基于广义直觉语言算子的多属性群决策方法

针对属性权重未知,属性值为直觉语言数的多属性决策问题,提出了一种基于直觉语言熵和广义直觉语言算子的群决策方法.定义了直觉语言熵,并利用直觉语言熵确定属性权重,提出了三种直觉语言算子:广义直觉语言加权几何平均(GILWGA)算子、广义直觉语言有序加权几何(GILOWG)算子及广义直觉语言混合几何(GILHG)算子.利用GILWGA和GILHG算子集结信息,采用基于直觉语言数的得分函数及精确函数进行方案排序与择优,最后通过一个算例说明了该方法的有效性和合理性.     

毕达哥拉斯模糊优先集成算子及其决策应用

作为直觉模糊集的推广形式,毕达哥拉斯模糊数能更好地刻画现实中的不确定性,此外在某些问题上,方案的属性之间往往具有优先关系,针对此类信息的集成问题,将毕达哥拉斯模糊数与优先集成算子相结合,提出了毕达哥拉斯模糊优先集成算子,包括毕达哥拉斯模糊优先加权平均算子和毕达哥拉斯模糊优先加权几何算子,并讨论了这些算子的性质。在此基础上,提出了毕达哥拉斯模糊优先集成算子的多属性决策方法,最后将其应用于国内四家航空公司服务质量评价中,说明了该算子的有效性和可行性。     

基于OWA算子的不同形式偏好信息的群决策方法

研究具有不同形式偏好信息的群决策问题.在描述效用值、序关系值、模糊判断矩阵和AHP判断矩阵等4种形式偏好信息的基础上,首先给出将不同形式的偏好信息转化为模糊判断矩阵形式的计算公式,然后基于OWA算子给出集结各决策者偏好信息和方案优选的方法,最后用一个算例证明了所提出方法的有效性.     

Pythagorean模糊幂Bonferroni集成算子及其决策应用

结合幂平均与Bonferroni平均集成算子的优点,定义了毕达哥拉斯模糊幂Bonferroni平均和毕达哥拉斯模糊加权幂Bonferroni平均集成算子,其不仅考虑了数据信息之间的整体均衡性,还考虑了属性之间可能存在的相互关联关系。研究了这些集成算子的优良性质和特殊情形,并在此基础上提出了一种属性间存在相关性的毕达哥拉斯模糊多属性决策方法。将其应用于国内航空公司的服务质量评价中,并与现有方法进行分析比较,验证了所提方法的有效性和可行性。     

Support-intuitionistic模糊集集成算子及其决策应用

介绍Support-intuitionistic模糊集(SIFS)的概念,定义SIFS运算法则和客观权重,在此基础上提出SIFS加权算术平均算子和加权几何平均算子并证明相关定理。建立基于SIFS模糊信息的决策方法及定义SIFS得分函数和精确函数,利用SIFS支持度确定目标属性的权重使得属性权重成为客观值,加强集成结果的客观性。通过实例验证了该决策方法适用于处理基于SIFS模糊信息环境的决策问题。     

一种基于不确定信息的决策方法

提出了一种基于不确定信息的决策方法,该方法从统一决策模型的角度给出了候选决策集的构造方法、候选决策从证据焦元获得的属性级支持度的计算方法、决策矩阵的构造方法、候选决策获得的证据级支持度的计算方法等．该方法的特点在于将基元和非基元决策的选择问题统一起来加以考虑,另外,决策者可以通过设定模型中的函数形式,决定决策精度和决策风险之间的折衷策略。     

一种基于信息测度的多属性决策方法

单值中智集（SVN）可以用来表示现实情况中存在的不确定性和不一致信息。信息测度在支持向量网络理论中占有重要地位,近年来受到越来越多的关注。本文提出一种基于单值中智信息测度的多属性决策方法。首先介绍信息度量的3个公理化定义,其中包括熵、相似性测度和交叉熵。然后,基于余弦函数构造信息测度公式,进一步讨论熵、相似测度和交叉熵之间的关系及其相互转换。在此基础上,提出一种基于信息测度公式的单值中智集多属性决策方法。最后,给出城市污染评价的数值实例,论证该方法的适用性和有效性。     

