A goal programming method for obtaining interval weights from an interval comparison matrix

Crisp comparison matrices lead to crisp weight vectors being generated. Accordingly, an interval comparison matrix should give an interval weight estimate. In this paper, a goal programming (GP) method is proposed to obtain interval weights from an interval comparison matrix, which can be either consistent or inconsistent. The interval weights are assumed to be normalized and can be derived from a GP model at a time. The proposed GP method is also applicable to crisp comparison matrices. Comparisons with an interval regression analysis method are also made. Three numerical examples including a multiple criteria decision-making (MCDM) problem with a hierarchical structure are examined to show the potential applications of the proposed GP method.     

The interval-valued fuzzy TOPSIS method and experimental analysis

The purpose of this paper is to extend the TOPSIS method based on interval-valued fuzzy sets in decision analysis. Hwang and Yoon developed the technique for order preference by similarity to ideal solution (TOPSIS) in 1981. TOPSIS has been widely used to rank the preference order of alternatives and determine the optimal choice. Considering the fact that it is difficult to precisely attach the numerical measures to the relative importance of the attributes and to the impacts of the alternatives on these attributes in some cases, therefore, the TOPSIS method has been extended for interval-valued fuzzy data in this paper. In addition, a comprehensive experimental analysis to observe the interval-valued fuzzy TOPSIS results yielded by different distance measures is presented. A comparative analysis of interval-valued fuzzy TOPSIS rankings from each distance measure is illustrated with discussions on consistency rates, contradiction rates, and average Spearman correlation coefficients. Finally, a second-order regression model is provided to highlight the effects of the number of alternatives, the number of attributes, and distance measures on average Spearmen correlation coefficients.     

Sensitivity analysis for product design selection with an implicit value function

In product design selection the decision maker (DM) often does not have enough information about the end users’ needs to state the “preferences” with precision, as is required by many of the existing selection methods. We present, for the case where the DM gives estimates of the preferences, a concept for calculating a “robustness index.” The concept can be used with any iterative selection method that chooses a trial design for each iteration, and uses the DM’s preference parameters at that trial design to eliminate some design options which have lower value than the trial design. Such methods, like our previously published method, are applicable to cases where the DM’s value function is implicit. Our robustness index is a metric of the allowed variation between the actual and estimated preferences for which the set of non-eliminated trial designs (which could be singleton) will not change. The DM, through experience, can use the robustness index and other information generated in calculating the index to determine what action to take: make a final selection from the present set of non-eliminated designs; improve the precision of the preference estimates; or otherwise cope with the imprecision. We present an algorithm for finding the robustness index, and demonstrate and verify the algorithm with an engineering example and a numerical example.     

一种基于决策者风险态度的区间数多指标决策方法

针对具有区间数的多指标决策问题，提出了一种新的决策分析方法。该方法的思路是：首先通过引入决策的风险态度因子将区间数决策问题映射为传统的点值决策问题。然后给出了基于TOPSIS的方案排序方法，最后通过对风险态度因子的不同取值可进行方案排序的灵敏度分析。     

基于有序梯形模糊灰色关联TOPSIS的多属性决策方法

研究了有序梯形模糊数来表示不确定语言环境下的灰色关联TOPSIS多属性决策问题。首先应用有序梯形模糊数标度方案属性偏好信息,在传统梯形模糊数基础上增加了一个方向属性,使得决策信息的表示更加细腻;提出了有序梯形模糊环境下多属性决策灰色关联TOPSIS综合优选算法,引入了距离和灰色关联度相结合的综合贴近度公式,实现最优方案与理想方案的位置与曲线形状的一致性;最后通过制造系统内流动控制实例说明了所提出有序梯形模糊灰色关联TOPSIS方法的可行性和有效性。     

基于区间直觉梯形模糊数的改进TOPSIS多属性决策方法

研究了属性权重完全未知的区间直觉梯形模糊数的多属性决策问题,结合TOPSIS方法定义了相对贴近度及总贴近度公式.首先由区间直觉梯形模糊数的Hamming距离给出了每个方案的属性与正负理想解的距离,基于此,给出了相对贴近度矩阵,根据所有决策方案的综合贴近度最小化建立多目标规划模型,从而确定属性的权重值,然后根据区间直觉梯形模糊数的加权算数平均算子求出各决策方案的总贴近度,根据总贴近度的大小对方案进行排序;最后,通过实例分析说明该方法的可行性和有效性.     

基于信息熵的属性约简在多属性决策中的应用

属性约简是在信息系统中的一个重要操作.分类是属性约简的基础,且直接在大数据集上进行属性约简往往存在效率低下的问题.以分类为基础提出了一种基于信息熵的信息系统属性约简算法.算法通过信息熵的计算,在属性约简的同时对原信息系统逐层分解,从而实现了属性的约简并缩小了搜索空间.提出了依据信息熵来确定属性的不必要性及简约属性集,应用在多属性决策中所带来的优势.     

