多源密度集结算子及其性质分析

对已有密度加权平均(DWA)中间算子进行拓展,给出了新的密度加权几何平均(DWGA)中间算子.在密度(DM)中间算子的结构上,系统地定义了若干密度合成算子,从而拓展了密度信息集结算子的可选种类,同时,统一并明确了一些称谓,这使得DM算子类的结构更为清晰了.着重对密度集结(DM□)算子的性质进行了分析,证明了DM□算子具有置换不变性、幂等性、介值性及奈件单调性等优良性质,并给出了条件单调性的判定程序,将规划模型融入该判定程序中,通过对模型的求解及最优目标值的观测可以就特定情形下DM□算子的"单调性"性质做出判断.通过分析发现,DM□算子具备多种基础算子的通用形式,因而在归纳的基础上给出了DM□算子的"全拓性"性质.最后,用一个算例对DM□算子的性质进行了数值验证.     

不确定集结算子及其在多属性决策中的应用

针对方案评估中属性信息的不确定性,提出了一个基于不确定信息的多属性集结算子。该算子将有序加权平均(OWA)算子和广义平均算子相结合而成的广义有序加权平均(GOWA)算子推广到不确定的环境中,提出了一个广义不确定有序加权平均(GUOWA)算子。并且给出了基于GUOWA算子的不确定多属性决策方法,最后的实例说明该方法的有效性和合理性。     

基于多源密度信息集结算子的组合评价方法

基于密度加权平均（density weighted averaging, DWA）中间算子的集结性质,构建了面向组合评价的DWA For ce算子,该算子对用于“组合评价”的“甄别奖惩”思想进行了方法性的拓展,可通过参数的控制对“甄别奖惩”的程度进行无限级的调节。DWAFor ce算子具有适合组合评价问题的多种优良性质,并能对点数据或向量数据进行处理,同时具备了组合优化评价值或序值的集结结构。最后用一个算例验证了DWAFor ce算子的有效性及一些新颖的特征。     

诱导密度算子及其性质分析

对密度算子进行拓展研究,提出了诱导密度算子的概念并对其进行了性质分析.对诱导变量进行了界定,给出了一种以诱导变量为基准的元素聚类方法;在此基础上,基于分组后各组的群组特征,给出了密度加权向量的确定方法;将诱导密度中间算子与已知的信息集结算子合成,得到了诱导密度算子,并对诱导密度算子的性质进行了分析.最后,通过一个算例对诱导密度算子的应用进行了说明.     

基于纯语言混合几何平均算子的多属性群决策方法

在纯语言加权几何平均(PLWGA)算子和推广的有序加权平均(EOWA)算子基础上给出纯语言混合几何平均(PLHGA)算子,研究了专家权重、属性权重及属性值均以语言形式给出的纯语言多属性群决策问题,提出了一种纯语言多属性群决策方法。最后将该方法应用于解决虚拟企业中的战略合作伙伴选择问题。     

三参数区间数据信息集成算子及其在决策中的应用

研究了三参数区间数据信息的集成问题.基于连续区间数据有序加权平均(C-OWA)算子和有序加权几何(C-OWG)算子,定义了连续三参数区间数据有序加权平均(CP-OWA)算子和有序加权几何(CP-OWG)算子,并将这两种算子进行拓展,提出了加权的CP-OWA(WCP-OWA)算子和加权的CP-OWG(WCP-OWG)算子,研究了它们的一些性质.基于这些算子,提出了一种属性权重和属性值均以三参数区间数形式给出的不确定多属性决策方法,该方法利用CP-OWA算子对三参数区间数属性权重进行处理,利用WCP-OWA算子或WCP-OWG算子对三参数区间数属性值进行集成.最后,进行了实例分析.     

基于评价局部环境的双目标协同优化评价法

称评价局部环境是根据具体评价问题生成的,以评价参与者为节点,参与者之间的评价关系为链接构成的评价群体网络结构.通过将节点(评价参与者)网络结构信息与节点(评价参与者)属性信息融合,根据评价群体网络结构特征寻找适当的群组评价方法,构建群组评价的平面数据集并开发了平面密度加权平均算子(平面密度加权算术平均算子(PDWA算予)和平面密度加权几何平均算子(PDWGA算子)),通过对评价群体类型具有一贯性或可变性区分,定义了评价群体的合作型协同和竞争型协同,构建相应的规划模型对不同类型的评价群体进行优化,应用平面密度加权平均算子对评价信息进行集结从而得到最终评价结果.     

