Linguistic hesitant intuitionistic fuzzy decision-making method based on VIKOR

Linguistic hesitant intuitionistic fuzzy set, which allows an element having several linguistic evaluation values and each linguistic argument having several intuitionistic fuzzy memberships, is a power tool to model uncertain information existing in multiple attribute decision-making problems. In this paper, we propose new methods by using TOPSIS and VIKOR for multiple attribute decision-making problems, in which evaluation values are in the form of linguistic hesitant intuitionistic fuzzy elements. Different situations of attribute weight information are considered. If attribute weights are partly known, a linear programming model is set up based on the idea that reasonable weights should make the relative closeness of each alternative evaluation value to the linguistic hesitant intuitionistic fuzzy positive ideal solution as large as possible. If attribute weights are unknown completely, an optimization model is set up based on the maximum deviation method. A numerical example is presented to illustrate feasibility and practical advantages of the proposed method. We compare the alternatives’ rankings derived from the linguistic hesitant intuitionistic fuzzy TOPSIS method with those derived from the hesitant fuzzy linguistic TOPSIS and the hesitant intuitionistic fuzzy TOPSIS approach to further illustrate their advantages.

     

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.     

基于直觉模糊推理的多属性群决策方法研究*

针对属性取值以直觉模糊数形式给出的多属性决策问题,提出了基于直觉模糊推理的多属性群决策方法。首先针对专家的评价信息构建直觉决策推理规则,然后根据规则之间的关系给出了决策推理模型,进而给出了基于直觉模糊推理的决策方法;最后通过购房实例验证了该方法的正确性和有效性。     

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.

     

Multiple attribute group decision-making methods with unknown weights in intuitionistic fuzzy setting and interval-valued intuitionistic fuzzy setting

To better solve the corresponding multiple attribute group decision-making problem with unknown weights, multiple attribute group decision-making methods with completely unknown weights of decision-makers and incompletely known weights of attributes are proposed in intuitionistic fuzzy setting and interval-valued intuitionistic fuzzy setting. In the group decision-making method, two weight models are proposed based on the score function to determine the weights of both experts and attributes from the intuitionistic fuzzy decision matrices and the interval-valued intuitionistic fuzzy decision matrices. Then, overall evaluation formulas of weighted scores for each alternative are introduced in the intuitionistic fuzzy setting and the interval-valued intuitionistic fuzzy setting to obtain the ranking order of alternatives and the most desirable one(s). Finally, two numerical examples demonstrate the applicability and benefit of the proposed methods.     

基于云模型的区间直觉模糊数多属性群决策

针对属性值为区间直觉模糊数的多属性群决策问题,考虑到模糊性和随机性对群决策过程及结果的影响,本研究将利用云模型理论结合区间直觉模糊数的特征,运用灰色关联系数法和信息熵理论确定专家和属性权重,通过信息集结构建综合评价云模型.不同于传统的区间直觉模糊数的排序方法,本研究利用云模型的3En规则将区间直觉模糊数进行云转换并通过云相似度确定方案的综合评价值和犹豫度,然后对决策方案进行比较分析.研究结果表明:该方法能够科学有效地进行决策,进而为决策方提供科学依据.     

多粒度支持直觉模糊粗糙集的多属性决策方法

针对多属性决策中多个相互冲突的属性信息使决策者很难做出决策判断的问题,文中从支持直觉模糊集的角度研究该问题.首先,在支持直觉模糊集的基础上,结合多粒度粗糙集理论,构造乐观、悲观两种多粒度支持直觉模糊粗糙集模型,分析两种模型之间的相互关系,讨论相关性质.然后,利用t-模和t-余模定义拟合函数,提出多粒度支持直觉模糊粗糙集的多属性决策求解方法,同时定义得分函数和精确函数排序决策结果,提取相应的决策规则,设计算法.实例分析表明,文中方法使决策者在处理信息冲突的多属性决策问题时可根据实际需求选择最优决策方案     

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。     

An interactive method for dynamic intuitionistic fuzzy multi-attribute group decision making

This paper investigates the dynamic intuitionistic fuzzy multi-attribute group decision making (DIF-MAGDM) problems, in which all the attribute values provided by multiple decision makers (DMs) at different periods take the form of intuitionistic fuzzy numbers (IFNs), and develops an interactive method to solve the DIF-MAGDM problems. The developed method first aggregates the individual intuitionistic fuzzy decision matrices at different periods into an individual collective intuitionistic fuzzy decision matrix for each decision maker by using the dynamic intuitionistic fuzzy weighted averaging (DIFWA) operator, and then employs intuitionistic fuzzy TOPSIS method to calculate the individual relative closeness coefficient of each alternative for each decision maker and obtain the individual ranking of alternatives. After doing so, the method utilizes the hybrid weighted averaging (HWA) operator to aggregate all the individual relative closeness coefficients into the collective relative closeness coefficient of each alternative and obtain the aggregate ranking of alternatives, by which the optimal alternative can be selected. In addition, the spearman correlation coefficient for both the aggregate ranking and individual ranking of alternatives is calculated to measure the consensus level of the group preferences. Finally, a numerical example is used to illustrate the developed method.     

