基于区间直觉梯形模糊数的改进TOPSIS多属性决策方法

研究了属性权重完全未知的区间直觉梯形模糊数的多属性决策问题,结合TOPSIS方法定义了相对贴近度及总贴近度公式.首先由区间直觉梯形模糊数的Hamming距离给出了每个方案的属性与正负理想解的距离,基于此,给出了相对贴近度矩阵,根据所有决策方案的综合贴近度最小化建立多目标规划模型,从而确定属性的权重值,然后根据区间直觉梯形模糊数的加权算数平均算子求出各决策方案的总贴近度,根据总贴近度的大小对方案进行排序;最后,通过实例分析说明该方法的可行性和有效性.     

不完全信息下的区间直觉模糊数的多属性决策方法

针对属性权重信息不完全的区间直觉模糊的多属性决策问题,提出灰色关联分析的决策方法.该方法首先确定各属性下的最佳和最劣方案,确定各方案与理想方案的灰色关联系数,然后在属性权重信息不完全的情况下,建立基于理想点的最优决策模型,求出属性权重,进而根据与理想方案的相对贴近度对各方案进行排序,最后用实例对该方法进行了说明,理论分析和数据结果表明了方法的可行性和有效性.     

基于投影模型的区间直觉模糊多属性决策方法研究

本文首先定义了一种新区间直觉模糊投影方法,其能更好地度量投影向量之间的相关性。其次,根据区间直觉模糊正负理想方案与备选方案的投影关系, 构建了基于投影方法的未知属性权重求解模型,并在此基础上设计了一种基于投影值的贴近度方法,能实现对备选方案有效排序;最后,用实例验证了该方法的有效性和可行性。     

区间粗糙数多属性决策方法

针对属性值为区间粗糙数,属性权重部分已知和属性权重未知两种情形的多属性决策问题,本文利用灰色关联分析的思想方法,构建了一种区间粗糙数多属性决策方法。本文首先利用区间粗糙数的运算法则和期望值比较,确定最优理想方案和最劣理想方案,并基于灰色关联度分析方法构建了属性权重部分已知、属性权重未知两种情形的多目标优化模型,从而确定属性权重和属性权重表达式,进而获得各方案的综合评价值和方案排序。最后以一个实例验证模型的有效性与适用性。     

基于新型区间直觉三角模糊熵的多属性决策方法

在进行区间直觉模糊多属性决策时,有时属性权重是未知的,针对这一问题,提出一种新型区间直觉三角模糊熵的决策方法.首先,给出该新型区间直觉三角模糊熵定义和相关定理,应用该区间直觉三角模糊熵确定属性的权重.然后,基于逼近理想解排序法(TOPSIS)的思想,采用改进的加权欧几里得距离,进行区间直觉模糊群决策,并给出决策步骤.最后,将该方法应用在供应链选择的群决策问题中,通过算例实验验证了该方法的有效性与可行性.     

基于区间值毕达哥拉斯模糊数的TOPSIS方法及其在学生推优中的应用

毕达哥拉斯模糊是对模糊集和直觉模糊集的推广.研究了基于区间值毕达哥拉斯模糊集和模糊逼近理想解(TOPSIS)的多属性决策方法.考虑了属性信息的不同情况,包括属性信息完全已知,部分可知和完全未知的情况.对于部分可知情况,通过求解线性规划模型确定属性的权重;对于完全未知的情况,利用相对贴近系数确定属性的权重.给出了具体的算法步骤,最后将该方法应用到学生的推优问题上,实例说明新方法的有效性和合理性.     

基于模糊熵-熵权法的混合多属性决策方法

针对决策信息以区间数、直觉模糊数和语言变量给出的混合多属性决策问题,提出了基于模糊熵-熵权法的混合多属性决策方法。通过规范化的方法把区间数转化为直觉模糊数,建立了直觉模糊数与语言变量的对应关系,把混合多属性决策信息统一在同一决策框架下;然后利用熵权法确定属性的客观权重区间,通过求解属性信息模糊熵最小的线性规划模型得到属性客观权重;再与主观赋权方法相结合确定属性的组合权重;最后应用相对熵排序法得到方案的最终排序结果。算例分析表明方法的可行性和实用性。     

混合型多属性决策的灰色关联分析法

针对属性权重信息不完全且属性取值为精确数,区间数和模糊数相结合的混合型多属性决策问题,提出了一种基于理想解的多属性决策的灰色关联分析方法.首先将三种不同形式的属性值均转化为区间数形式,然后依据灰色关联分析的思路,给出了解决该问题的计算步骤,其核心是构建并求解一个单目标最优化模型,得到每个方案与正、负理想方案的关联度,进而计算出每个方案对正理想方案的相对关联度,即可得到所有方案的排序结果.最后给出了一个数值例子,结果表明方法简单,有效和易于计算.     