拓展的C2OWA 算子及其在不确定多属性决策中的应用

把Yager提出的连续区间数据OWA(C-OWA)算子进行拓展,提出了加权的C-OWA(WC-OWA)算子、有序加权的C-OWA(OWC-OWA)算子、以及组合的C-OWA(CC-OWA)算子,研究了它们的一些性质.基于这些算子,分别在单人决策和群决策这两种情形下,提出了属性权重确知、且属性值以区间数形式给出的不确定多属性决策方法.最后,进行了实例分析.     

直觉不确定语言集成算子及在群决策中的应用

直觉不确定语言数是直觉模糊数和不确定语言变量值的拓展. 针对直觉不确定语言信息的集成问题, 定义了直觉不确定语言数运算法则和大小比较方法, 提出了直觉不确定语言的加权算术平均算子(IULWAA)、直觉不确定语言的有序加权平均算子(IULOWA)以及直觉不确定语言的混合加权平均算子(IULHA)及这些算子的性质. 在此基础上, 提出一种属性权重确知且属性值以直觉不确定语言数形式给出的多属性群决策方法. 最后通过实例分析证明了该方法的有效性.     

基于二维密度加权算子的群体评价信息集结方法

群体评价中已有的信息集结算子都没有考虑到信息分布的疏密情况,且其评价信息又通常为二维数据,为此,提出了一种基于二维密度加权算子的群体评价信息集结方法.定义了二维密度加权算术平均(TDWA)算子和二维密度加权几何平均(TDWGA)算子2种新的集结算子.将新算子应用于群体评价的信息集结中,并分别给出了群体评价(二维)数据的分组与群体密度权向量的具体确定方法.最后,给出了一个具体的集结算例.     

Generalization of the linguistic aggregation operator and its application in decision making

A generalization of the linguistic aggregation functions (or operators) is presented by using generalized and quasiarithmetic means.Firstly,the linguistic weighted generalized mean (LWGM) and the linguistic generalized ordered weighted averaging (LGOWA) operator are introduced.These aggregation functions use linguistic information and generalized means in the weighted average (WA) and in the ordered weighted averaging (OWA) function.They are very useful for uncertain situations where the available information cannot be assessed with numerical values but it is possible to use linguistic assessments.These aggregation operators generalize a wide range of aggregation operators that use linguistic information such as the linguistic generalized mean (LGM),the linguistic OWA (LOWA) operator and the linguistic ordered weighted quadratic averaging (LOWQA) operator.We also introduce a further generalization by using quasi-arithmetic means instead of generalized means obtaining the quasi-LWA and the quasi-LOWA operator.Finally,we develop an application of the new approach where we analyze a decision making problem regarding the selection of strategies.     

信息集成算子加权向量的对称性研究

对信息集成算子加权向量的对称性进行了研究.提出了升序加权算术平均(AOWAA)算子和语言AOWAA算子,分别给出了降序加权算术平均(DOWAA)算子和升序加权算术平均(AOWAA)算子、降序加权几何平均(DOWGA)算子和升序加权几何平均(AOWGA)算子、以及语言DOWAA算子和语言AOWAA算子的一个等价条件,并证明了在加权向量是对称的情况下:1)利用DOWAA算子对若干个互补判断矩阵进行集成所得到的群判断矩阵仍为互补判断矩阵;2)利用DOWGA算子对若干个互反判断矩阵进行集成所得到的群判断矩阵仍为互反判断矩阵;3)利用语言DOWAA算子对若干个语言互补判断矩阵进行集成所得到的群判断矩阵仍为语言互补判断矩阵.最后探讨了一些常用加权向量的对称性问题.     

Some Generalized Single Valued Neutrosophic Linguistic Operators and Their Application to Multiple Attribute Group Decision Making

This paper proposes a group decision making method based on entropy of neutrosophic linguistic sets and generalized single valued neutrosophic linguistic operators. This method is applied to solve the multiple attribute group decision making problems under single valued neutrosophic liguistic environment, in which the attribute weights are completely unknown. First, the attribute weights are obtained by using the entropy of neutrosophic linguistic sets. Then three generalized single valued neutrosophic linguistic operators are introduced, including the generalized single valued neutrosophic linguistic weighted averaging(GSVNLWA) operator, the generalized single valued neutrosophic linguistic ordered weighted averaging(GSVNLOWA) operator and the generalized single valued neutrosophic linguistic hybrid averaging(GSVNLHA) operator, and the GSVNLWA and GSVNLHA operators are used to aggregate information. Furthermore, similarity measure based on single valued neutrosophic linguistic numbers is defined and used to sort the alternatives and obtain the best alternative. Finally,an illustrative example is given to demonstrate the feasibility and effectiveness of the developed method.     