基于信息熵的模糊多属性决策供应商选择方法

提出了一种针对供应商选择最优决策问题的基于信息熵的模糊多属性决策方法。针对供应商的多属性决策问题,确定属性集,利用信息熵求出各属性权重,运用模糊数排序方法对方案的模糊效用值进行排序,以确定最优方案。最后以某企业为例做了实例分析,将此方法应用于对这五个供应商进行评分排序,并从中选择出最为合适的供应商,表明此方法行之有效。     

A New Generalized Pythagorean Fuzzy Information Aggregation Using Einstein Operations and Its Application to Decision Making

The objective of this article is to extend and present an idea related to weighted aggregated operators from fuzzy to Pythagorean fuzzy sets (PFSs). The main feature of the PFS is to relax the condition that the sum of the degree of membership functions is less than one with the square sum of the degree of membership functions is less than one. Under these environments, aggregator operators, namely, Pythagorean fuzzy Einstein weighted averaging (PFEWA), Pythagorean fuzzy Einstein ordered weighted averaging (PFEOWA), generalized Pythagorean fuzzy Einstein weighted averaging (GPFEWA), and generalized Pythagorean fuzzy Einstein ordered weighted averaging (GPFEOWA), are proposed in this article. Some desirable properties corresponding to it have also been investigated. Furthermore, these operators are applied to decision‐making problems in which experts provide their preferences in the Pythagorean fuzzy environment to show the validity, practicality, and effectiveness of the new approach. Finally, a systematic comparison between the existing work and the proposed work has been given.     

Power Aggregation Operators of Simplified Neutrosophic Sets and Their Use in Multi-attribute Group Decision Making

The simplified neutrosophic set (SNS) is a useful generalization of the fuzzy set that is designed for some practical situations in which each element has different truth membership function, indeterminacy membership function and falsity membership function. In this paper, we develop a series of power aggregation operators called simplified neutrosophic number power weighted averaging (SNNPWA) operator, simplified neutrosophic number power weighted geometric (SNNPWG) operator, simplified neutrosophic number power ordered weighted averaging (SNNPOWA) operator and simplified neutrosophic number power ordered weighted geometric (SNNPOWG) operator. We present some useful properties of the operators and discuss the relationships among them. Moreover, an approach to multi-attribute group decision making (MAGDM) within the framework of SNSs is developed by the above aggregation operators. Finally, a practical application of the developed approach to deal with the problem of investment is given, and the result shows that our approach is reasonable and effective in dealing with uncertain decision making problems.      

Some Hesitant Fuzzy Einstein Aggregation Operators and Their Application to Multiple Attribute Group Decision Making

Hesitant fuzzy sets, as a new generalized type of fuzzy set, has attracted scholars’ attention due to their powerfulness in expressing uncertainty and vagueness. In this paper, motivated by the idea of Einstein operation, we develop a family of hesitant fuzzy Einstein aggregation operators, such as the hesitant fuzzy Einstein Choquet ordered averaging operator, hesitant fuzzy Einstein Choquet ordered geometric operator, hesitant fuzzy Einstein prioritized weighted average operator, hesitant fuzzy Einstein prioritized weighted geometric operator, hesitant fuzzy Einstein power weighted average operator, and hesitant fuzzy Einstein power weighted geometric operator. And we also study some desirable properties and generalized forms of these operators. Then, we apply these operators to deal with multiple attribute group decision making under hesitant fuzzy environments. Finally, a numerical example is provided to illustrate the practicality and validity of the proposed method.     

基于概率犹豫信息集成方法的群决策模型*

现有犹豫模糊集在描述决策信息时会导致决策信息大量损失,因此文中基于概率犹豫模糊信息集成算子,构建多属性群决策模型.首先在概率犹豫模糊环境下引入Archimedean范数,定义概率犹豫模糊运算法则.基于该运算法则,提出广义概率犹豫模糊有序加权平均(GPHFOWA)算子和广义概率犹豫模糊有序加权几何(GPHFOWG)算子,并讨论它们的基本性质.然后分析GPHFOWA算子和GPHFOWG算子的常见形式和相互关系.最后运用提出的2类算子构建概率犹豫模糊多属性群决策模型,并且通过供应商的选择实例验证决策模型的可行性和有效性.     

