一种带参数的区间粗糙数型多属性决策方法

针对带参数的区间粗糙数型多属性决策问题,首先定义了带参数的区间粗糙数的期望和方差,以期望值和方差集结函数的优劣度得到正负理想点,然后提出了一种积分形式的带参数型的区间粗糙数新的相离度,并根据已有的加权区间粗糙的距离平均算子（WIRDAA）概念,构建含参数的区间粗糙数型MADM的熵值法模型得到最终排序,最后以一个实例说明该方法的可行性。     

三参数区间数多属性决策的后悔理论方法

本文将后悔理论方法用于解决三参数区间数多属性决策问题.首先,提出一种将三参数区间数转换为两参数区间数的方法,避免了传统三参数区间数在大小比较方面不确定信息的遗失.其次,依据两参数区间数决策信息计算不同状态下备选方案及正理想方案各属性的效用值,从而可得各备选方案的后悔–欣喜值及综合感知效用值.然后,针对权重范围已知的情况,通过构建备选方案综合感知效用最大化优化模型求得属性权重;针对权重信息完全未知的情况,提出一种基于注水原理的属性权重求解方法.最后,利用属性权重加权求和方法得到备选方案综合效用值,从而通过比较综合效用值得到方案的排序结果.     

基于CBR和MADM的多Agent推荐系统

为解决目前基于CBR的推荐系统只考虑属性值全部为精确或全部为非精确数据的情况,提出一种基于MADM的多Agent推荐系统框架。在考虑了属性分类的基础上设计了基于距离的混合数据类型的相似性度量算法及TOPSIS多属性决策方法,设计了该系统各组成部分功能、结构和流程。模拟算例演示了案例推理及多属性决策在本系统的应用过程,结果表明该系统有较好的实用性。     

A note on the TOPSIS method in MADM problems with linguistic evaluations

The TOPSIS method, commonly known as the technique for order preference by similarity to ideal solutions, is one of the most popular approaches used in multi-attribute decision making (MADM). The fundamental procedure of the traditional TOPSIS method is rather straightforward, the ranking position of an alternative depends on its relative closeness to the positive ideal solution and the negative ideal solution, respectively. In order to encompass uncertain and ambiguous decision elements, an extension of the original TOPSIS method has been coined. With the help of fuzzy sets based TOPSIS, an overwhelming trend of fuzzy decision making applications has been witnessed. In the present work, however, it is found that the extended fuzzy TOPSIS method is unable to distinguish all the different alternatives under linguistic environment. Moreover, the undistinguishable alternatives are countless in quantity, and they have formed specific patterns with respect to the parameters of TOPSIS methods. To dampen this ranking ambiguity, we designed a set of supplemental methods to construct a revised TOPSIS approach with linguistic evaluations. Correspondingly, the sufficiency of the revised TOPSIS method to guarantee total orders has been proven. Furthermore, a numerical example concerning the production line improvement of a manufacturing company is demonstrated to validate the feasibility and supremacy of the proposed method. Finally, a series of further discussions are performed to shed some lights on the impacts caused by the changes of the alternative quantity, the attribute quantity, and the type of linguistic term.     

An interval difference based evidential reasoning approach with unknown attribute weights and utilities of assessment grades

In this paper, the concept of interval difference is firstly defined. Then, an interval difference based evidential reasoning approach is proposed to analyze multiple attribute decision making problems in three situations, including (1) unknown attribute weights and utilities of assessment grades, (2) unknown attribute weights, and (3) unknown utilities of assessment grades. Three optimization models are constructed to identify potentially optimal alternatives in the three situations. For each potentially optimal alternative, three pairs of optimization problems are constructed to generate the optimized intervals of attribute weights and utilities of assessment grades or one of them. By using the optimized intervals, the interval difference of potentially optimal alternatives is calculated and used to generate their rank-order. This process is repeated until all alternatives are identified as potentially optimal alternatives. A complete rank-order of all alternatives is then generated. The performance of six executive cars is assessed using the proposed approach to demonstrate its applicability and validity.     