三参数区间数调和平均算子及决策应用

针对决策信息以三参数区间数据形式给出的多属性决策问题,提出了一些新的三参数区间数据信息的集成算子和决策方法。基于连续区间数据有序加权调和平均(C OWHA)算子,定义了连续的三参数区间数据有序加权调和平均(CP OWHA)算子,并将该算子进行了拓展,提出了加权调和CP OWHA(WHCP OWHA)算子、有序加权调和CP OWHA(OWHCP OWHA)算子和组合的CP OWHA(CCP OWHA)算子。进一步证明了WHCP OWHA算子和OWHCP OWHA算子均为CCP OWHA算子的特例。CCP OWHA算子同时推广了WHCP OWHA算子和OWHCP OWHA算子,CCP OWHA算子不仅考虑了每个数据的自身重要性程度,而且还体现了该数据所在位置的重要性程度。基于WHCP OWHA算子和CCP OWHA算子,提出了一种属性权重和专家权重均为确定实数且属性值为三参数区间数的多属性群决策方法。最后给出了一个数值例子,结果表明该方法有效。     

Generalized ordered weighted averaging operators based method for MADM in intuitionistic fuzzy set setting

Multiattribute decision making (MADM) problems, in which the weights and ratings of alternatives are expressed with intuitionistic fuzzy (IF) sets, are investigated. Firstly, the relative degrees of membership and the relative degrees of non-membership are formulated as IF sets, the weights and values of alternatives on both qualitative and quantitative attributes may be expressed as IF sets in a unified way. Then a MADM method based on generalized ordered weighted averaging operators is proposed. The proposed method is illustrated with a numerical example.     

Interval-valued intuitionistic fuzzy aggregation operators

The notion of the interval-valued intuitionistic fuzzy set (IVIFS) is a generalization of that of the Atanassov’s intuitionistic fuzzy set. The fundamental characteristic of IVIFS is that the values of its membership function and non-membership function are intervals rather than exact numbers. There are various averaging operators defined for IVIFSs. These operators are not monotone with respect to the total order of IVIFS, which is undesirable. This paper shows how such averaging operators can be represented by using additive generators of the product triangular norm, which simplifies and extends the existing constructions. Moreover, two new aggregation operators based on the ukasiewicz triangular norm are proposed, which are monotone with respect to the total order of IVIFS. Finally, an application of the interval-valued intuitionistic fuzzy weighted averaging operator is given to multiple criteria decision making.     

Ordered weighted distance measure

The aim of this paper is to develop an ordered weighted distance （OWD） measure, which is the generalization of some widely used distance measures, including the normalized Hamming distance, the normalized Euclidean distance, the normalized geometric distance, the max distance, the median distance and the rain distance, etc. Moreover, the ordered weighted averaging operator, the generalized ordered weighted aggregation operator, the ordered weighted geometric operator, the averaging operator, the geometric mean operator, the ordered weighted square root operator, the square root operator, the max operator, the median operator and the rain operator are also the special cases of the OWD measure. Some methods depending on the input arguments are given to determine the weights associated with the OWD measure. The prominent characteristic of the OWD measure is that it can relieve （or intensify） the influence of unduly large or unduly small deviations on the aggregation results by assigning them low （or high） weights. This desirable characteristic makes the OWD measure very suitable to be used in many actual fields, including group decision making, medical diagnosis, data mining, and pattern recognition, etc. Finally, based on the OWD measure, we develop a group decision making approach, and illustrate it with a numerical example.     

基于模糊C-OWA算子的模糊多属性决策方法

将连续区间数据OWA(C-OWA)算子扩展到模糊环境,提出了一些新的模糊C-OWA(FC-OWA)算子,如加权FC-OWA(WFC-OWA)算子、悲观WFC-OWA(PWFC-OWA)算子和乐观WFC-OWA(OWFC-OWA)算子,并研究了它们的一些性质.基于PWFC-OWA算子和OWFC-OWA算子,提出了属性值和属性权重为梯形模糊数的多属性决策方法.最后通过算例说明了方法的可行性和有效性.