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。     

区间直觉乘法偏好信息下的多属性决策方法

对直觉乘法集（intuitionistic multiplicative set）进行推广,提出了区间直觉乘法集的概念。为了表达方便,定义了区间直觉乘法数,给出了区间直觉乘法数的基本运算法则。定义了区间直觉乘法数的得分函数和精确函数,并给出了区间直觉乘法数的一种排序方法。定义了区间直觉乘法数的加权平均算子和加权几何算子,进而给出决策者对方案的偏好信息以区间直觉乘法数给出的决策方法,并进行实例分析。     

区间直觉梯形模糊几何Heronian平均算子及应用

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,提出了一种区间直觉梯形模糊几何加权Heronian平均算子（IVITFGWHM）的决策方法。基于IVITFN的运算法则和几何Heronian平均（GHM）算子,定义了IVITFGHM算子和IVITFGWHM算子。研究了这些算子的一些性质,建立基于IVITFGWHM算子的MAGDM模型,结合排序方法进行决策。通过MAGDM算例验证了该算子的有效性与可行性。     

C-POWGA算子及其在不确定多属性决策中的应用

为了降低不确定多属性决策中区间决策信息集成时的计算复杂度,将连续区间有序加权几何平均（C-OWGA）算子和Power几何平均算子相结合,提出一种连续区间Power有序加权几何平均（C-POWGA）算子,并提出了一种基于C-POWGA算子的不确定多属性群决策方法;通过某银行的员工绩效考核来说明该方法的可行性和有效性。     

基于标准否定函数的WIC-IVIFOWA算子及其应用

首先,通过实例探究现存连续区间直觉模糊有序加权平均(C-IVIFOWA)算子的不足,引入标准否定函数(standard negation),构造对偶连续区间有序加权平均(DC-OWA)算子,进而提出改进的连续区间直觉模糊有序加权平均(IC-IVIFOWA)算子;然后,针对多个区间直觉模糊评价信息的集结问题,基于IC-IVIFOWA算子提出改进的加权连续区间直觉模糊有序加权平均(WIC-IVIFOWA)算子,证明了算子的相关性质;最后,运用WIC-IVIFOWA算子提出一种区间直觉模糊多属性决策方法,并通过实例表明所提出方法的有效性.     

一种基于区间灰色语言变量几何加权集成算子的 多属性群决策方法

针对属性值和属性权重均为区间灰色语言变量的多属性群决策问题,提出一种基于区间灰色语言变量的加权几何集成算子的多属性群决策方法.首先,给出区间灰色语言变量的定义和运算规则;然后详细介绍了区间灰色语言变量加权几何集成算子、区间灰色语言变量有序加权几何集成算子、区间灰色语言变量混合加权几何集成算子,以及利用这些算子进行群决策的方法;最后,通过实例说明了所提出方法的决策步骤,并验证了方法的有效性.     

基于诱导型直觉不确定语言集成算子的应急预案评估群决策方法

针对在应急预案评估决策中,决策信息以直觉不确定语言数形式表征的多属性群决策问题,提出了基于诱导型直觉不确定语言集成算子的应急预案评估群决策方法。在直觉不确定语言数的运算法则基础上构建了诱导型直觉不确定语言有序加权平均(I-IULOWA)算子、诱导型直觉不确定语言有序加权几何(I-IULOWG)算子、诱导型直觉不确定语言混合加权(I-IULHA)算子和诱导型直觉不确定语言混合加权几何(I-IULHG)算子,探讨上述算子的若干性质及一些特例;同时,给出了基于距离测度的方法来确定属性权重。最后,通过具体的应急突发事件案例验证该方法的可行性和有效性。     

区间直觉模糊连续熵及其多属性决策方法

提出了区间直觉模糊连续熵,并且研究了一种新的处理区间直觉模糊多属性决策问题的方法。基于连续有序加权平均（COWA）算子,给出了区间直觉模糊连续熵的概念,并且证明了区间直觉模糊连续熵满足区间直觉模糊熵的公理化定义的四个条件。在此基础上,针对属性权重信息完全未知的决策问题,通过衡量每一属性所含的信息量来确定属性权重。依据备选方案与理想方案间的加权相关系数,给出了一种新的区间直觉模糊多属性决策方法。实验结果验证了新的决策方法的可行性和有效性。     

