基于区间二元语义偏好关系一致性偏差的群决策方法

为了避免群决策过程中信息的损失和集结结果的不精确性,将诱导有序加权平均(IOWA)算子和连续区间有序加权平均(C-OWA)算子拓展至区间二元语义环境中,提出一种诱导连续区间二元语义有序加权平均(IC2TLOWA)算子。针对区间二元语义偏好关系提出连续二元语义偏好关系的概念,定义基于连续二元语义偏好关系一致性偏差的诱导连续区间二元语义有序加权平均(CI-IC2TLOWA)算子,并提出一种基于该算子的区间二元语义群决策方法.最后通过算例说明该方法的可行性和有效性。     

航空维修信息系统的一种事前评价方法

融合目标规划、网络分析法和集结算子,提出一种航空维修信息系统的事前评价方法.用目标规划处理资源约束,用网络分析法处理相关性,用集结算子将评价者的评价信息集结成群评价信息.选择诱导有序加权欧氏平均算子作为集结算子,并与已有的诱导有序加权调和平均算子、诱导有序加权几何平均算子、诱导有序加权平均算子三种算子进行了对比,结果表明新算子的有效性.给出保序条件下数据分量的可变范围.     

基于改进灰色关联度的IOWA算子最优组合预测模型

通过引进诱导有序加权平均(IOWA)算子和改进灰色关联度的计算式,提出了新的基于改进灰色关联度的IOWA算子的组合预测模型.方法可以克服传统的组合预测方法赋予不变的加权平均系数和以单一误差指标作为预测精度衡量的缺陷.定义基于改进灰色关联度的IOWA算子的优性组合预测的概念,最后给出实例分析表明了新模型能有效地提高组合预测精度.     

基于IOWC-GOWMA算子和指数支撑度的区间型组合预测模型北大核心

将连续区间的广义有序加权多重平均(C-GOWMA)算子和诱导有序加权平均(IOWA)算子相结合,提出一种新的诱导有序加权连续区间广义有序加权多重平均(IOWC-GOWMA)算子,该算子同时考虑区间数自身、数据位置两个因素,可以将区间数转换成实参数,进一步构建基于IOWC-GOWMA算子和指数支撑度的区间型组合预测模型。最后通过实例分析说明该区间组合预测模型的合理性和有效性,并对参数进行了详细的灵敏度分析。     

基于Sugeno测度的半一致模有序加权平均算子及其递归集成器设计

在提出和研究基于Sugeno测度的半一致模有序加权平均算子的基础上,结合基于Sugeno测度的半一致模有序加权平均算子orness测度的特点,在假定基于Sugeno测度的半一致模有序加权平均算子orness测度不变的条件下,对基于非可加测度的半一致模有序加权平均算子的递归集成器进行了设计,提出和研究了递归集成原理,讨论了其计算方法及相关性质。     

Research on Compatibility and Consistency of Combination Judgment Matrices with Multi-granularity Linguistic Terms Based on 1-LIOWA Operators

定义了多粒度语言判断矩阵的基于专家重要性的语言诱导有序加权平均(I-LIOWA)算子的概念,利用I-LIOWA算子集结基于不同粒度语言判断矩阵而得到组合语言判断矩阵,并且研究了组合语言判断矩阵、其导出矩阵和特征矩阵的之间相容性和一致性的一些性质,为群决策中使用语言偏好信息提供了理论依据.     

广义毕达哥拉斯正态模糊集成算子及其决策应用

将毕达哥拉斯模糊数与直觉正态模糊数相结合,提出了毕达哥拉斯正态模糊数,研究了其运算和运算性质,定义了毕达哥拉斯正态模糊数的得分函数和精确函数,实现其大小排序.然后,针对毕达哥拉斯正态模糊信息的集成问题,提出毕达哥拉斯正态模糊有序加权平均(PNFOWA)算子、广义有序加权平均(GPNFOWA)算子和毕达哥拉斯正态模糊有序加权几何平均(PNFOWGA)算子及广义有序加权几何平均(GPNFOWGA)算子,并研究了其性质.最后,提出基于广义毕达哥拉斯正态模糊集成算子的多属性决策方法,并通过实例说明该方法的有效性.     

