基于方案偏好和部分权重信息的模糊多属性决策方法

研究了只有部分权重信息且决策者对方案的偏好信息以三角模糊数互反判断矩阵形式给出的模糊多属性决策问题.首先为得到属性权重,给出一种结合主观模糊偏好信息和客观决策信息的极小化极大偏差模型;然后,运用加性加权法求出各方案的模糊综合属性值,并利用已有的三角模糊数排序公式求得决策方案的排序;最后,通过算例说明了该方法的可行性和有效性.     

基于直觉梯形模糊TOPSIS的多属性群决策方法

提出一种改进的逼近理想解排序(TOPSIS)方法,即直觉梯形模糊TOPSIS多属性群决策方法。首先,应用直觉梯形模糊数形式表示方案属性偏好和属性权重信息且专家权重完全未知;然后,利用直觉梯形模糊数间距离测度和期望值及直觉梯形模糊加权平均算子来确定决策者权重信息和属性权重信息;进而给出直觉梯形模糊环境下方案优选的算法;最后,通过算例进一步说明了该直觉梯形模糊TOPSIS方法的有效性。     

一种对方案有偏好的Vague集多属性决策方法

研究了方案属性值和偏好值均为Vague值的多属性决策问题。针对相关文献中,将由Vague值表示的方案属性值与偏好值转化为直觉模糊数,并根据直觉模糊数表示的方案属性值与偏好值之间的偏差建立规划模型并求解属性权重这一过程,分析了建立的规划模型的不合理性。提出通过最小化直觉模糊数表示的方案综合值与偏好值的偏差,建立并求解一个规划模型计算属性权重的改进方法。通过将Vague值转化为模糊值,利用模糊值矩阵的线性序构造模糊优先矩阵,并对其进行分割,从而实现方案的排序择优。通过一个实例说明了该方法的可行性。     

基于交叉熵的ITFN的多属性决策方法

针对属性值为直觉梯形模糊数且属性权重完全未知的多属性决策问题,提出了一种基于交叉熵的决策方法。给出期望值的方法将直觉梯形模糊数转化为直觉模糊数,进而提出直觉模糊数的交叉熵等概念及相关性质。基于各方案与正理想方案的总区别信息最小化原则,建立非线性模型,求出属性权重。用实例说明该方法的有效性。     

区间直觉模糊决策中专家与属性权重确定方法

针对评价信息为区间直觉模糊的多属性群决策问题中,决策者与属性的权重均未知的情况,提出一种排序方法。为求解属性值权重,从区间直觉模糊数的几何意义出发,基于熵值最大化原理,求出属性的权重,得到每位专家对每个方案的综合评价值。基于专家个体与专家群体意见之间的灰色关联度以及熵最大化原理,建立模型求出各决策者的权重。在此基础上综合所有专家意见得到评价值,并对方案比较排序。算例验证了此方法的合理有效性。     

基于前景和量子理论的模糊多属性决策方法

针对属性权重不完全确定且属性偏好值为区间直觉模糊数的多属性决策问题,提出一种基于前景理论和量子进化算法的模糊多属性决策方法。该方法根据前景理论及模糊数距离公式,定义区间直觉模糊数的前景价值函数,同时将决策者对方案的风险偏好纳入决策行为中,以此来构建方案综合前景值最大化的非线性规划模型。通过引入量子进化算法,求解模型得出最优权重向量。最终根据方案前景值确定出方案的排序。该方法适用于模糊决策环境,能满足决策者不提供确定属性权重的要求,并充分考虑决策者风险心理因素对决策行为的影响,具有广泛的应用价值。数值算例说明了该方法的有效性和可行性。     

基于二次规划的直觉模糊数的多属性决策方法

针对属性权重完全未知且属性值为直觉模糊数的多属性决策问题,提出了一种新的决策方法。首先引入了直觉模糊数的一些运算法则、得分函数和精确函数等概念。然后构建了一个二次规划模型,通过求解该模型获得属性的权重。接着利用直觉模糊加权平均(IFWA)算子对属性值进行集结,得到方案的综合属性值。最后利用得分函数和精确函数对方案进行排序并择优。给出的算例说明了该方法的实用性和可行性。     

基于累积前景理论和Choquet积分的直觉梯形模糊多属性决策

针对属性值为直觉梯形模糊数且属性存在关联性的风险决策问题, 提出一种基于累积前景理论和Choquet积分的直觉梯形模糊多属性决策方法。根据直觉梯形模糊数距离公式定义了直觉梯形模糊信息的前景价值函数, 通过价值函数和决策权重函数计算方案单属性前景值, 并运用Choquet积分融合属性间存在关联性的前景价值信息获得方案综合前景值, 根据综合前景值的大小实现方案的排序和优选。风险投资实例分析说明了该方法的可行性。     

基于改进熵和新得分函数的区间直觉模糊多属性决策

针对决策信息为区间直觉模糊数且属性权重完全未知的多属性决策问题, 提出基于改进的区间直觉模糊熵和新得分函数的决策方法. 首先, 利用改进的区间直觉模糊熵确定属性权重; 然后, 利用区间直觉模糊加权算术平均算子集成信息, 得到各备选方案的综合属性值, 进而指出现有得分函数存在排序失效或排序不符合实际的不足, 同时给出一个新的得分函数, 并以此对方案进行排序; 最后, 通过实例表明了所提出方法的有效性.