区间直觉二元语言集成算子及其群决策方法

基于下标以零为中心对称的语言评估标度,将区间不确定二元语言集与区间直觉模糊集结合,提出区间直觉二元语言集及变量的概念;讨论区间直觉二元语言变量的运算及可能度;提出区间直觉二元语言加权算术平均算子、区间直觉二元语言有序加权平均算子,并在此基础上,通过可能度矩阵对区间直觉二元语言变量进行排序提出区间直觉二元语言混合加权平均算子;最后基于这些算子构建了一种新的直觉模糊多属性群决策方法,并将其运用于供应商选择过程中。     

基于不同类型残缺判断矩阵的群决策方法

定义了一系列残缺不确定判断矩阵的概念，并且定义了一种连续区间数据有序加权几何（C-OWG）算子．利用连续区间数据有序加权平均（C-OWA）子和C-OWG算予等转化途径把不同类型的残缺不确定判断矩阵均一致化为残缺期望值互补判断矩阵，进而提出一种基于不同类型残缺判断矩阵的群决策方法．最后通过实例验证了方法的可行性和有效性．     

Some induced geometric aggregation operators with intuitionistic fuzzy information and their application to group decision making

With respect to multiple attribute group decision making (MAGDM) problems in which both the attribute weights and the expert weights take the form of real numbers, attribute values take the form of intuitionistic fuzzy numbers or interval-valued intuitionistic fuzzy numbers, some new group decision making analysis methods are developed. Firstly, some operational laws, score function and accuracy function of intuitionistic fuzzy numbers or interval-valued intuitionistic fuzzy numbers are introduced. Then two new aggregation operators: induced intuitionistic fuzzy ordered weighted geometric (I-IFOWG) operator and induced interval-valued intuitionistic fuzzy ordered weighted geometric (I-IIFOWG) operator are proposed, and some desirable properties of the I-IFOWG and I-IIFOWG operators are studied, such as commutativity, idempotency and monotonicity. An I-IFOWG and IFWG (intuitionistic fuzzy weighted geometric) operators-based approach is developed to solve the MAGDM problems in which both the attribute weights and the expert weights take the form of real numbers, attribute values take the form of intuitionistic fuzzy numbers. Further, we extend the developed models and procedures based on I-IIFOWG and IIFWG (interval-valued intuitionistic fuzzy weighted geometric) operators to solve the MAGDM problems in which both the attribute weights and the expert weights take the form of real numbers, attribute values take the form of interval-valued intuitionistic fuzzy numbers. Finally, some illustrative examples are given to verify the developed approach and to demonstrate its practicality and effectiveness.     

Some induced intuitionistic fuzzy aggregation operators applied to multi-attribute group decision making

In this paper, we define various induced intuitionistic fuzzy aggregation operators, including induced intuitionistic fuzzy ordered weighted averaging (OWA) operator, induced intuitionistic fuzzy hybrid averaging (I-IFHA) operator, induced interval-valued intuitionistic fuzzy OWA operator, and induced interval-valued intuitionistic fuzzy hybrid averaging (I-IIFHA) operator. We also establish various properties of these operators. And then, an approach based on I-IFHA operator and intuitionistic fuzzy weighted averaging (WA) operator is developed to solve multi-attribute group decision-making (MAGDM) problems. In such problems, attribute weights and the decision makers' (DMs') weights are real numbers and attribute values provided by the DMs are intuitionistic fuzzy numbers (IFNs), and an approach based on I-IIFHA operator and interval-valued intuitionistic fuzzy WA operator is developed to solve MAGDM problems where the attribute values provided by the DMs are interval-valued IFNs. Furthermore, induced intuitionistic fuzzy hybrid geometric operator and induced interval-valued intuitionistic fuzzy hybrid geometric operator are proposed. Finally, a numerical example is presented to illustrate the developed approaches.     

A possibility degree method for interval-valued intuitionistic fuzzy multi-attribute group decision making

The ranking of interval-valued intuitionistic fuzzy sets (IVIFSs) is very important for the interval-valued intuitionistic fuzzy decision making. From the probability viewpoint, the possibility degree of comparison between two interval-valued intuitionistic fuzzy numbers (IVIFNs) is defined by using the notion of 2-dimensional random vector, and a new method is then developed to rank IVIFNs. Hereby the ordered weighted average operator and hybrid weighted average operator for IVIFNs are defined based on the Karnik–Mendel algorithms and employed to solve multi-attribute group decision making problems with IVIFNs. The individual overall attribute values of alternatives are obtained by using the weighted average operator for IVIFNs. By using the hybrid weighted average operator for IVIFNs, we can obtain the collective overall attribute values of alternatives, which are used to rank the alternatives. A numerical example is examined to illustrate the effectiveness and flexibility of the proposed method in this paper.     