基于广义WOWA算子的Pythagorean模糊决策方法

针对Pythagorean模糊信息的决策问题,构建广义Pythagorean模糊信息加权有序加权平均(PF-GWOWA)算子。首先,提出PF-GWOWA算子,并证明Pythagorean模糊广义加权平均(PF-GWA)算子、Pythagorean模糊加权有序加权平均(PF-WOWA)算子与Pythagorean模糊加权平均(PF-WA)算子均为PF-GWOWA算子的特例;其次,根据GWOWA算子属性综合权重计算模型,利用PF-GWOWA算子对信息进行集结;最后,通过算例分析和传统方法对比,说明本文提出方法的合理性与有效性。     

基于专家重要性的语言诱导有序加权平均算子的多粒度语言组合判断矩阵的相容性和一致性

定义了多粒度语言判断矩阵的基于专家重要性的语言诱导有序加权平均(I-LIOWA)算子的概念,利用I-LIOWA算子集结基于不同粒度语言判断矩阵而得到组合语言判断矩阵,并且研究了组合语言判断矩阵、其导出矩阵和特征矩阵的之间相容性和一致性的一些性质,为群决策中使用语言偏好信息提供了理论依据。     

区间直觉正态模糊数集成算子及其在决策中的应用

研究了区间直觉正态模糊数(IVINFN)决策信息及其集成算子。首先,定义了区间直觉正态模糊数的概念,提出了运算法则;其次,给出了区间直觉正态模糊数诱导有序加权平均(IVINFN-IOWA)算子和区间直觉正态模糊数诱导有序加权几何(IVINFN-IOWGA)算子的概念,探讨了其性质;在此基础上,分别定义了基于均值和标准差的区间直觉正态模糊数的得分函数和精确函数,给出其排序方法。最后,针对属性值为区间直觉正态模糊数且权重已知的多属性决策问题,给出了其决策方法,并进行了实例分析,结果表明该决策方法是有效的。     

基于Theil不等系数的IOWHA算子组合预测模型及其应用

Theil不等系数是一种度量预测精度的另一种相关性指标,将Theil不等系数和IOWHA算子的概念相结合,提出一种新的基于Theil不等系数的IOWHA算子最优组合预测模型,并定义了优性组合预测的概念.利用该模型对税收收入进行了组合预测,结果表明该组合预测方法是可行和有效的,且该模型是一种优性组合预测.     

诱导有序加权平均算子在水资源状况评估中的应用

水资源短缺风险状况评价是一项多目标的复杂决策过程,在水资源短缺风险评价的层次分析决策中应用协商评价确定各属性的权重.对评价者给出的区间赋值信息进行分类,确定各类信息的协商区间和协商值;然后利用所导出的有序加权平均(IOWA)算子对各类信息的协商区间和协商值进行集成,在此基础上提出了一种确定协商评价问题属性权重的方法,实例分析证明该方法具有实用性和可操作性是可行的.     

基于COWA算子的不同类型残缺判断矩阵集结方法

本文研究了决策信息以残缺不确定判断矩阵形式给出的群体决策问题。将残缺不确定区间互反判断矩阵转化为残缺不确定区间互补判断矩阵。基于COWA算子,定义了期望值函数,把残缺不确定区间互反判断矩阵转化成残缺实判断矩阵进行排序,减少了决策信息的丢失。利用IOWA算子来集结群体判断矩阵。最后通过算例说明了该方法的可行性和有效性。     

基于IOWA算子的欧式范数综合评价方法

针对综合评价信息不完整、分布不均匀以及现实中人们总是主观性地经常“向后看”这一问题,提出了基于区间数有序加权平均算子(IOWA算子)的欧式范数综合评价方法。本文首先介绍了IOWA算子的相关知识;然后依据IOWA算子的特点,运用正态分布确定其位置加权向量,并与欧式范数结合形成加权欧式范数;最后运用一个算例验证了方法的有效性,既能充分考虑评价信息的分布情况,又使得评价更加客观准确。     

Induced aggregation operators in the VIKOR method and its application in material selection

In this paper, a hybrid decision making approach integrating induced aggregation operators into VIKOR is proposed for tackling multicriteria problems with conflicting and noncommensurable (different units) criteria. For doing so, we develop a new distance aggregation operator called the induced ordered weighted averaging standardized distance (IOWASD) operator. It is an aggregation operator that provides a wide range of standardized distance measures between the maximum and the minimum by using the induced OWA (IOWA) operator. The main advantage of the IOWA-based VIKOR (IOWA-VIKOR) is that it is able to reflect the complex attitudinal character of the decision maker by using order inducing variables and provide much more complete information for decision making. We also studied some of the IOWASD’s main properties and different particular cases and further generalized it by using the induced generalized OWA (IGOWA) operator. Finally, we apply the integrated IOWA-VIKOR method in a multi-criteria decision making problem regarding the selection of materials and the results are compared for different types of standardized distance aggregation operators.     