对TOPSIS法用于综合评价的改进

本文指出了 TOPSIS法用于综合评价所存在的问题 ,并提出了相应的改进方法 ,使 TOPSIS法用于综合评价以及多目标决策分析更趋完善 ,所得分析评价结果更合理更客观     

图书馆图书供应商选择的PROMETHEE/TOPSIS决策模型

图书供应商选择对图书馆各项功能的实现和未来的发展有着重要影响,这一重要问题的解决方法受到很多学者的关注。在构建图书供应商评价指标体系的基础上,提出了一种供应商选择的PROMETHEE／TOPSIS决策模型。模型通过向具有完全补偿性的TOPSIS方法中引入偏好函数,并结合摆动赋权方法,减少了决策信息的损失和扭曲,更好地反映了图书供应商间的差别。最后通过实例证明了该模型的有效性和实用性。     

基于“奖优罚劣”的区间数多指标决策的TOPSIS方法

针对区间数多指标系统的决策特点,对指标数据初始化处理时,利用"奖优罚劣"原则,提出了一种易于计算且实用的[-1,1]线性变换算子,然后定义正、负理想方案,给出了区间数多指标决策问题的TOPS IS方法.该模型为区间数多指标决策提供了一种科学、实用的方法,并利用现有的实例来证实此方法的科学性与可行性.     

模糊群决策的逼近于理想解排序法

首先给出一致性互补判断矩阵元素与排序权重的一种新逻辑关系,并以模糊极大集和模糊极小集作为模糊正理想解和模糊负理想解。然后,通过α-截集将模糊数转化为α水平下的区间数,并构造基于贴近度的可能度矩阵,利用所提出的逻辑关系确定在α水平下的排序权重。最后集结各水平下的权重得到最终的排序权重。     

基于蒙特卡洛仿真的理想点决策方法及其应用

首先分析了传统TOPS IS方法的基本原理和计算步骤,指出了传统TOPS IS方法应用时存在的限制与不足,提出了基于计算机蒙特卡洛仿真方法与传统理想点方法相结合的思想,该方法可以利用评测所给的区间值,既方便表述评测结果,也充分利用了评测结果,更加接近实际情况,因而,有助于提高决策质量.最后,通过复杂工程系统设计决策一个算例验证了该法的可行性与有效性.     

基于区间值直觉模糊集的TOPSIS多属性决策

基于区间值直觉模糊集,提出了一种新的TOPSIS模糊多属性决策方法。首先介绍区间直觉模糊集的概念,定义了两个区间值直觉模糊集之间的距离;然后根据TOPSIS方法的原理,定义了两个区间值直觉模糊集的接近系数,通过计算备选方案到区间值直觉模糊正理想解和负理想解的距离来确定接近系数,从而判断备选方案的优劣次序。最后,通过一个具体实例来说明这种方法的有效性和具体计算过程。     

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。     

Extension of the TOPSIS method for decision making problems under interval-valued intuitionistic fuzzy environment

TOPSIS is one of the well-known methods for multiple attribute decision making (MADM). In this paper, we extend the TOPSIS method to solve multiple attribute group decision making (MAGDM) problems in interval-valued intuitionistic fuzzy environment in which all the preference information provided by the decision-makers is presented as interval-valued intuitionistic fuzzy decision matrices where each of the elements is characterized by interval-valued intuitionistic fuzzy number (IVIFNs), and the information about attribute weights is partially known. First, we use the interval-valued intuitionistic fuzzy hybrid geometric (IIFHG) operator to aggregate all individual interval-valued intuitionistic fuzzy decision matrices provided by the decision-makers into the collective interval-valued intuitionistic fuzzy decision matrix, and then we use the score function to calculate the score of each attribute value and construct the score matrix of the collective interval-valued intuitionistic fuzzy decision matrix. From the score matrix and the given attribute weight information, we establish an optimization model to determine the weights of attributes, and construct the weighted collective interval-valued intuitionistic fuzzy decision matrix, and then determine the interval-valued intuitionistic positive-ideal solution and interval-valued intuitionistic negative-ideal solution. Based on different distance definitions, we calculate the relative closeness of each alternative to the interval-valued intuitionistic positive-ideal solution and rank the alternatives according to the relative closeness to the interval-valued intuitionistic positive-ideal solution and select the most desirable one(s). Finally, an example is used to illustrate the applicability of the proposed approach.     

基于Hausdauff度量的模糊TOPSIS方法研究

针对模糊多属性决策中的模糊 TOPSIS方法 ,提出了一种基于 Hausdauff度量的模糊 TOPSIS方法 .首先由模糊极大集与模糊极小集确定模糊多属性决策问题的理想解与负理想解 ,进而由 Hausdauff度量获得不同备选方案到理想解与负理想解的距离及其贴近度 ,根据贴近度指标对方案进行排序 ,为决策者提供决策支持 .最后以 L-R梯形模糊数为例进行了实例研究 .     

基于投影模型的区间直觉模糊多属性决策方法研究

本文首先定义了一种新区间直觉模糊投影方法,其能更好地度量投影向量之间的相关性。其次,根据区间直觉模糊正负理想方案与备选方案的投影关系, 构建了基于投影方法的未知属性权重求解模型,并在此基础上设计了一种基于投影值的贴近度方法,能实现对备选方案有效排序;最后,用实例验证了该方法的有效性和可行性。     

区间三角模糊多属性决策的GRA扩展方法

针对属性权重信息部分己知且属性值以区间三角模糊数形式给出的多属性决策问题,提出了一种基于灰色关联分析(GRA)扩展的决策方法.首先给出了区间三角模糊数的定义,然后依据传统GRA法的基本思想建立了区间三角模糊数多属性决策问题的决策步骤.最后给出了一个实例分析,所得结果表明了方法的实用性和可行性.