区间直觉模糊信息的集成方法及其在决策中的应用

对区间直觉模糊信息的集成方法进行了研究.定义了区间直觉模糊数的一些运算法则,并基于这些运算法则,给出区间直觉模糊数的加权算术和加权几何集成算子.定义了区间直觉模糊数的得分函数和精确函数,进而给出了区间直觉模糊数的一种简单的排序方法.最后提供了一种基于区间直觉模糊信息的决策途径,并进行了实例分析.     

Multiattribute decision making based on interval-valued intuitionistic fuzzy values

In this paper, we present a new multiattribute decision making method based on the proposed interval-valued intuitionistic fuzzy weighted average operator and the proposed fuzzy ranking method for intuitionistic fuzzy values. First, we briefly review the concepts of interval-valued intuitionistic fuzzy sets and the Karnik–Mendel algorithms. Then, we propose the intuitionistic fuzzy weighted average operator and interval-valued intuitionistic fuzzy weighted average operator, based on the traditional weighted average method and the Karnik–Mendel algorithms. Then, we propose a fuzzy ranking method for intuitionistic fuzzy values based on likelihood-based comparison relations between intervals. Finally, we present a new multiattribute decision making method based on the proposed interval-valued intuitionistic fuzzy weighted average operator and the proposed fuzzy ranking method for intuitionistic fuzzy values. The proposed method provides us with a useful way for multiattribute decision making based on interval-valued intuitionistic fuzzy values.     

Interval-valued intuitionistic fuzzy Frank aggregation operators and their applications to multiple attribute group decision making

Interval-valued intuitionistic fuzzy numbers (IVIFNs), which contain three ranges: the membership degree range, the non-membership degree range, and the hesitancy degree range, are very suitable to be used for depicting uncertain or fuzzy information. In this paper, we study the aggregation techniques of IVIFNs with the help of Frank operations. We first extend the Frank t-conorm and t-norm to interval-valued intuitionistic fuzzy environments and introduce several new operations of IVIFNs, such as Frank sum, Frank product, Frank scalar multiplication, and Frank exponentiation, based on which we develop several new interval-valued intuitionistic fuzzy aggregation operators, including the interval-valued intuitionistic fuzzy Frank weighted averaging operator and the interval-valued intuitionistic fuzzy Frank weighted geometric operator. We further establish various properties of these operators, give some special cases of them, and analyze the relationships between these operators. Moreover, we apply these operators to develop an approach for dealing with multiple attribute group decision making with interval-valued intuitionistic fuzzy information. Finally, a numerical example is provided to illustrate the practicality and effectiveness of the developed operators and approach.

     

An approach for multiple attribute group decision making problems with interval-valued intuitionistic trapezoidal fuzzy numbers

This article proposes an approach to resolve multiple attribute group decision making (MAGDM) problems with interval-valued intuitionistic trapezoidal fuzzy numbers (IVITFNs). We first introduce the cut set of IVITFNs and investigate the attitudinal score and accuracy expected functions for IVITFNs. Their novelty is that they allow the comparison of IVITFNs by taking into accounting of the experts’ risk attitude. Based on these expected functions, a ranking method for IVITFNs is proposed and a ranking sensitivity analysis method with respect to the risk attitude is developed. To aggregate the information with IVITFNs, we study the desirable properties of the interval-valued intuitionistic trapezoidal fuzzy weighted geometric (IVITFWG) operator, the interval-valued intuitionistic trapezoidal fuzzy ordered weighted geometric (IVITFOWG) operator, and the interval-valued intuitionistic trapezoidal fuzzy hybrid geometric (IVITFHG) operator. It is worth noting that the aggregated value by using these operators is also an interval-valued intuitionistic trapezoidal fuzzy value. Then, based on these expected functions and aggregating operators, an approach is proposed to solve MAGDM problems in which the attribute values take the form of interval-valued intuitionistic fuzzy numbers and the expert weights take the form of real numbers. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.