基于TOPSIS的属性关联直觉模糊多属性决策方法

针对属性值为直觉模糊数,已知部分属性偏好关系及属性交互类型的属性关联多属性决策问题给出决策方法.首先定义方案到正(负)理想方案的距离及各方案与正理想方案相对贴近度.然后以极大化各方案与相对贴近度为目标建立优化模型,确定出属性集的模糊测度.进而基于直觉模糊Choquet积分算子计算各方案的直觉模糊综合评价值,再根据直觉模糊数的得分值及精确度得到方案的排序.最后通过实例验证了方法的有效可行性.     

基于区间灰数多属性群决策建模技术的卫生应急综合评价研究

多属性灰色群决策建模方案设计为立足点,引入区间灰数、相离度、逼近理想点、群决策集结算法知识,在属性权重为实数、区间灰数或优化运算形式下,经属性值规范化后制定理想方案.首先,计算区间灰数相离度、灰色关联系数、灰色关联度,讨论以理想方案贴近度确定排序或择优.然后,改进为群体专家独立决策环境下,由属性矩阵虚构理想方案并计算关联度、贴近度,与专家权重集结为贴近度矩阵,由逼近理想点思路排序及择优.最后,由疾控机构卫生应急能力评价案例验证可行性,区间灰数、属性测度、专家权重以及属性群决策信息利用充分,这套建模方案对于类似问题也有推介意义.     

A grey relational projection method for multi-attribute decision making based on intuitionistic trapezoidal fuzzy number

With respect to multiple attribute decision making (MADM) problems in which the attribute value takes the form of intuitionistic trapezoidal fuzzy number, and the attribute weight is unknown, a new decision making analysis methods are developed. Firstly, some operational laws and expected values of intuitionistic trapezoidal fuzzy numbers, and distance between two intuitionistic trapezoidal fuzzy numbers, are introduced. Then information entropy method is used to determine the attribute weight, and the grey relational projection method combined grey relational analysis method and projection method is proposed, and to rank the alternatives are done by the relative closeness to PIS which combines grey relational projection values from the positive ideal solution and negative ideal solution to each alternative. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.     

Some geometric aggregation operators based on interval intuitionistic uncertain linguistic variables and their application to group decision making

With respect to multiple attribute group decision making (MAGDM) problems in which both the attribute weights and the expert weights take the form of crisp numbers, and attribute values take the form of interval-valued intuitionistic uncertain linguistic variables, some new group decision making analysis methods are developed. Firstly, some operational laws, expected value and accuracy function of interval-valued intuitionistic uncertain linguistic variables are introduced. Then, an interval-valued intuitionistic uncertain linguistic weighted geometric average (IVIULWGA) operator and an interval-valued intuitionistic uncertain linguistic ordered weighted geometric (IVIULOWG) operator have been developed. Furthermore, some desirable properties of the IVIULWGA operator and the IVIULOWG operator, such as commutativity, idempotency and monotonicity, have been studied, and an interval-valued intuitionistic uncertain linguistic hybrid geometric (IVIULHG) operator which generalizes both the IVIULWGA operator and the IVIULOWG operator, was developed. Based on these operators, an approach to multiple attribute group decision making with interval-valued intuitionistic uncertain linguistic information has been proposed. Finally, an illustrative example is given to verify the developed approaches and to demonstrate their practicality and effectiveness.     

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.     

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.     

Some interval-valued intuitionistic uncertain linguistic Choquet operators and their application to multi-attribute group decision making

In this study a generated admissible order between interval-valued intuitionistic uncertain linguistic numbers using two continuous functions is introduced. Then, two interval-valued intuitionistic uncertain linguistic operators called the interval-valued intuitionistic uncertain linguistic Choquet averaging (IVIULCA) operator and the interval-valued intuitionistic uncertain linguistic Choquet geometric mean (IVIULCGM) operator are defined, which consider the interactive characteristics among elements in a set. In order to overall reflect the correlations between them, we further define the generalized Shapley interval-valued intuitionistic uncertain linguistic Choquet averaging (GS-IVIULCA) operator and the generalized Shapley interval-valued intuitionistic uncertain linguistic Choquet geometric mean (GS-IVIULCGM) operator. Moreover, if the information about the weights of experts and attributes is incompletely known, the models for the optimal fuzzy measures on expert set and attribute set are established, respectively. Finally, a method to multi-attribute group decision making under interval-valued intuitionistic uncertain linguistic environment is developed, and an example is provided to show the specific application of the developed procedure.     

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。     

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.     

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.