     

三角直觉模糊决策的权重函数方法

研究了属性值为三角直觉模糊数的多属性决策问题,提出了一种基于权重函数的决策方法。给出了三角直觉模糊数的定义、运算法则和截集;定义了三角直觉模糊数关于隶属函数和非隶属函数的精确值和模糊度,以及精确值的指标和模糊度的指标,给出了三角直觉模糊数的排序方法,并将其应用到属性值为三角直觉模糊数的多属性决策问题中;给出了属性值为三角直觉模糊数的多属性决策的步骤;通过数值算例分析和验证了该方法的有效性。     

MADM method based on prospect theory and evidential reasoning approach with unknown attribute weights under intuitionistic fuzzy environment

This paper proposes an intuitionistic fuzzy decision method based on prospect theory and the evidential reasoning approach, aiming at analyzing multi-attribute decision making problems in which the criteria values are intuitionistic fuzzy numbers and the information of attributes weights is unknown. Firstly, the measures of entropy and cross entropy are defined for intuitionistic fuzzy sets by taking into consideration the preference of decision maker towards hesitancy degree. Secondly, combined with bounded rationality, the prospect decision matrix is calculated in the light of prospect theory and intuitionistic fuzzy distance. Thirdly, the correlational analyses are conducted between the attribute weights and three indicators which are entropy, cross entropy and prospect value, and optimization models for identifying attribute weights are built under the circumstances that the weights are incomplete and unknown. Finally, in order to avoid the loss of decision making information, the evidential reasoning approach is applied to the calculation of comprehensive prospective values for all alternatives. Following the value calculation, the ranking and the optimal alternative are determined based on the comprehensive prospective values. Illustrating examples demonstrate that the proposed method is reasonable and feasible.     

基于粗糙集的直觉模糊TOPSIS多属性决策方法

针对属性值为直觉模糊信息且属性权重完全未知的多属性决策问题,提出了一种基于粗糙集的直觉模糊TOPSIS多属性决策方法.首先给出了直觉模糊信息的正、负理想点的求法,根据属性值与理想点的贴近度和给定的阈值求得判断矩阵,再根据判断矩阵对属性约简,确定各属性的权重,最后依据TOPSIS思想计算各方案与理想点的加权贴近度,得到方案的排序,并通过算例的分析比较验证了此方法的有效性.     

属性权重不确定条件下的区间直觉模糊多属性决策

在区间直觉模糊集(Interval-valued intuitionistic fuzzy set, IVIFS)的框架内,重点研究了属性权重在一定约束条件下和属性权重完全未知的 多属性群决策问题.首先利用区间直觉模糊集成算子获得方案在属性上的综合区间直觉模糊决策矩阵,进一步依据逼近理想解排序法(Technique for order preference by similarity to an ideal solution, TOPSIS) 的思想计算候选方案和理想方案的加权距离,最后确定方案排序.其中针对属性权重在一定约束条件下的决策问题,提出了基于 区间直觉模糊集精确度函数的线性规划方法,用以解决属性权重求解问题.针对属性权重完全未知的决策问题,首先定义了区间直觉 模糊熵,其次通过熵衡量每一属性所含的信息量来求解属性权重.实验结果验证了决策方法的有效性和可行性.     

用区间直觉模糊集方法对属性权重未知的群求解其多属性决策

本文首先提出群区间直觉模糊有序加权几何(groupinterval-valuedintuitionistic fuzzy orderedweighted geometric,GIVIFOWG)算子和群区间直觉模糊有序加权平均(group interval-valued intuitionistic fuzzy ordered weighted averaging,GIVIFOWA)算子.利用GIVIFOWG算子或GIVIFOWA算子聚集群的决策矩阵以获得方案在属性上的综合区间直觉模糊决策矩阵(collectiveinterval-valuedintuitionistic fuzzy decision-matrix,CIVIFDM).然后定义了一个考虑犹豫度的区间直觉模糊熵(interval-valuedintuitionistic fuzzyentropy,IVIFE);通过熵衡量每个属性所含的信息来求解属性权重.最后,提出基于可能度的接近理想解的区间排序法(interval technique for order preference by similarity to an ideal solution,ITOPSIS)和区间得分函数法.在ITOPSIS法中,依据区间距离公式计算候选方案和理想方案的属性加权区间距离,进而采用ITOPSIS准则对各方案进行排序;在区间得分函数法中,算出CIVIFDM中各方案的得分值以及精确值,然后利用区间得分准则对各方案进行排序.实验结果验证了决策方法的有效性和可行性.     