Continuous interval-valued intuitionistic fuzzy aggregation operators and their applications to group decision making

In this paper, we introduce a new operator called the continuous interval-valued intuitionistic fuzzy ordered weighted averaging (C-IVIFOWA) operator for aggregating the interval-valued intuitionistic fuzzy values. It combines the intuitionistic fuzzy ordered weighted averaging (IFOWA) operator and the continuous ordered weighted averaging (C-OWA) operator by a controlling parameter, which can be employed to diminish fuzziness and improve the accuracy of decision making. We further apply the C-IVIFOWA operator to the aggregation of multiple interval-valued intuitionistic fuzzy values and obtain a wide range of aggregation operators including the weighted C-IVIFOWA (WC-IVIFOWA) operator, the ordered weighted (OWC-IVIFOWA) operator and the combined C-IVIFOWA (CC-IVIFOWA) operator. Some desirable properties of these operators are investigated. And finally, we give a numerical example to illustrate the applications of these operators to group decision making under interval-valued intuitionistic fuzzy environment.     

Multi-criteria decision-making method based on normal intuitionistic fuzzy-induced generalized aggregation operator

Normal intuitionistic fuzzy numbers (NIFNs), which use normal fuzzy numbers to express their membership and non-membership functions, can reflect the evaluation information exactly in different dimensions. In this paper, we are committed to apply NIFNs to multi-criteria decision-making (MCDM) problems, and meanwhile some new aggregation operators are proposed, including normal intuitionistic fuzzy weighted arithmetic averaging operator, normal intuitionistic fuzzy weighted geometric averaging operator, normal intuitionistic fuzzy-induced ordered weighted averaging operator, normal intuitionistic fuzzy-induced ordered weighted geometric averaging operator and normal intuitionistic fuzzy-induced generalized ordered weighted averaging operator (NIFIGOWA). Based on the NIFIGOWA operator, an approach is introduced to solve MCDM problems where the criteria values are NIFNs and the criteria weight information is fixed. Finally, the proposed method is compared to the existing methods by virtue of a numerical example to verify its feasibility and rationality.     

The OWA-based consensus operator under linguistic representation models using position indexes

When using linguistic approaches to solve decision problems, we need linguistic representation models. The symbolic model, the 2-tuple fuzzy linguistic representation model and the continuous linguistic model are three existing linguistic representation models based on position indexes. Together with these three linguistic models, the corresponding ordered weighted averaging operators, such as the linguistic ordered weighted averaging operator, the 2-tuple ordered weighted averaging operator and the extended ordered weighted averaging operator, have been developed, respectively. In this paper, we analyze the internal relationship among these operators, and propose a consensus operator under the continuous linguistic model (or the 2-tuple fuzzy linguistic representation model). The proposed consensus operator is based on the use of the ordered weighted averaging operator and the deviation measures. Some desired properties of the consensus operator are also presented. In particular, the consensus operator provides an alternative consensus model for group decision making. This consensus model preserves the original preference information given by the decision makers as much as possible, and supports consensus process automatically, without moderator.     

Multiple criteria decision making method based on normal interval‐valued intuitionistic fuzzy generalized aggregation operator

On the basis of the normal intuitionistic fuzzy numbers (NIFNs), we proposed the normal interval‐valued intuitionistic fuzzy numbers (NIVIFNs) in which the values of the membership and nonmembership were extended to interval numbers. First, the definition, the properties, the score function and accuracy function of the NIVIFNs are briefly introduced, and the operational laws are defined. Second, some aggregation operators based on the NIVIFNs are proposed, such as normal interval‐valued intuitionistic fuzzy weighted arithmetic averaging operator, normal interval‐valued intuitionistic fuzzy ordered weighted arithmetic averaging operator, normal interval‐valued intuitionistic fuzzy hybrid weighted arithmetic averaging operator, normal interval‐valued intuitionistic fuzzy weighted geometric averaging operator, normal interval‐valued intuitionistic fuzzy ordered weighted geometric averaging operator, normal interval‐valued intuitionistic fuzzy hybrid weighted geometric averaging operator, and normal interval‐valued intuitionistic fuzzy generalized weighted averaging operator, normal interval‐valued intuitionistic fuzzy generalized ordered weighted averaging operator, normal interval‐valued intuitionistic fuzzy generalized hybrid weighted averaging operator, and some properties of these operators, such as idempotency, monotonicity, boundedness, commutativity, are studied. Further, an approach to the decision making problems with the NIVIFNs is established. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness. © 2015 Wiley Periodicals, Inc. Complexity 21: 277–290, 2016