梯形直觉模糊数集成算子及在决策中的应用研究

在直觉模糊集理论基础上,用梯形模糊数表示直觉模糊数的隶属度和非隶属度,进而提出了梯形直觉模糊数;然后定义了梯形直觉模糊数的运算法则,给出了相应的证明,并基于这些法则,给出了梯形直觉模糊加权算数平均算子(TIFWAA)、梯形直觉模糊数的加权二次平均算子(TIFWQA)、梯形直觉模糊数的有序加权二次平均算子(TIFOWQA)、梯形直觉模糊数的混合加权二次平均算子(TIFHQA)并研究了这些算子的性质;建立了不确定语言变量与梯形直觉模糊数的转化关系,并证明了转化的合理性;定义了梯形直觉模糊数的得分函数和精确函数,给出了梯形直觉模糊数大小比较方法;最后提供了一种基于梯形直觉模糊信息的决策方法,并通过实例结果证明了该方法的有效性。     

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。     

梯形模糊有序加权几何算子及其在决策中的应用

针对梯形模糊数据信息的集成问题,给出了梯形模糊数两两比较的可能度公式和梯形模糊有序加权几何(TFOWG)算子.基于可能度公式和TFOWG算子,提出了一种准则权重信息完全未知且准则值以梯形模糊数形式给出的不确定多准则决策方法.最后,实例分析表明了该方法的可行性和有效性.     

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。     

广义毕达哥拉斯正态模糊集成算子及其决策应用

将毕达哥拉斯模糊数与直觉正态模糊数相结合,提出了毕达哥拉斯正态模糊数,研究了其运算和运算性质,定义了毕达哥拉斯正态模糊数的得分函数和精确函数,实现其大小排序.然后,针对毕达哥拉斯正态模糊信息的集成问题,提出毕达哥拉斯正态模糊有序加权平均(PNFOWA)算子、广义有序加权平均(GPNFOWA)算子和毕达哥拉斯正态模糊有序加权几何平均(PNFOWGA)算子及广义有序加权几何平均(GPNFOWGA)算子,并研究了其性质.最后,提出基于广义毕达哥拉斯正态模糊集成算子的多属性决策方法,并通过实例说明该方法的有效性.     

直觉三角模糊数密度算子及其决策应用

首先提出了一种直觉三角模糊数集聚类的方法,然后考虑到属性信息分布的疏密程度,针对属性值为直觉三角模糊数的多属性决策问题提出了直觉三角模糊数密度算子,给出了密度算子与已有几种信息集结算子合成的形式,并研究了直觉三角模糊数密度算子的性质.最后通过一个决策算例说明了直觉三角模糊数密度算子的有效性.     

基于广义WOWA算子的Pythagorean模糊决策方法

针对Pythagorean模糊信息的决策问题,构建广义Pythagorean模糊信息加权有序加权平均(PF-GWOWA)算子。首先,提出PF-GWOWA算子,并证明Pythagorean模糊广义加权平均(PF-GWA)算子、Pythagorean模糊加权有序加权平均(PF-WOWA)算子与Pythagorean模糊加权平均(PF-WA)算子均为PF-GWOWA算子的特例;其次,根据GWOWA算子属性综合权重计算模型,利用PF-GWOWA算子对信息进行集结;最后,通过算例分析和传统方法对比,说明本文提出方法的合理性与有效性。     

直觉正态模糊数幂均算子及其决策应用

将幂均算子推广到直觉正态模糊数决策环境中。定义了直觉正态模糊数的运算,研究了运算性质。在此基础上,提出直觉正态模糊数幂均(INFPA)算子、有序加权幂均(INFPOWA)算子、广义直觉正态模糊数幂均(GINFPA)算子和广义有序加权幂均(GINFPOWA)算子,分析了GINFPA算子的特殊形式并研究其性质。针对属性值为直觉正态模糊数的多属性决策问题,提出基于GINFPA算子的决策方法。最后,通过一个算例说明决策方法的有效性和可行性。     

毕达哥拉斯模糊数密度算子及其决策应用

针对属性值为毕达哥拉斯模糊数的多属性决策问题,考虑到属性信息分布的疏密程度,提出了毕达哥拉斯模糊数密度集结(PFDM)算子。利用得分函数,提出一种毕达哥拉斯模糊数集有效聚类的方法,进而给出PFDM算子的密度加权向量,并构建PFDM算子与经典算子的合成形式,同时分析了PFDM算子相关性质。最后,提出基于PFDM算子的多属性决策方法,并通过决策实例说明了该方法的可行性和有效性。     

