梯形模糊数直觉模糊Bonferroni平均算子及其应用

本文研究决策信息为梯形模糊数直觉模糊数(TFNIFN)且属性间存在相互关联的多属性群决策(MAGDM)问题,提出一种基于梯形模糊数直觉模糊加权Bonferroni平均(TFNIFWBM)算子的决策方法.首先,介绍了TFNIFN的概念和运算法则,基于这些运算法则和Bonferroni平均(Bonferroni mean,BM)算子,定义了梯形模糊数直觉模糊Bonferroni平均算子和TFNIFWBM算子.然后,研究了这些算子的一些性质,建立基于TFNIFWBM算子的多属性群决策模型,结合排序方法进行决策.最后,将该方法应用在MAGDM中,算例结果表明了该方法的有效性与可行性.     

三角直觉模糊决策的变权方法

研究了属性值为三角直觉模糊数的多属性决策问题,提出了一种基于变权综合的决策方法。首先,针对三角直觉模糊数,提出一种新的三角直觉模糊排序方法;其次,定义了三角直觉模糊变权加权算术平均算子和三角直觉模糊变权加权几何平均算子;然后,提出一种基于三角直觉模糊变权集成算子的多属性决策方法;最后,数值算例说明了该方法的有效性。     

Exponential operations for intuitionistic fuzzy numbers and interval numbers in multi-attribute decision making

Intuitionistic fuzzy numbers (IFNs) have already been applied to many fields, especially in multi-attribute decision making (MADM). Based on the basic operational laws and information aggregation methods of IFNs, MADM with intuitionistic fuzzy information has become more and more popular. In this paper, we investigate the MADM problems where the attribute values take the form of interval numbers and the weight information on the attributes are expressed as IFNs. We first propose a novel exponential operational law based on IFNs and interval numbers, and then study some of its desirable properties. Based on the exponential operational law, we put forward an intuitionistic fuzzy weighted exponential aggregation operator, and utilize it to develop a MADM method. Finally, we apply our method to solve the decision making problem under uncertainty.     

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     

直觉模糊熵与加权决策算法

直觉模糊熵是直觉模糊集理论中的一个重要概念,反映了直觉模糊集的模糊程度和不确定程度.首先给出一种新的直觉模糊熵,并运用到多属性直觉模糊决策问题中.决策时根据直觉模糊熵计算属性权重,再综合决策者的偏好对各属性权重进行修正,然后使用直觉模糊集结算子和得分函数对方案进行排序,从而获得最优方案.     

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.     

Multi-person multi-attribute decision making models under intuitionistic fuzzy environment

Intuitionistic fuzzy numbers, each of which is characterized by the degree of membership and the degree of non-membership of an element, are a very useful means to depict the decision information in the process of decision making. In this article, we investigate the group decision making problems in which all the information provided by the decision makers is expressed as intuitionistic fuzzy decision matrices where each of the elements is characterized by intuitionistic fuzzy number, and the information about attribute weights is partially known, which may be constructed by various forms. We first use the intuitionistic fuzzy hybrid geometric (IFHG) operator to aggregate all individual intuitionistic fuzzy decision matrices provided by the decision makers into the collective intuitionistic fuzzy decision matrix, then we utilize the score function to calculate the score of each attribute value and construct the score matrix of the collective intuitionistic fuzzy decision matrix. Based on the score matrix and the given attribute weight information, we establish some optimization models to determine the weights of attributes. Furthermore, we utilize the obtained attribute weights and the intuitionistic fuzzy weighted geometric (IFWG) operator to fuse the intuitionistic fuzzy information in the collective intuitionistic fuzzy decision matrix to get the overall intuitionistic fuzzy values of alternatives by which the ranking of all the given alternatives can be found. Finally, we give an illustrative example.     

基于区间粗糙直觉模糊数的多属性决策方法

研究了区间粗糙直觉模糊多属性决策。探讨了区间粗糙直觉模糊数的运算法则及其性质;定义了区间粗糙直觉模糊数的得分函数和精确函数,进而给出其排序方法;给出了区间粗糙直觉模糊数的变权算术平均和变权几何平均算子,并且建立了区间粗糙直觉模糊数的多属性决策模型;实例验证了所提出决策方法的有效性。     

基于集对分析联系数的信息不完全直觉模糊多属性决策

信息不完全直觉模糊多属性决策是一类不确定性决策问题,其不确定性来自属性权重信息不完全和属性值的直觉模糊数表示.为了系统地刻画直觉模糊多属性决策中的不确定性,避免直觉模糊多属性决策中利用得分函数做决策的片面性和不准确性,可以将信息不完全的权重和直觉模糊数表示的属性值转化成集对分析理论中的联系数,并建立信息不完全直觉模糊多属性决策模型,通过对不确定性进行分析后作出决策.实例应用表明该决策方法具有合理性和可行性.     

