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.     

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。     

基于直觉模糊交互影响算子的多属性决策方法

针对属性权重未知,属性值为直觉模糊数的多属性决策问题,并考虑到直觉模糊集隶属度与非隶属度的相互影响关系,提出了一种基于直觉模糊熵和直觉模糊交互影响算子的决策方法.利用直觉模糊熵求出属性权重,引入三种直觉模糊交互影响算子:广义直觉模糊交互影响加权平均算子,广义直觉模糊交互影响有序加权平均算子和广义直觉模糊交互影响混合平均算子,利用交互影响算子来集结信息得到方案综合评价值,通过改进的得分函数对方案进行排序选优.最后,通过一个算例说明了该决策方法的合理性和有效性.     

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。     

区间犹豫模糊Bonferroni mean算子在多属性决策中的应用

针对在信息集成时, 需要考虑输入变量之间的相互影响以及专家评价值为区间犹豫模糊信息的多属性决策问题, 提出一种基于区间犹豫模糊Bonferroni mean算子的多属性决策方法。考虑到由于Bonferroni mean(BM)算子能够良好的反映输入变量之间相互影响, 首次提出了评价值为区间犹豫模糊集信息环境下的两种新的集成算子, 即区间犹豫模糊Bonferroni mean(IVHFBM)算子和区间犹豫模糊几何Bonferroni mean(IVHFGBM)算子。并讨论了其相关的一些特性。同时基于输入变量会具有不同重要程度的情况, 定义了区间犹豫模糊加权Bonferroni mean(IVHFWBM)算子和区间犹豫模糊加权几何Bonferroni mean(IVHFWGBM)算子。针对评价信息以区间犹豫模糊集表示的决策问题, 提出了基于IVHFWBM算子和IVHFWGBM算子的多属性决策方法。最后通过实例证明了该方法的可行性和有效性。     

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.     

概率犹豫模糊Maclaurin几何对称平均算子及其群决策模型

属性信息的集成已经成为模糊决策领域一个重要的研究课题.基于概率犹豫模糊加权Maclaurin几何对称平均算子构建了一种新的多属性群决策算法.首先,定义了Maclaurin几何对称平均(MGSM)算子,并进一步将该算子引入到概率犹豫模糊环境下,结合Archimedean范数的思想,提出了概率犹豫模糊Maclaurin几何对称平均(PHFMGSM)算子;其次,探讨了PHFMGSM算子具有的优良性质以及几种特殊表达形式;随后,基于提出的概率犹豫模糊加权Maclaurin几何对称平均(PHFWMGSM)算子,构建了一种新的概率犹豫模糊多属性群决策算法;最后,通过采购数据库的实例发现,PHFWMGSM算子性质优良、计算简单、稳定性好且灵活可靠,且提出的群决策模型是更为合理有效.     

直觉梯形模糊语言Frank算子及其在决策中的应用

本文在直觉梯形模糊语言集的基础上,引入了Frank算子,提出一组新的算子——直觉梯形模糊语言Frank集结算子,并将其应用到多属性决策中。首先,本文提出了直觉梯形模糊语言集Frank算子的表达式,并给出相应的运算规则。然后提出了直觉梯形模糊语言Frank加权算术平均(ITrFLFWA)算子、直觉梯形模糊语言Frank加权几何平均(ITrFLFWG)算子、直觉梯形模糊语言Frank广义加权平均(ITrFLGFWA)算子等,并证明了其具有幂等性、有界性、单调性等性质。最后,通过实例验证了直觉梯形模糊语言Frank算子可以有效解决直觉梯形模糊语言环境下的多属性决策问题。     

概率犹豫模糊Bonferroni平均算子及其决策应用

研究了属性值为概率犹豫模糊元的多属性决策问题。考虑到属性间的相互影响关系,提出基于Bonferroni平均算子的概率犹豫模糊多属性决策方法。首先,为避免概率犹豫模糊元运算时计算量过大的情形,提出新的运算法则。其次,定义了概率犹豫模糊Bonferroni平均算子和概率犹豫模糊几何Bonferroni平均算子,并讨论了其性质。另外,为比较概率犹豫模糊元大小,定义了概率犹豫模糊符号距离。最后,通过实例说明所提方法的应用过程。     

广义直觉模糊指标的构造及其应用

针对现有广义直觉模糊指标的构造并未利用直觉模糊集广义补算子的不足,本文首先利用直觉模糊广义补算子给出了一种新的广义直觉模糊指标的构造法,其次对广义直觉模糊指标所具有的性质进行了严格证明,最后将其用于图像阈值化分割并给出其直觉模糊广义补算子参数的选取方法.实验结果表明,本文所提出的广义直觉模糊指标构造法是有效的,对于光照不均匀图像能获得满意的分割效果.     