中小型制造企业供应伙伴选择的UVAHP群决策法

针对中小型制造企业零部件供应伙伴的选择问题,在分析AHP(层次分析法)优、缺点的基础上,提出了一种为克服AHP的缺点而采用不确定投票表决的方法来构造判断矩阵,且统一处理伙伴选择的各评价指标下的区间数值型属性值与不确定语言型属性值、增益指标属性值与损益指标属性值的UVAHP协作伙伴选择方法.给出了该方法的基本原理和基本步骤,建立了其相应的数学模型,并通过实例验证了其正确性.该方法对于中小型制造企业零部件供应商选择具有较高的参考价值.     

基于Vague集的模糊决策方法

目前在智能领域中对Vague集的研究已越来越广泛与深入．并运用于决策问题中．为了更加有效地进行模糊决策，提出了一个基于Vague集的模糊决策方法．在这个方法中，对约束条件，从它出现的可能性和不出现的可能性以及未知是否出现的可能性三个方面去综合处理．使得决策更加准确和有效．还给出了一个实例说明这种基于Vague集的模糊决策方法．这个基于Vague集的模糊决策方法的提出，为决策系统提供了一个有用的工具．     

一种基于混合多属性的VIKOR群决策方法

针对含有多种属性和混合评价信息群决策问题,提出一种基于直觉模糊VIOKR的评价方法.首先,将不同类型属性值转换为直觉模糊数处理混合评价信息,降低了评价的随机性和模糊性,接着建立最小偏差优化模型计算指标以及专家权重,解决了专家和属性的权重信息未知的问题;引入VIKOR理论集结评价值对评价对象进行评价排序,并与TOPSIS方法进行了对比,说明了本算法的可行性和可信度.最后以某型电源车虚拟训练系统为研究对象,对人员业务水平决策进行实例研究,结果表明该群决策方法能够有效实现决策,具有较好的工程应用价值.     

Majority Clusters‐Density Ordered Weighting Averaging: A Family of New Aggregation Operators in Group Decision Making

In the process of aggregation, it is necessary, especially for group decision‐making (GDM) problems, to consider distributed characteristic hidden in aggregates. In this case, clustering has been a common way for discovering the implicit distributed structures. This paper mainly investigates the characteristic of majority clusters, rather than majority elements and develops a new class of aggregation operators denominated majority clusters density‐ordered weighting averaging (MC‐DOWA) operators. Furthermore, we discuss properties of these operators and calculate the associated weights. Finally, a numerical example is provided to illustrate the application of the MC‐DOWA operators, and the aggregations are compared with those of the other three aggregation operators: majority additive‐OWA (MA‐OWA), dependent OWA (DOWA) and cluster‐based DOWA (Clus‐DOWA) operators.     

Linguistic Discriminative Aggregation in Multicriteria Decision Making

Several new aggregation operators are proposed in the context of multicriteria decision making (MCDM) in the linguistic domain. The proposed operators first infer the discrimination index, based on the extent of variability in the various linguistic evaluations against a criterion. This value is then utilized in the actual aggregation step to discriminate among the alternatives. Besides, the proposed operators also take into account the a priori weights associated with the criteria. The proposed concepts are illustrated through an example in group MCDM.     

基于Vague集的多准则模糊决策方法

基于Vague集的模糊决策方法的提出，为决策系统提供了一个有用的工具．对模糊条件下的多准则决策问题，指出了采用Vague集进行多准则模糊决策的现有计分函数的不足，根据Vague集的性质提出了二种新的方案选择方法：记分函数法和加权记分函数法。对已有的Vgue集记分函数法进行了分析与联系，并通过例子阐明本文方法的有效性和优越性．     

Intuitionistic Fuzzy Power Aggregation Operator Based on Entropy and Its Application in Decision Making

Atanassov's intuitionistic fuzzy set (IFS) is a generalization of a fuzzy set that can express and process uncertainty much better. There are various averaging operators defined for IFSs. In this paper, a new type of operator called an intuitionistic fuzzy entropy weighted power average ggregation operator is proposed. The entropy among IFSs is taken into consideration to determine the weights. What's more, the similarity is considered to measure the support degree between two elements of the IFS. Compared with other classical power average operators, the proposed operator is completely driven by data and fully takes into account the relationship among values. Finally, an illustrative example of multiple attribute group decision making is presented to show that the proposed operator is effective and practical.     

三角直觉模糊决策的权重函数方法

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。