三角直觉模糊数型VIKOR方法

针对备选方案的属性值为三角直觉模糊数且权重为实数的多属性决策问题,研究了三角直觉模糊数型VIKOR方法。首先,本文提出了一种基于偏好指标的三角直觉模糊数排序方法;其次,根据VIKOR方法的基本思想,提出了求解三角直觉模糊数型VIKOR方法的步骤,并在可接受优势和决策过程的稳定条件下对备选方案进行排序,得到折衷解;最后,在最大群体效用权重为0.5的情况下,用第三方物流服务商选择为例说明了该方法的有效性和可行性。     

一种基于Choquet积分的多属性直觉模糊决策方法

研究了决策者对方案的主观偏好值以及属性值均为直觉模糊数的且属性间存在关联的多属性决策问题.利用Choquet模糊积分作为集结算子,构建了基于属性关联的M OD和SOD模型.通过求解模型获得属性的权重,进而给出了一种新的直觉模糊多属性决策方法.最后通过一个算例说明了该决策方法的有效性和可行性.     

基于模糊数直觉模糊PG算子的多属性决策方法

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PG(TFNIFPG)算子的决策方法.首先,基于TFNIFN的运算法则和PG(Power Geometric)算子,定义了TFNIFPG算子.然后,研究了该算子的一些性质,建立基于TFNIFPG算子的MAGDM模型,结合排序方法进行决策.最后通过某项目投资算例验证了该算子的有效性与可行性.     

三角模糊数直觉模糊PA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PA （TFNIFPA）算子的决策方法.首先,基于TFNIFN的运算法则和PA （Power Average）算子,定义了TFNIFPA算子.然后,研究了该算子的一些性质,建立基于TFNIFPA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.     

直觉模糊GM(1,1)模型及其在灰色发展决策的应用

研究了以直觉模糊数为对象的GM(1,1)模型并运用到灰色发展决策方法。利用灰色系统理论中核和灰度的内涵,将直觉模糊数的犹豫度和记分函数结合构建了直觉模糊数序列 GM(1,1)预测模型,从而实现了直觉模糊数的预测。在此基础上结合变权原理提出了基于直觉模糊数的灰色发展决策方法。最后,算例分析说明了该方法的合理性和可行性。     

基于直觉梯形模糊偏好相似度的多属性决策方法

在解决模糊多属性决策问题中,相似度是一种有效的方法.针对已有的相似度的不足,构造了一种新的两个矢量之间的相似度,证明其满足相似度的性质,并把它应用解决直觉梯形模糊偏好多属性决策问题.方法用语言值的直觉梯形模糊数来表示决策方案的信息,通过计算每个决策方案的期望矢量,与正理想方案和负理想方案的期望矢量的相对相似度,并由相对相似度大小来排列决策方案.最后用一案例来讨论方法的可行性,数值结果表明方法计算简单,实用性强.     

一种基于不完备直觉模糊信息的TOPSIS方法

多属性决策过程中,每个方案的属性值有时体现为由直觉模糊数所刻划的语言变量,通过定义直觉模糊数间的距离,首先提出了基于直觉模糊数的TOPSIS方法;其次,考虑到在实际问题中往往会遇到不完备直觉模糊信息的事实,提出一种将不完备直觉模糊数完备化的方法,并建立了基于不完备直觉模糊信息的TOPSIS方法,同时通过实例说明该方法的有效性以及在多属性决策中的应用.     

基于交叉影响的IFWGA算子及其在多属性决策中的应用

不同直觉模糊数在信息集结过程中,其隶属度与非隶属度之间可能存在着相互影响.提出了直觉模糊数上的改进的乘法运算和幂运算,重新给出了直觉模糊加权几何平均算子和直觉模糊有序加权几何平均算子的表达式,并研究了他们的一些性质.最后通过实例说明了新的IFWGA集成算子在多属性决策中的应用是可行和有效的.     

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.     

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.     

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.