An interval-valued intuitionistic fuzzy multiattribute group decision making framework with incomplete preference over alternatives

This article proposes a framework to handle multiattribute group decision making problems with incomplete pairwise comparison preference over decision alternatives where qualitative and quantitative attribute values are furnished as linguistic variables and crisp numbers, respectively. Attribute assessments are then converted to interval-valued intuitionistic fuzzy numbers (IVIFNs) to characterize fuzziness and uncertainty in the evaluation process. Group consistency and inconsistency indices are introduced for incomplete pairwise comparison preference relations on alternatives provided by the decision-makers (DMs). By minimizing the group inconsistency index under certain constraints, an auxiliary linear programming model is developed to obtain unified attribute weights and an interval-valued intuitionistic fuzzy positive ideal solution (IVIFPIS). Attribute weights are subsequently employed to calculate distances between alternatives and the IVIFPIS for ranking alternatives. An illustrative example is provided to demonstrate the applicability and effectiveness of this method.     

基于直觉模糊集和证据理论的群决策方法

针对属性值和权重均为直觉模糊数的多属性决策问题,提出一种基于直觉模糊集和证据理论的群决策方法.首先,对专家给出的每个方案的属性值和属性权重进行证据合成,在此基础上合成每个方案的所有属性值;然后,基于直觉模糊集相似度确定专家的相对权重,修正方案证据,并合成所有专家证据,得到方案的信任区间,根据信任区间的大小对方案进行排序;最后,通过数值案例验证了所提出方法的有效性和合理性.     

Enhancing PROMETHEE method with intuitionistic fuzzy soft sets

The notion of intuitionistic fuzzy soft sets (IFSSs) provides an effective tool for solving multiple attribute decision making with intuitionistic fuzzy information. The most crucial issue in decision making based on IFSSs is how to derive the ranking of alternatives from the information quantified in terms of intuitionistic fuzzy values. In this study, we propose a new extension of the preference ranking organization method for enrichment evaluation (PROMETHEE), by taking advantage of IFSSs. In addition to presenting a myriad of new notions, such as intuitionistic fuzzy membership (or nonmembership) deviation matrices, intuitionistic fuzzy membership (or nonmembership) preference matrices, and aggregated intuitionistic fuzzy preference matrices, we put more emphasis on the construction of three distinct preference structures and related utility functions on the corresponding weakly ordered sets by considering the positive, negative, and net flows of the alternatives based on the aggregated intuitionistic fuzzy preference matrix. We present a new algorithm for solving multiple attribute decision-making problems with the extended PROMETHEE method based on IFSSs. Moreover, a benchmark problem concerning risk investment is investigated to give a comparative analysis and show the feasibility of our approach.     

Nonlinear optimization models for multiple attribute group decision making with intuitionistic fuzzy information

Intuitionistic fuzzy numbers are very useful for experts to depict in depth their fuzzy preference information over objects. In this work, we investigate multiple attribute group decision‐making problems in which the attribute values provided by experts are expressed in intuitionistic fuzzy numbers, each of which is composed of a membership degree, a nonmembership degree and a hesitancy degree, and the weight information about both the experts and the attributes is to be determined. We first make different types of attribute values uniform so as to facilitate interattribute comparisons and employ the simple additive weighting method to fuse all the individual opinions into the group one. We then develop two nonlinear optimization models, one minimizing the divergence between each individual opinion and the group one, and the other minimizing the divergence among the individual opinions, from which two exact formulae can be obtained to derive the weights of experts. Similarly, from the viewpoint of maximizing group consensus, we establish a nonlinear optimization model based on all the individual intuitionistic fuzzy decision matrices to determine the weights of attributes. The simple additive weighting method is used to aggregate all the intuitionistic fuzzy attribute values corresponding to each alternative, and then the score function and the accuracy function are employed to rank and select the given alternatives. Moreover, we extend all the above results to interval intuitionistic fuzzy situations, and finally apply the developed models to an air‐condition system selection problem. © 2010 Wiley Periodicals, Inc.     

方案偏好已知的三角模糊数型多属性决策方法

研究决策者对方案偏好已知、属性值以三角模糊数形式给出且属性权重信息不能完全确知的多属性决策问题.提出了基于模糊比例值的决策方法和基于模糊偏差度的决策方法,这两种方法首先建立一个线性规划模型,通过求解该模型获得属性权重;然后,基于三角模糊数两两比较的可能度公式及三角模糊数排序公式,对决策方案进行排序和择优;最后,通过实例验证了方法的可行性和有效性.     

基于粗糙集技术的压缩近邻规则

针对各决策时段的时间权重及属性权重已知情况下属性值以直觉模糊数形式给出的动态多属性决策问题,提出了一种基于多准则妥协解排序(VIKOR)拓展的决策分析方法。首先利用给出的动态直觉模糊加权平均(DIF-WA)算子集成各时段的评价值,以获取各方案的综合评价值。然后依据传统VIKOR法的基本思想,结合直觉模糊数的距离公式,对整个方案集进行排序并择优。最后给出一个实例分析,所得结果表明了该方法的可行性和有效性。