基于混合型评价矩阵的多属性群决策方法

本文针对具有语言型、直觉模糊数和区间直觉模糊数三种评价信息的混合型多属性群决策问题, 提出一种基于属性权重和专家权重均未知的决策方法. 首先, 定义新的转换函数, 可将不同粒度的语言评价信息统一成区间直觉模糊数; 然后, 基于支持度确定未知属性权重, 并在综合考虑区间直觉模糊数熵值和相似度的基础上, 建立了一种新的专家权重确定模型; 在将混合型决策矩阵转换成区间直觉模糊决策矩阵后, 利用IIFWA算子依次集结个体决策矩阵, 从而得出方案集的排序. 最后, 应用在ERP选优问题中, 验证了方法的有效性.     

基于诱导型区间直觉模糊混合算子的群决策方法

针对属性值以区间直觉模糊数形式给出的多属性群决策问题,提出了两种融合信息更加全面的诱导型区间直觉模糊混合集结算子.利用提出的区间直觉模糊数的熵值度量方法来确定诱导变量,并结合基于支持度的数值依赖型集结算子,通过综合考虑位置、数据自身重要性及信息包含量,提出了诱导型区间直觉模糊混合平均(Ⅰ-ⅡFHA)算子和诱导型区间直觉模糊混合几何(Ⅰ-ⅡFHG)算子,分析了相关性质,进而给出一种区间直觉模糊多属性群决策方法,实例研究表明了所研方法的适应性与有效性.     

直觉不确定语言集成算子及在群决策中的应用

直觉不确定语言数是直觉模糊数和不确定语言变量值的拓展. 针对直觉不确定语言信息的集成问题, 定义了直觉不确定语言数运算法则和大小比较方法, 提出了直觉不确定语言的加权算术平均算子(IULWAA)、直觉不确定语言的有序加权平均算子(IULOWA)以及直觉不确定语言的混合加权平均算子(IULHA)及这些算子的性质. 在此基础上, 提出一种属性权重确知且属性值以直觉不确定语言数形式给出的多属性群决策方法. 最后通过实例分析证明了该方法的有效性.     

区间直觉纯语言信息的集结方法及其在群决策中的应用

对区间直觉纯语言信息的集结方法进行了研究.定义了区间直觉纯语言集及其运算法则和区间直觉纯语言变量的得分函数和精确函数,给出了一种简单的区间直觉纯语言变量的排序方法.进一步,提出了一些基于区间直觉纯语言信息及其运算法则的信息集结算子.在此基础上,给出了一种专家权重、属性权重及属性值均以语言标度形式给出的区间直觉纯语言信息集结方法,并将此方法应用到多属性群决策中.最后通过实例分析表明了该方法的有效性和可行性.     

基于直觉不确定语言新集成算子的多属性决策方法

对于直觉不确定语言环境下的多属性决策问题,给出一种基于直觉不确定语言变量新型集成算子的多属性决策方法.该方法采用阿基米德T-模和S-模定义直觉不确定语言变量的新运算法则,避免了现有运算法则不满足封闭性的不足;并基于新运算法则提出对权重进行自适应确定或调整的直觉不确定语言加权算术平均(IULWA)算子.以及定义直觉不确定语言变量新的期望值和精确值,给出直觉不确定语言变量的一种排序方法.进而提出一种属性权重值为实数且属性值为直觉不确定语言变量的多属性决策方法.最后,通过算例分析说明该方法的有效性和可行性.     

基于区间对偶犹豫不确定语言广义Banzhaf Choquet积分算子的多属性决策方法

基于将对偶犹豫模糊集和语言变量相结合定义对偶犹豫模糊语言集的思路,提出了区间对偶犹豫不确定语言集的概念,研究了区间对偶犹豫不确定语言变量相关的基本理论与方法,并针对属性值为区间对偶犹豫不确定语言信息的关联多属性决策问题,提出了相应的决策方法.首先,定义了区间对偶犹豫不确定语言变量的概念、运算法则、得分函数、精确函数、海明距离以及排序方法.然后,提出了区间对偶犹豫不确定语言广义Banzhaf Choquet积分算子并证明了该算子的一些性质.为了确定属性集的模糊测度,建立了基于离差最大化方法以及Banzhaf函数的模型.进而,给出一种用于解决属性权重部分未知,属性值为区间对偶犹豫不确定语言变量的关联多属性决策方法.最后,通过算例验证了该方法的有效性.     

基于熵最大化的区间直觉模糊多属性群决策方法

针对决策信息为区间直觉模糊数且属性权重完全未知的多属性群决策问题, 提出了一种基于信息熵的决策方法. 为保证决策的完善性, 首先从区间直觉模糊数的几何意义出发, 提出了一种相对合理的比较方法, 同时定义了一种区间直觉模糊矩阵的规范化方法, 并详细论证了方法的相关性质. 该方法不仅能够保证区间直觉模糊数的形式, 而且最大程度的降低了信息损失. 接着, 提出一种基于区间直觉模糊值熵最大化的权重确定方法, 最后, 将该方法应用在ERP选优的群决策问题中, 用一个实例验证了方法的有效性.     

一种基于区间直觉判断矩阵的群决策方法

提出了区间直觉偏好信息的有序加权集成算子和混合集成算子;定义了区间直觉判断矩阵及其得分矩阵和精确矩阵等新概念,详细研究了它们的性质;探讨了区间直觉判断矩阵、直觉判断矩阵以及互补判断矩阵之间的关系;基于算术集成算子和混合集成算子,给出了一种决策者对决策方案的偏好信息为区间直觉判断矩阵的群决策方法;最后,利用实例对方法的有效性进行了说明.     

