三角模糊数直觉模糊Bonferroni平均算子及其应用

针对决策信息为三角模糊数直觉模糊数(TFNIFN)且属性间存在相互关联的多属性群决策(MAGDM)问题,提出了一种基于三角模糊数直觉模糊加权Bonferroni平均(TFNIFWBM)算子的决策方法。首先,基于TFNIFN的运算法则和Bonferroni平均(BM)算子,定义了三角模糊数直觉模糊BM算子和TFNIFWBM算子;然后,研究了这些算子的一些性质,建立基于TFNIFWBM算子的MAGDM模型,结合排序方法进行决策。最后通过MAGDM算例验证了该算子的有效性与可行性。     

模糊数直觉模糊几何集成算子及其在决策中的应用

模糊数直觉模糊集是直觉模糊集的拓展.针对模糊数直觉模糊信息的集成问题,定义了模糊数直觉模糊数的一些运算法则,基于这些法则给出了一些新的几何集成算子,即模糊数直觉模糊加权几何(FIFWG)算子、模糊数直觉模糊有序加权几何(FIFOWG)算子和模糊数直觉模糊混合几何(FIFHG)算子.在此基础上,提出一种属性权重确知且属性值以模糊数直觉模糊数形式给出的多属性群决策方法.最后通过实例分析结果证明了该方法的有效性.     

多属性群决策的直觉梯形模糊数法

采用直觉梯形模糊数刻画专家的评价信息,提出一种新的多属性群决策方法.定义了直觉梯形模糊数的期望值、预期得分、有序加权集成算子和混合集成算子;建立了基于直觉梯形模糊数的多属性群决策模型;通过混合集成算子得到方案的群体综合评估值,根据期望值和预期得分给出群决策结果.实例分析验证了所提出方法的有效性.     

基于区间直觉梯形模糊数的多属性决策方法

对区间直觉梯形模糊数进行研究．探讨了区间直觉梯形模糊数的运算法则及其性质;给出了区间直觉梯形模糊数的加权算术平均和加权几何平均算子,定义了区间直觉梯形模糊数的得分函数和精确函数,进而给出其排序方法;建立了基于区间直觉梯形模糊数的多属性决策模型,并提出了相应的决策方法．实例分析验证了所提出方法的有效性．     

基于二次规划的直觉模糊数的多属性决策方法

针对属性权重完全未知且属性值为直觉模糊数的多属性决策问题,提出了一种新的决策方法。首先引入了直觉模糊数的一些运算法则、得分函数和精确函数等概念。然后构建了一个二次规划模型,通过求解该模型获得属性的权重。接着利用直觉模糊加权平均(IFWA)算子对属性值进行集结,得到方案的综合属性值。最后利用得分函数和精确函数对方案进行排序并择优。给出的算例说明了该方法的实用性和可行性。     

直觉模糊数密度集成算子及其应用

针对有数据分布疏密偏好的直觉模糊问题,提出基于密度集成算子的集结方法.首先,借助差异度和相似度构建距离测度公式,结合树图思想给出一种简单的直觉模糊数聚类方法;然后,讨论决策者偏好与密度权向量的关系,并在此基础上定义两种新的算子-----直觉模糊密度加权平均集成算子和直觉模糊密度混合算术平均集成算子,后者具有更优良的性质.最后,通过算例验证了所提出方法的有效性.     

区间直觉模糊几何Bonferroni平均算子及其应用

研究了决策信息为区间直觉模糊数（IVIFN）且属性间存在相互关联的多属性群决策（MAGDM）问题,提出一种基于区间直觉模糊几何加权Bonferroni平均（IVIFGWBM）算子的决策方法。介绍了IVIFN的概念和运算法则,基于这些运算法则和几何Bonferroni平均（GBM）算子,定义了区间直觉模糊几何Bonferroni平均（IVIFGBM）算子和IVIFGWBM算子。研究了这些算子的一些性质,建立基于IVIFGWBM算子的MAGDM模型,结合排序方法进行决策。将该方法应用在一个MAGDM问题中,结果表明了该方法的有效性与可行性。     

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。     

直觉梯形模糊数MADM问题的灰色关联分析法

针对属性权重信息完全已知且属性值以直觉梯形模糊数形式给出的多属性决策问题,提出了一种灰色关联分析方法。首先给出了直觉梯形模糊数的定义、距离和性质,然后依据传统的灰色关联分析法的基本思想建立了直觉梯形模糊数多属性决策问题的决策步骤。最后给出了一个实例分析,其结果表明了该方法的实用性和有效性。     