Generalized intuitionistic fuzzy geometric aggregation operators and their application to multi-criteria decision making

In this paper, we extend the generalized weighted geometric and generalized ordered weighted geometric operators to intuitionistic fuzzy environments, that is, we develop a series of generalized intuitionistic fuzzy geometric operators to aggregate input arguments that are expressed by intuitionistic fuzzy values based on Archimedean t-conorm and t-norm. Then some desired properties of these aggregation operators are investigated. The relations between these operators and some existing intuitionistic fuzzy geometric aggregation operators are discussed in detail. Furthermore, applying these proposed operators, we develop an approach for multi-criteria decision making with intuitionistic fuzzy information. Finally, a practical example is given to verify the developed approach and to demonstrate its practicality and effectiveness.     

基于Archimedean三角模的犹豫直觉模糊语言信息群决策方法

针对语言术语集下标运算不封闭的问题,基于Archimedean三角模讨论了犹豫直觉模糊语言信息下的封闭运算体系。首先提出基于Archimedean三角模的犹豫直觉模糊语言集,然后给出了相应的得分函数、精确函数、排序规则和集结算子,给出一种基于Archimedean三角模的犹豫直觉模糊语言信息的群决策方法,最后用一个实例说明了方法的有效性和优越性。     

区间值模糊集和区间值模糊推理

本文在单位区间的一切子区间集Ⅰ[0,1]上引入t-范、t-余范、交(∩)、并(∪)等概念,在此基础上定义了区间值模糊集中的新的交并运算和区间值模糊关系的新的合成运算,得出若干有趣的性质,并将其应用于区间值模糊推理的合成规则上。     

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     

Resolution of composite fuzzy relation equations based on Archimedean triangular norms

Lately, the sup-t-norm composition of fuzzy relations has been used instead of the well-known max–min. Thus, there is a need for methods of studying and solving sup-t-norm fuzzy relation equations (t is any t-norm). In this paper, the solution existence problem is first studied and solvability criteria for composite fuzzy relation equations of any t-norm are given. Then, a methodology for solving fuzzy relation equations based on sup-t composition, where t is an Archimedean t-norm, is proposed. This resolution method is simpler and faster than those proposed for covering all the continuous t-norms. The result is important, since, as is shown in the paper, the only continuous t-norm that is not Archimedean is the “minimum”.     

$M$-半群的直觉$(S,T)$-模糊$M$-子半群的性质

K.T.Atanassov在1986年首先引入直觉模糊集的概念,本文利用s-范数和t-范数,引入M-半群的直觉(S,T)-模糊M-子半群的概念,刻画其性质和特征,我们再进一步给出了直觉(S,T)-直积的概念,并由此探讨了一些有意义的相关结论。     

Dynamic Aggregation Operators Based on Intuitionistic Fuzzy Tools and Einstein Operations

The idea of combine aggregation and intuitionistic fuzzy information plays essential role in multi criteria decision making (MCDM) process. However, this new branch has attracted researchers that study in different fields recently. In this paper, we study MCDM problems with intuitionistic fuzzy environment. Firstly, we introduce some operations related with Einstein t-norm and t-conorm such as, Einstein sum, product and exponentiation. After that, we define dynamic intuitionistic fuzzy Einstein averaging (DIFWA${}^{?}$) operator and dynamic intuitionistic fuzzy Einstein geometric averaging (DIFWG${}^{?}$) operator. Their notable property is that collect and aggregate values in different period based on Einstein operations in intuitionistic fuzzy set (IFS)s. In addition, we compare the defined operators with the existing intuitionistic fuzzy dynamic operators and get the corresponding relations. We establish two methods using with DIFWA${}^{?}$ and DIFWG${}^{?}$ to solve MCDM problems with intuitionistic fuzzy tools. Finally, an illustrated example is presented to show the applicability of the introduced methods.