基于区间粗糙数的多属性决策方法及应用

针对传统多属性决策模型中大量指标的复杂性和模糊性导致实际决策结果不准确的问题,提出了一种基于区间粗糙数的改进DEMATEL-VIKOR多属性优化决策模型。首先,在区间粗糙数的基础上对传统的DEMATEL方法和VIKOR方法分别进行改进;其次将一种新的归一化加权几何Bonferroni平均算子运用在改进的DEMATEL-VIKOR混合模型中,根据量化结果对各准则进行影响因素分析进而计算折中的可行解;最后,分别从敏感性分析、理论分析及方法比较三种角度对备选方案进行排序,从而得到最优备选方案,应用城市滨水区景观后期综合评价的算例结果表明,该改进算法在不确定和不完备信息环境下的决策结果更具可行性和有效性。     

区间数动态多属性决策的VIKOR扩展方法

针对各决策阶段的时间权重以及属性权重已知,属性值以区间数形式给出的动态多属性决策问题,提出一种新的决策方法.该方法依据传统多准则妥协解排序法(VIKOR)的基本思路,结合区间数的运算规则,计算各阶段各方案的评价值,进而引入不确定动态加权平均(UDWA)算子进行集成,以获取各方案整体评价值的区间数.借助于区间数两两比较的可能度公式和模糊互补判断矩阵公式,对其进行比较,从而得到整个方案集的排序.最后以第3方逆向物流服务商的选择为实例进行分析,所得结果表明了该方法的可行性和有效性.     

战场目标打击顺序的多属性决策方法

提出了一种战场目标打击顺序的多属性决策方法,该方法把主观和客观信息集成起来,通过一个数学规划模型把获得的战场目标客观信息与决策者给出的主观权重偏好信息有机地集成,使属性的权重可在决策者主观基础上根据战场态势动态调整,利用TOPSIS方法排定目标的打击顺序,为战场目标的打击顺序问题提出了一种新的解决方法.     

基于熵权的区间数多属性决策方法

研究了属性权重未知且属性值为区间数的多属性决策问题。首先针对一般区间数排序方法完全依赖区间数中点值的缺陷,提出了一种改进的排序方法;接着给出了改进的区间数判断矩阵规范化方法;然后依据多属性决策中传统熵权确定方法的思路,结合区间数决策矩阵的特点提出了一种确定属性熵权的方法;最后通过一个算例说明了该方法的实用性和有效性。     

Industrial robot selection using a novel decision making method considering objective and subjective preferences

Robots with vastly different capabilities and specifications are available for a wide range of applications. Selection of a robot from among the large number available in the market to suit a particular application and production environment has become a difficult task. Many methods for robot selection have been developed to date. Keeping in view the research works on industrial robot selection, a subjective and objective integrated multiple attribute decision making method is proposed in this paper for the purpose of robot selection. The method considers the objective weights of importance of the attributes as well as the subjective preferences of the decision maker to decide the integrated weights of importance of the attributes. Furthermore, the method uses fuzzy logic to convert the qualitative attributes into the quantitative attributes. Three examples are presented to illustrate the potential of the proposed method.     

属性和专家客观权重未知的区间数群决策方法

针对偏好信息为区间数形式、属性和专家客观权重未知的多属性群决策问题,提出通过属性评价值之间偏离程度的熵值分析和建立目标最小化的非线性规划模型确定属性客观权重,并结合属性主观权重获得属性综合权重;通过灰色关联法分析专家综合评价和群体综合评价之间一致性程度确定专家客观权重,并利用自适应迭代法求得稳定的专家权重;构造了一个新的区间数比较的可能度公式,并基于此公式,给出了方案排序问题的解决方法。通过算例分析及与其他方法对比,验证了所提出方法的可行性和有效性。最后,分析了相关参数对决策结果的影响。     

基于联系数的区间粗糙数多属性决策方法

定义了正态分布的区间粗糙数,补充联系数的运算法则。利用集对分析的不确定性理论,建立了区间粗糙数的均值-方差联系数模型,针对属性值为区间粗糙数且权重已知的区间粗糙数多属性决策问题,提出了一种基于联系数的区间粗糙数多属性决策方法,并给出了决策的步骤。最后,通过实例分析,表明该方法的有效性和实用性,且计算简单易行。     