基于直觉梯形模糊TOPSIS的多属性群决策方法

提出一种改进的逼近理想解排序(TOPSIS)方法,即直觉梯形模糊TOPSIS多属性群决策方法。首先,应用直觉梯形模糊数形式表示方案属性偏好和属性权重信息且专家权重完全未知;然后,利用直觉梯形模糊数间距离测度和期望值及直觉梯形模糊加权平均算子来确定决策者权重信息和属性权重信息;进而给出直觉梯形模糊环境下方案优选的算法;最后,通过算例进一步说明了该直觉梯形模糊TOPSIS方法的有效性。     

OWA aggregation of intuitionistic fuzzy sets

We recall the concept of an intuitionistic fuzzy subset (IFS). Fundamental to an IFS is the fact that it is defined using two values, a degree of membership and degree of non-membership. The ordered weighted averaging (OWA) operator is introduced and several of its features are described. Particularly notable is the idea of the dual of an OWA operator. We next discuss the aggregation of a collection of IFS using a prescribed OWA operator. It is shown that while the aggregation of the degrees of membership is performed using the prescribed OWA operator, the aggregation of the degrees of non-membership requires use of the dual of the prescribed OWA operator. The Choquet integral aggregation operator is introduced and applied to the aggregation of IFSs. Here again the concept of the dual is needed to perform the aggregation of the degrees of non-membership. We also discuss the aggregation of IFSs using the Sugeno integral. Fundamental to this work is our realisation of the importance of the concept of the dual operators in dealing with the aggregation of IFS.     

Induced intuitionistic fuzzy Choquet integral operator for multicriteria decision making

Yager (Fuzzy Sets, Syst 2003;137:59–69) extended the idea of order‐induced aggregation to the Choquet aggregation and defined induced Choquet ordered averaging operator. In this paper, an induced intuitionistic fuzzy Choquet (IFC) integral operator is proposed for the multiple criteria decision making. Some of its properties are investigated. Furthermore, an induced generalized IFC integral operator is introduced. It is worth mentioning that most of the existing intuitionistic fuzzy aggregation operators are special cases of this induced aggregation operator. A decision procedure based on the proposed induced aggregation operator is developed for solving the multicriteria decision‐making problem in which all the decision information is represented by intuitionistic fuzzy values. An illustrative example is given for demonstrating the applicability of the proposed decision procedure. © 2011 Wiley Periodicals, Inc.     

Two-tuple linguistic utility aggregation operator and its applications to group decision-making

This paper aims to develop an aggregation operator for two-tuple linguistic information based on utility function, which characterizes the influence of decision makers' psychological factors on the linguistic aggregation process. First, we propose a new two-tuple linguistic ordered utility aggregation (TOU) operator, and then, we investigate its properties that are suitable for any utility function. Subsequently, we derive a specific form of the TOU operator, which is called the two-tuple linguistic generalized ordered weighted utility averaging-hyperbolic absolute risk aversion (TOHU) operator, under the hyperbolic absolute risk aversion utility function. Then, we further investigate its families including a wide range of aggregation operators. To determine the weights of the TOHU operator, which take the form of two-tuple linguistic, we establish an optimization weighting model by combining the information of input arguments and subjective considerations of decision makers. Furthermore, we propose a two-tuple linguistic aggregation method to deal with the multiple attribute group decision-making (MAGDM) problem based on the TOHU operator. Finally, we provide an example to demonstrate the application of the TOHU operator to MAGDM.     

毕达哥拉斯犹豫模糊集成算子及其决策应用

针对毕达哥拉斯犹豫模糊多属性决策中,集成算子的重要作用以及集成算子不完善的情况,较为系统地研究了毕达哥拉斯犹豫模糊集成算子。为此,在毕达哥拉斯模糊数的运算和运算法则基础上,定义了毕达哥拉斯犹豫模糊有序加权平均算子（PHFOWA）、广义有序加权平均算子（GPHFOWA）和混合平均算子（PHFHA）,以及毕达哥拉斯犹豫模糊有序加权几何平均算子（PHFOWG）、广义有序加权几何平均算子（GPHFOWG）和混合几何平均算子（PHFHG）,并结合数学归纳法,分别给出了它们的计算公式,讨论了它们的有界性、单调性和置换不变性等性质。建立了基于毕达哥拉斯犹豫模糊集成算子的多属性决策方法,并应用算例和相关方法比较说明了决策方法的可行性与有效性。     

