relations and incomplete multiplicative preference relations, respectively; (2) it does not need to unify the different structures of incomplete preferences, and thus can simplify the calculation and avoid distorting the given preference information; and (3) it can sufficiently reflect and adjust the subjective desirability of decision makers in the process of interaction. A practical example is also provided to illustrate the developed approach.     

Correlation coefficient of interval-valued intuitionistic fuzzy sets and its application to multiple attribute group decision making problems

In this paper, we investigate the group decision making problems in which all the information provided by the decision-makers is presented as interval-valued intuitionistic fuzzy decision matrices where each of the elements is characterized by interval-valued intuitionistic fuzzy number (IVIFN), and the information about attribute weights is partially known. First, we use the interval-valued intuitionistic fuzzy hybrid geometric (IIFHG) operator to aggregate all individual interval-valued intuitionistic fuzzy decision matrices provided by the decision-makers into the collective interval-valued intuitionistic fuzzy decision matrix, and then we use the score function to calculate the score of each attribute value and construct the score matrix of the collective interval-valued intuitionistic fuzzy decision matrix. From the score matrix and the given attribute weight information, we establish an optimization model to determine the weights of attributes, and then we use the obtained attribute weights and the interval-valued intuitionistic fuzzy weighted geometric (IIFWG) operator to fuse the interval-valued intuitionistic fuzzy information in the collective interval-valued intuitionistic fuzzy decision matrix to get the overall interval-valued intuitionistic fuzzy values of alternatives, and then rank the alternatives according to the correlation coefficients between IVIFNs and select the most desirable one(s). Finally, a numerical example is used to illustrate the applicability of the proposed approach.     

基于直觉模糊集的全区间决策方法

针对属性值为直觉模糊集且属性权重已知的模糊多属性决策问题,本文基于直觉模糊算术加权平均算子,提出了一种基于直觉模糊集的全区间决策方法。全区间决策函数引入了态度指标k,从而可以反映决策者态度的变化,从0到1变化k值,可以在整个区间内挖掘决策信息的变化,与得分函数法和基于距离TOPSIS贴近度方法相比,将过去的点值判断延伸至全区间判断,避免了决策信息的丢失现象,决策更加准确合理。实例计算表明该方法的正确性、有效性和合理性,具有一定的推广借鉴价值。     

Extension of the VIKOR method for group decision making with interval-valued intuitionistic fuzzy information

The aim of this paper is to extend the VIKOR method for multiple attribute group decision making in interval-valued intuitionistic fuzzy environment, in which all the preference information provided by the decision-makers is presented as interval-valued intuitionistic fuzzy decision matrices where each of the elements is characterized by interval-valued intuitionistic fuzzy number, and the information about attribute weights is partially known, which is an important research field in decision science and operation research. First, we use the interval-valued intuitionistic fuzzy hybrid geometric operator to aggregate all individual interval-valued intuitionistic fuzzy decision matrices provided by the decision-makers into the collective interval-valued intuitionistic fuzzy decision matrix, and then we use the score function to calculate the score of each attribute value and construct the score matrix of the collective interval-valued intuitionistic fuzzy decision matrix. From the score matrix and the given attribute weight information, we establish an optimization model to determine the weights of attributes, and then determine the interval-valued intuitionistic positive-ideal solution and interval-valued intuitionistic negative-ideal solution. We use the different distances to calculate the particular measure of closeness of each alternative to the interval-valued intuitionistic positive-ideal solution. According to values of the particular measure, we rank the alternatives and then select the most desirable one(s). Finally, a numerical example is used to illustrate the applicability of the proposed approach.     

基于集对分析联系数的信息不完全直觉模糊多属性决策

信息不完全直觉模糊多属性决策是一类不确定性决策问题,其不确定性来自属性权重信息不完全和属性值的直觉模糊数表示.为了系统地刻画直觉模糊多属性决策中的不确定性,避免直觉模糊多属性决策中利用得分函数做决策的片面性和不准确性,可以将信息不完全的权重和直觉模糊数表示的属性值转化成集对分析理论中的联系数,并建立信息不完全直觉模糊多属性决策模型,通过对不确定性进行分析后作出决策.实例应用表明该决策方法具有合理性和可行性.     

基于时间度的动态直觉模糊多属性妥协决策

针对当前动态直觉模糊多属性决策方法存在的不足,提出一种基于时间度的动态直觉模糊妥协决策方法。引入时间度准则,基于逼近理想解法融合主客观两类赋权法,获得兼顾主观偏好和样本客观信息的时序权重,克服现有时序权重主观赋值的随意性,同时运用直觉模糊熵(IFE)确定不同时序状态下各属性权重;根据动态直觉模糊加权几何算子(DIFWG)集结不同时序直觉模糊决策矩阵,构造动态直觉模糊综合决策矩阵,并利用VIKOR法,提供兼顾群体效用最大化与个体后悔最小化的各方案妥协折中排序,得到与理想解最近的妥协方案;以分布式创新企业合作伙伴选择为例,验证该方法在实际决策过程中的可行性和有效性。     

考虑决策者风险偏好的区间直觉模糊多属性群决策方法

提出了一种考虑决策者风险偏好且属性权重信息不完全的区间直觉模糊数多属性群决策方法。同时考虑相似度和接近度,确定每一属性的决策者权重。为了考虑决策者风险偏好对决策结果的影响和避免区间直觉模糊矩阵的渐进性,引入了决策者风险偏好系数,将集结后的综合决策矩阵转换成区间数矩阵。然后,为了客观地求出属性权重信息不完全环境下属性的权重,构建了基于区间直觉模糊交叉熵的属性权重目标规划模型,该模型不仅考虑了评价值的偏差,也强调了评价值自身的可信度。最后,通过研发项目选择问题的实例分析说明了所提方法的合理性和优越性。     

证据视角下考虑多参考点的直觉模糊多属性决策模型

针对直觉模糊多属性决策中,决策者内心同时存在多个独立参考点并且各属性之间相互关联的问题,进一步考虑智能传感设备在决策中的参考作用,提出证据视角下考虑多参考点的直觉模糊多属性决策模型。模型首先利用证据理论融合各传感器数据,得到各状态的mass函数;其次,考虑决策者内心同时存在多个参考点,利用价值函数得到各状态下多参考点价值矩阵;进一步,针对属性间的关联性,利用模糊积分得到各状态下不同方案的综合评价值;再次,利用基于证据理论的直觉模糊诱导有序加权平均(DS-IFIOWA)算子将各状态下不同方案的综合评价值进行集结,得到方案的总评价值,并以此对方案进行排序和优选。最后,利用数值算例验证了模型的有效性和可行性。