基于云模型的Pythagorean模糊语言多属性决策方法

针对专家给出的属性值为Pythagorean模糊语言且专家权重与属性权重均未知的多属性决策问题进行了研究,提出一种基于云模型的多属性决策方法。首先,根据Pythagorean模糊语言决策信息的距离熵计算得到属性权重;其次,计算决策矩阵间的距离从而得到各决策专家权重;再次,构建Pythagorean模糊云模型决策矩阵并利用专家权重和属性权重进行信息集结;最后,基于TOPSIS方法求取正、负理想解,依据理想解计算各方案贴近度并据此对各备选方案进行排序选择。案例分析表明,该方法优化了复杂环境下的决策,避免了决策信息的丢失,能够较好解决决策信息的不确定性和决策过程的随机性,具有一定的可行性和有效性。     

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.     

Robot selection by using generalized interval-valued fuzzy numbers with TOPSIS

The aim of this paper is to propose a method to aggregate the opinion of several decision makers on different criteria, regarding a set of alternatives, where the judgment of the decision makers are represented by generalized interval-valued trapezoidal fuzzy numbers. A generalized interval valued trapezoidal fuzzy number based technique for order preference by similarity to ideal solution is proposed that can reflect subjective judgment and objective information in real life. The weights of criteria and performance rating values of criteria are linguistic variables expressed as generalized interval-valued trapezoidal fuzzy numbers. Finally, an illustrative example is provided to elaborate the proposed method for the selection of a suitable robot according to our requirements.     

区间数多属性决策中一种带有可能度的排序方法

为解决具有不确定性区间数的多属性决策中的方案排序问题,在考虑落在区间内的评价值（即被认为随机变量）服从正态分布的情况下,针对方案综合评价值所在的区间存在相互交叉部分的情形,提出了关于区间数之间相互比较的可能度的概念,并结合给出了有可能度的方案排序方法。通过此方法可计算出一个方案优于另一个方案的可能度。     

基于MADM和ID3的高校教师科研业绩量化评估

高校科研数据库中已存贮了教师大量的科研成果数据,如何有效,快速地从海量数据中挖掘教师科研业绩,公平、合理地评价其科研能力,并做出相应的决策,已成为高校决策者十分关注的问题.在此,提出结合MADM(多属性决策)与数据挖掘的决策树ID3算法建立数据挖掘模型,以高校教师科研业绩为对象,科学地进行量化评估,从而为决策者的管理工作提供更加客观的信息.     

基于区间二型模糊熵的多属性决策方法

针对属性权重信息完全未知的区间二型模糊多属性决策问题,提出了一种基于区间二型模糊熵的多属性决策方法。为了量化区间二型模糊集的不确定信息,通过引入模糊因子、犹豫因子和区间因子建立了区间二型模糊熵的公理化准则,并分别基于欧氏距离、海明距离和广义距离给出了三种熵计算公式。同时,根据决策问题中总体不确定性最小化的原则,结合熵公式构建数学规划模型来确定属性权重,利用得分函数给出了具体的决策步骤,并通过实例分析验证了该决策方法的有效性和灵活性。     

信息对抗中多属性决策模型的研究

在分析信息对抗重要作用的基础上,针对各种决策理论在信息对抗中的应用,利用不确定性理论,建立基于理想点的多属性决策模型,给出决策结论的可靠性分析。     

A new distance measure for interval valued intuitionistic fuzzy sets and its application to group decision making problems with incomplete weights information

The aim of this study is to introduce a novel generalized distance measure for interval valued intuitionistic fuzzy sets and to illustrate the applicability of the proposed distance measure to group decision making problems. Firstly, a generalized distance measure is proposed along with proofs satisfying its axioms. Then, a comparison between the proposed distance measure and well-known distance measures is performed in terms of counter-intuitive cases. Subsequently, the extension of TOPSIS method, in which the proposed distance measure is used to calculate separation measures, to an interval valued intuitionistic fuzzy (IVIF) environment is demonstrated to solve multi-criteria group decision making (MCGDM) problems using optimal criteria weights determined with linear programming model based on the concept of maximizing relative closeness coefficient. Finally, two illustrative examples are provided for proof-of-concept purposes and to demonstrate benefits of using the proposed distance measure over the existing ones in IVIF TOPSIS method for MCGDM problems.