一种基于粗集的残缺语言区间信息的多属性群决策方法

针对具有残缺语言区间信息的多属性群决策问题,提出了一种基于粗糙集理论的新的求解方法.对残缺语言区间信息多属性群决策问题进行了描述,采用LOWA算子将不同专家给出的评价信息集结为群体评价信息;通过计算不同方案之间的偏差来度量不同方案之间的相似性,对属性集进行约简,并确定属性权重;进一步地,通过计算每个方案的综合评价值判断方案优劣.最后,给出了一个算例.     

基于FV-OWA算子的不确定多属性决策方法

对基于模糊数Vague集的不确定多属性决策方法进行了研究.定义了模糊数Vague值的一些运算法则,基于这些法则,给出了一种模糊数Vague值的有序加权平均(FV-OWA)算子.基于FV-OWA算子,提出了一种属性权重完全未知、且方案的属性评估信息以模糊数Vague值形式给出的不确定多属性决策方法.最后,进行了实例分析.     

Approach to Group Decision Making Based on Interval-Valued Intuitionistic Judgment Matrices

In this article, the ordered weighted aggregation operator and hybrid aggregation operator are developed for aggregating interval-valued intuitionistic preference information. Interval-valued intuitionistic judgment matrix and its score matrix and accuracy matrix are defined. Some of their desirable properties are investigated in detail. The relationships among interval-valued intuitionistic judgment matrix, intuitionistic judgment matrix, and complement judgment matrix, are discussed. On the basis of the arithmetic aggregation operator and hybrid aggregation operator, an approach to group decision making with interval-valued intuitionistic judgment matrices is given. Finally, a practical example is provided to verify the effectiveness of the developed approach.     

Interval-valued intuitionistic fuzzy aggregation operators

The notion of the interval-valued intuitionistic fuzzy set (IVIFS) is a generalization of that of the Atanassov’s intuitionistic fuzzy set. The fundamental characteristic of IVIFS is that the values of its membership function and non-membership function are intervals rather than exact numbers. There are various averaging operators defined for IVIFSs. These operators are not monotone with respect to the total order of IVIFS, which is undesirable. This paper shows how such averaging operators can be represented by using additive generators of the product triangular norm, which simplifies and extends the existing constructions. Moreover, two new aggregation operators based on the ukasiewicz triangular norm are proposed, which are monotone with respect to the total order of IVIFS. Finally, an application of the interval-valued intuitionistic fuzzy weighted averaging operator is given to multiple criteria decision making.     

Some interval-valued intuitionistic uncertain linguistic hybrid Shapley operators

Two interval-valued intuitionistic uncertain linguistic hybrid operators cal ed the induced interval-valued intuitionistic uncertain linguistic hybrid Shapley averaging （I-IIULHSA） operator and the induced interval-valued intuitionistic uncertain linguistic hybrid Shapley geometric （I-IIULHSG） operator are defined. These operators not only reflect the importance of elements and their ordered positions, but also consider the correlations among elements and their ordered positions. Since the fuzzy measures are defined on the power set, it makes the problem exponentially complex. In order to simplify the complexity of solving a fuzzy measure, we further define the induced interval-valued intuitionistic uncertain linguistic hybrid λ-Shapley averaging （I-IIULHλSA） operator and the induced interval-valued intuitionistic uncertain linguistic hybrid λ-Shapley geometric （I-IIULHλSG） operator. Moreover, an approach for multi-attribute group decision making under the interval-valued intuitionistic uncertain linguistic environment is developed. Finally, a numerical example is provided to verify the developed procedure and demonstrate its practicality and feasibility.     

Aggregation and decision making using intuitionistic multiplicative triangular fuzzy information

The intuitionistic triangular fuzzy set is a generalization of the intuitionistic fuzzy set. In practical applications, we find that the results derived by using the traditional intuitionistic triangular fuzzy aggregation operators based on intuitionistic triangular fuzzy sets are sometimes inconsistent with intuition. To overcome this issue, based on the [1/9, 9] scale, we define the concepts of intuitionistic multiplicative triangular fuzzy set and intuitionistic multiplicative triangular fuzzy number, and then we discuss their operational laws and some desirable properties. Based on the operational laws, we develop a series of aggregation operators for intuitionistic multiplicative triangular fuzzy information, and then apply them to propose an approach to multi-attribute decision making under intuitionistic fuzzy environments. Finally, we use a practical example involving the evaluation of investment alternatives of an investment company to demonstrate our aggregation operators and decision making approach.     

Generalization of the linguistic aggregation operator and its application in decision making

A generalization of the linguistic aggregation functions (or operators) is presented by using generalized and quasiarithmetic means.Firstly,the linguistic weighted generalized mean (LWGM) and the linguistic generalized ordered weighted averaging (LGOWA) operator are introduced.These aggregation functions use linguistic information and generalized means in the weighted average (WA) and in the ordered weighted averaging (OWA) function.They are very useful for uncertain situations where the available information cannot be assessed with numerical values but it is possible to use linguistic assessments.These aggregation operators generalize a wide range of aggregation operators that use linguistic information such as the linguistic generalized mean (LGM),the linguistic OWA (LOWA) operator and the linguistic ordered weighted quadratic averaging (LOWQA) operator.We also introduce a further generalization by using quasi-arithmetic means instead of generalized means obtaining the quasi-LWA and the quasi-LOWA operator.Finally,we develop an application of the new approach where we analyze a decision making problem regarding the selection of strategies.