直觉模糊优先有序加权距离算子及其在多属性群决策中的应用

在一些多属性群决策问题中,属性间可能存在一定的优先等级,因此在决策过程中有必要考虑属性间的优先关系。本文首先基于COWA算子定义了一种新的直觉模糊值间的距离。其次,基于属性间的优先关系,利用直觉模糊值的熵值给出多属性群决策问题中关联权重的计算方法。为了解决具有优先级的直觉模糊多属性群决策问题,定义了直觉模糊优先有序加权距离(IFPOWD)算子,并且提出了基于IFPOWD算子的多属性群决策方法。最后,运用实例证明了方法的有效性。     

以直觉模糊熵改进权重的模糊数据关联算法

针对多中心点的观测数据存在不确定性的问题,首先将观测数据和预测数据进行直觉模糊化,然后利用直觉模糊熵改进直觉模糊集的数据权重,再计算直觉模糊集之间的加权距离以获得观测与预测数据的隶属度,最后依次搜索最大隶属度实现观测与预测的关联.通过实例将改进的直觉模糊C-均值聚类(IFCM)算法应用于数据关联计算,计算结果表明,存在模糊观测数据情况下,可以比较好的处理距离的权重信息,并得到更好的处理结果,实例证明算法是可行的.     

毕达哥拉斯模糊软集的相似性测度及其应用

直觉模糊软集不能处理隶属度与非隶属度之和大于1的情况,且现有的直觉模糊软集的相似性测度只考虑了隶属度与非隶属度,忽视了犹豫度。针对以上问题,本文提出了一种基于隶属度、非隶属度以及犹豫度三个参数的毕达哥拉斯模糊软集的相似性测度和加权相似性测度。在为加权相似性测度的权重取值时,本文基于现有文献中直觉模糊熵存在的缺陷建立一种改进的直觉模糊熵,利用熵权法计算权重。分别讨论两相似性测度公式的性质,最后将两相似性侧度公式应用在建筑材料的模式识别问题中。     

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.     

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.     

权重为直觉模糊数的直觉模糊多属性群决策方法

针对属性权重以直觉模糊数形式给出的直觉模糊多属性群决策问题,提出了一种新的集成算子,首先证明了该算子具有诸如单调性等良好的性质,然后将该算子应用到权重为直觉模糊数的直觉模糊多属性群决策方法中,给出了决策方法的一般步骤,最后用实例说明了该方法的有效性和实用性.     

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.     

广义直觉模糊信息粒度

直觉模糊信息粒度是度量直觉模糊粒结构不确定性的一种重要方法。本文针对直觉模糊信息粒度在度量直觉模糊粒结构上存在的不足进行分析。首先,介绍直觉模糊粒结构距离。其次,改进了基于偏序关系提出的直觉模糊信息粒度的公理化定义,从直觉模糊粒结构距离观点出发,以最细的直觉模糊粒结构为参照物,计算每个直觉模糊粒结构与最细的直觉模糊粒结构之间的距离,距离的值越大,这个直觉模糊粒结构的信息粒度越大。最后,通过例子验证结论的合理性。     

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.     

直觉模糊事件概率测度熵

针对模糊熵对不确定系统描述的缺陷,引入直觉模糊事件及其概率测度的概念,并给出了直觉模糊子集概率测度熵的定义,运用直觉模糊事件及其概率测度的基本性质,推导出了直觉模糊概率测度熵的一些基本定理,为不确定信息的描述和处理提供新的思路.     

Interval-valued intuitionistic fuzzy combined weighted averaging operator for group decision making

Determining the attribute weights, in the multiple attribute group decision-making analysis with interval-valued intuitionistic fuzzy information, plays a crucial role because of its direct effect on the optimal alternative. In this paper, we develop a new attribute weight based on the support and entropy measure of attribute values. Then, the interval-valued intuitionistic fuzzy combined weighted averaging (IVIFCWA) operator is proposed and its some primary properties are discussed. The IVIFCWA operator’s attribute values take the form of interval-valued intuitionistic fuzzy numbers and the principal component of the interval-valued intuitionistic fuzzy number is fully taken into account. Finally, a numerical example concerning the investment strategy is given to illustrate the validity and applicability of the proposed method.     

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。     

Same families of geometric aggregation operators with intuitionistic trapezoidal fuzzy numbers

The aim of this work is to present some cases of aggregation operators with intuitionistic trapezoidal fuzzy numbers and study their desirable properties. First, some operational laws of intuitionistic trapezoidal fuzzy numbers are introduced. Next, based on these operational laws, we develop some geometric aggregation operators for aggregating intuitionistic trapezoidal fuzzy numbers. In particular, we present the intuitionistic trapezoidal fuzzy weighted geometric (ITFWG) operator, the intuitionistic trapezoidal fuzzy ordered weighted geometric (ITFOWG) operator, the induced intuitionistic trapezoidal fuzzy ordered weighted geometric (I-ITFOWG) operator and the intuitionistic trapezoidal fuzzy hybrid geometric (ITFHG) operator. It is worth noting that the aggregated value by using these operators is also an intuitionistic trapezoidal fuzzy value. Then, an approach to multiple attribute group decision making (MAGDM) problems with intuitionistic trapezoidal fuzzy information is developed based on the ITFWG and the ITFHG operators. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.     

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.     

Correlation coefficient of interval-valued intuitionistic fuzzy sets and its application to multiple attribute group decision making problems

In this paper, we investigate the group decision making problems in which all the 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 (IVIFN), 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 then we use the obtained attribute weights and the interval-valued intuitionistic fuzzy weighted geometric (IIFWG) operator to fuse the interval-valued intuitionistic fuzzy information in the collective interval-valued intuitionistic fuzzy decision matrix to get the overall interval-valued intuitionistic fuzzy values of alternatives, and then rank the alternatives according to the correlation coefficients between IVIFNs and select the most desirable one(s). Finally, a numerical example is used to illustrate the applicability of the proposed approach.     

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.     

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.     

区间直觉梯形模糊Bonferroni平均算子及在多属性群决策中的应用

针对决策信息为区间直觉梯形模糊数(IVITFN)且属性间存在相互关联的多属性群决策(MAGDM)问题,提出一种基于加权区间直觉梯形模糊Bonferroni平均(WIVITFBM)算子的决策方法.首先,基于IVITFN的运算法则和Bonferroni平均(BM)算子,定义了区间直觉梯形模糊Bonferroni平均(VITFBM)算子和WIVITFBM算子.然后,研究了这些算子的一些性质,建立基于WIVITFBM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。     

直觉模糊多属性的意见集中排序法

研究了属性权重信息不完全确定,属性值为直觉模糊集的多属性决策问题。首先根据直觉模糊数的得分函数和精确函数对决策矩阵中的评价值比较大小,进而按属性集中的每个属性对方案排成线性序;然后通过计算赋权模糊优先矩阵确定方案的优属度,建立规划模型确定属性的权重;再利用加权算术算子对方案集结,得到专家对方案的排序,从而得到一种新的意见集中排序的决策方法。数值实例说明该方法的有效性和实用性,可为解决直觉模糊多属性决策提供新方法