广义毕达哥拉斯模糊集成算子及其决策应用

研究毕达哥拉斯模糊决策环境下的集成算子及其决策应用.给出拟加权几何集成算子和拟有序加权几何算子的概念, 并分析 它们的性质.将有序加权平均算子、有序加权几何算子、拟有序加权平均算子和拟有序加权几何算子推广到毕达哥拉斯 模糊决策环境, 定义毕达哥拉斯模糊有序加权平均算子、广义毕达哥拉斯模糊有序加权平均算子、毕达哥拉斯模糊有序加权几何算子、广义毕达哥拉斯模糊有序加权几何 算子、拟毕达哥拉斯模糊有序加权平均算子和拟毕达哥拉斯模糊有序加权几何算子.提出基于广义毕达哥拉斯模糊集成算子的决策方法, 并通过实例验证其可行性.     

Induced Heavy Moving Averages

This paper presents the induced heavy ordered weighted moving average (IHOWMA) operator. It is an aggregation operator that uses the main characteristics of three well‐known techniques: the moving average, induced operator, and heavy aggregation operator. This operator provides a parameterized family of aggregation operators that include the minimum, the maximum, and total operator as special cases. It can be used in a selection process, considering that not all decision makers have the same knowledge and expectations of the future. The main properties of this operator are studied including a wide range of families of IHOWMA operators, such as the heavy ordered weighted moving average operator and uncertain induced heavy ordered weighted moving average operator. The IHOWMA operator is also extended using generalized and quasi‐arithmetic means. An example in an investment selection process is also presented.     

基于语言型混合算子的模糊信息聚合方法

在多属性决策过程中经常会用到聚合算子,有序加权平均聚合(OWA)算子是最常用的聚合算子之一,通常用于聚合确切的数值.然而,现实世界部分信息的不确定性以及决策者对一些信息的模糊性,使得部分信息不能用确切的数值表示,从而导致OWA算子及其扩展算子向着多元化发展.对此,给出一种语言型混合有序加权平均聚合(LHOWA)算子,同时研究该算子所应具备的一些基本性质,并给出一种基于该算子的语言型信息聚合方法,用于多属性决策过程中模糊信息的聚合.最后,通过一个煤矿安全评价的算例对所提出方法的优越性进行了验证.     

Fuzzy Generalized Prioritized Weighted Average Operator and its Application to Multiple Attribute Decision Making

The prioritized weighted average (PWA) operator was originally introduced by Yager. The prominent characteristic of the PWA operator is that it takes into account prioritization among attributes and decision makers. By combining the idea of generalized mean and PWA operator, we propose a new prioritized aggregation operator called fuzzy generalized prioritized weighted average (FGPWA) operator for aggregating triangular fuzzy numbers. The properties of the new aggregation operator are studied out and their special cases are examined. Furthermore, based on the FGPWA operator, an approach to deal with multiple attribute group decision making problems under triangular fuzzy environments is developed. Finally, a practical example is provided to illustrate the multiple attribute group decision making process.     

改进的区间犹豫算子应用于物流企业选择决策

针对现有区间犹豫模糊Hamacher算子存在的缺陷，构建了一种基于改进的区间犹豫模糊Hamacher加权算子的群决策方法。在分析现有区间犹豫模糊Hamacher算子不能满足幂等性的基础上，定义新的区间犹豫模糊Hamacher四则运算；提出两种改进的区间犹豫模糊Hamacher加权算子，包括改进的区间犹豫模糊Hamacher有序加权平均（I-IVHFHOWA）算子和改进的区间犹豫模糊Hamacher有序加权几何（I-IVHFHOWG）算子，并详细探究它们的常用算子形式以及算子之间的内在联系；建立基于I-IVHFHOWA算子和I-IVHFHOWG算子的物流企业选择决策模型，并通过实例说明模型的有效性。     

区间直觉语言Frank集结算子及其在决策中的应用

基于区间直觉语言变量和Frank算子的概念,首先提出区间直觉语言环境下Frank算子的运算规则;然后介绍几种区间直觉语言Frank信息集成算子,如:区间直觉语言Frank加权算术平均算子、区间直觉语言Frank加权几何平均算子、区间直觉语言广义Frank加权算术平均算子等,并介绍各算子具有的性质,同时,基于上述算子提出两种属性权重为实数且属性值为区间直觉语言变量的多属性决策方法;最后,结合示例表明所提出方法的有效性和实用性.