A multi-attribute group decision-making method based on weighted geometric aggregation operators of interval-valued trapezoidal fuzzy numbers

With respect to the multiple attribute group decision making problems in which the attribute values take the form of generalized interval-valued trapezoidal fuzzy numbers (GITFN), this paper proposed a decision making method based on weighted geometric aggregation operators. First, some operational rules, the distance and comparison between two GITFNs are introduced. Second, the generalized interval-valued trapezoidal fuzzy numbers weighted geometric aggregation (GITFNWGA) operator, the generalized interval-valued trapezoidal fuzzy numbers ordered weighted geometric aggregation (GITFNOWGA) operator, and the generalized interval-valued trapezoidal fuzzy numbers hybrid geometric aggregation (GITFNHGA) operator are proposed, and their various properties are investigated. At the same time, the group decision methods based on these operators are also presented. Finally, an illustrate example is given to show the decision-making steps and the effectiveness of this method.     

基于灰色关联法和HA算子的Pythagorean模糊群决策方法

针对Pythagorean模糊群决策问题,提出一种基于Pythagorean模糊混合平均算子的决策方法。首先,提出一种基于Pythagorean模糊信息及其运算法则的Pythagorean模糊混合平均算子;其次,构建一种基于最大熵模型的属性位置权重定权方法,同时根据灰色关联方法提出一种属性客观权重计算方法,进而获得Pythagorean模糊混合平均算子的定权方法;利用Pythagorean模糊混合平均算子对单决策者信息进行融合,通过Pythagorean模糊加权平均算子对各专家信息进行融合,并依据得分函数与精确函数进行排序择优;最后,通过一个算例说明该方法的有效性和可行性。     

基于对偶犹豫模糊语言变量的多属性决策方法

首先定义了对偶犹豫模糊语言变量,然后给出其运算规则、得分值函数、精确值函数、比较规则以及对偶犹豫模糊语言变量的加权算术平均算子、有序加权算术平均算子和混合平均算子。针对属性值为对偶犹豫模糊语言变量的多属性决策问题,提出了一种基于对偶犹豫模糊语言变量集结算子的多属性决策方法。最后,结合国家电网公司合作单位选择问题,验证了该方法的有效性和可行性。     

基于改进得分函数的直觉梯形模糊数群体多属性决策方法

为考虑群体多属性决策问题中决策人的风险偏好,在直觉梯形模糊数的基础上,利用连续区间有序加权平均算子对直觉梯形模糊数进行化简,使其转换成直觉模糊数。并基于此提出了一种全新的得分函数。从而得到了一种全新的群体多属性决策方法,将其应用于具体算例中,给出了该方法的具体步骤并证明了有效性。     

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     

Multi-criteria decision-making method based on normal intuitionistic fuzzy-induced generalized aggregation operator

Normal intuitionistic fuzzy numbers (NIFNs), which use normal fuzzy numbers to express their membership and non-membership functions, can reflect the evaluation information exactly in different dimensions. In this paper, we are committed to apply NIFNs to multi-criteria decision-making (MCDM) problems, and meanwhile some new aggregation operators are proposed, including normal intuitionistic fuzzy weighted arithmetic averaging operator, normal intuitionistic fuzzy weighted geometric averaging operator, normal intuitionistic fuzzy-induced ordered weighted averaging operator, normal intuitionistic fuzzy-induced ordered weighted geometric averaging operator and normal intuitionistic fuzzy-induced generalized ordered weighted averaging operator (NIFIGOWA). Based on the NIFIGOWA operator, an approach is introduced to solve MCDM problems where the criteria values are NIFNs and the criteria weight information is fixed. Finally, the proposed method is compared to the existing methods by virtue of a numerical example to verify its feasibility and rationality.     

基于改进区间数密度集结算子指标群赋权方法

针对指标数据已知,而权重数据未知的群组赋权问题,给出了一种基于改进的区间数密度集结算子来进行指标群组赋权的决策方法。首先给出了区间数和区间数密度集结算子(IDM)的定义及性质,改进了以前区间数聚类的方法,应用直接法对一维区间数据组进行聚类,并定义了模糊统计量,以确定最为合理的一种聚类方式。然后基于改进的区间数密度集结算子这种数学模型,来解决指标值数据已知,而权重未知的群组赋权问题。最后举例说明该方法的可行性和实用性。     

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。     

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.