区间直觉模糊连续熵及其多属性决策方法

提出了区间直觉模糊连续熵,并且研究了一种新的处理区间直觉模糊多属性决策问题的方法。基于连续有序加权平均（COWA）算子,给出了区间直觉模糊连续熵的概念,并且证明了区间直觉模糊连续熵满足区间直觉模糊熵的公理化定义的四个条件。在此基础上,针对属性权重信息完全未知的决策问题,通过衡量每一属性所含的信息量来确定属性权重。依据备选方案与理想方案间的加权相关系数,给出了一种新的区间直觉模糊多属性决策方法。实验结果验证了新的决策方法的可行性和有效性。     

Some induced intuitionistic fuzzy aggregation operators applied to multi-attribute group decision making

In this paper, we define various induced intuitionistic fuzzy aggregation operators, including induced intuitionistic fuzzy ordered weighted averaging (OWA) operator, induced intuitionistic fuzzy hybrid averaging (I-IFHA) operator, induced interval-valued intuitionistic fuzzy OWA operator, and induced interval-valued intuitionistic fuzzy hybrid averaging (I-IIFHA) operator. We also establish various properties of these operators. And then, an approach based on I-IFHA operator and intuitionistic fuzzy weighted averaging (WA) operator is developed to solve multi-attribute group decision-making (MAGDM) problems. In such problems, attribute weights and the decision makers' (DMs') weights are real numbers and attribute values provided by the DMs are intuitionistic fuzzy numbers (IFNs), and an approach based on I-IIFHA operator and interval-valued intuitionistic fuzzy WA operator is developed to solve MAGDM problems where the attribute values provided by the DMs are interval-valued IFNs. Furthermore, induced intuitionistic fuzzy hybrid geometric operator and induced interval-valued intuitionistic fuzzy hybrid geometric operator are proposed. Finally, a numerical example is presented to illustrate the developed approaches.     

Novel intuitionistic fuzzy decision making models in the framework of decision field theory

The intuitionistic fuzzy decision making problems have gained great popularity recently. Most of the current methods depend on various aggregation operators that provide collective intuitionistic fuzzy values of alternatives to be ranked. Such collective information only depicts the overall characteristics of the alternatives but ignores the detailed contrasts among them. Most important of all, the current decision making procedure is not in accordance with the way that the decision makers (DMs) think about the decision making problems. In this paper, we develop a novel intuitionistic fuzzy decision making model in the framework of decision field theory. The decision making model emphasizes the contrasts among alternatives with respect to each attribute that competes and influences each other, and thus, the preferences for alternatives can dynamically evolve and provide the final optimal result. After that, we develop an intuitionistic fuzzy group decision making model based on decision field theory, and then make a practical case study on the application of the developed models to the “one belt, one road” investment decision making problems. Finally, we point out the characteristics and the limitations of our models in detail.     

直觉模糊环境下考虑有限理性特征的决策方法

针对决策者具有有限理性的心理特征且属性权重和自然状态发生概率完全未知的直觉模糊多属性决策问题,提出了一种基于前景理论和证据理论的多属性决策方法。首先,利用证据理论得到各自然状态发生的概率,进而确定自然状态的决策权重函数;其次,运用正态分布概率密度函数设计直觉模糊决策参考点,并依据属性值与决策参考点之间的差异计算价值函数矩阵,从而获得前景价值矩阵;以综合前景价值最大化为准则构建最优化模型用以确定属性权重,并依据各方案的综合前景价值进行优劣排序。最后,将所提方法应用于对游戏产品的选择开发实例中。对比实验表明,运用所提方法得到的决策结果合理可靠,且更能体现决策者的原始决策信息。     

基于直觉模糊云模型的TOPSIS多属性决策方法

针对属性值为直觉模糊数的多属性决策问题,提出了一种基于直觉模糊云模型的TOPSIS多属性决策方法。首先,利用直觉模糊云对备选方案的各个属性值进行描述,计算其数字特征——期望、熵和超熵;然后,构造各数字特征的决策矩阵,获得其对应的正、负理想解;最后,计算各数字特征与正、负理想解间的距离,进而获得综合贴近度,对备选方案进行排序,获得最优决策结果,并通过具体数值实例验证方法的合理性和有效性。     

一种基于混合多属性的VIKOR群决策方法

针对含有多种属性和混合评价信息群决策问题,提出一种基于直觉模糊VIOKR的评价方法.首先,将不同类型属性值转换为直觉模糊数处理混合评价信息,降低了评价的随机性和模糊性,接着建立最小偏差优化模型计算指标以及专家权重,解决了专家和属性的权重信息未知的问题;引入VIKOR理论集结评价值对评价对象进行评价排序,并与TOPSIS方法进行了对比,说明了本算法的可行性和可信度.最后以某型电源车虚拟训练系统为研究对象,对人员业务水平决策进行实例研究,结果表明该群决策方法能够有效实现决策,具有较好的工程应用价值.     

A ranking method for multiple attribute decision-making problems based on the possibility degrees of trapezoidal intuitionistic fuzzy numbers

To solve multiple attribute decision-making problems with attribute values or decision values characterized by trapezoidal intuitionistic fuzzy numbers (TIFNs), we define a trapezoidal intuitionistic fuzzy induced ordered weighted arithmetic averaging (TIFIOWA) operator, which is an extension of the induced ordered weighted arithmetic averaging operator. We derive and prove some related properties and conclusions of the TIFIOWA operator. To compare the TIFNs, we define possibility degrees of the TIFNs. Based on the possibility degrees of the TIFNs and the TIFIOWA operator, we construct a new method to determine the order of alternatives in multiple attribute decision making and to choose the best alternative. Finally, a numerical example shows that the developed method is feasible and effective.     

基于IITFN输入的复杂系统关联MAGDM方法

区间直觉梯形模糊数（Interval-valued intuitionistic trapezoidal fuzzy number,IITFN）是刻画复杂系统不确定性的有效工具. 基于进一步完善的IITFN 运算规则,讨论其局部封闭性. 由此定义IITFN 几何Bonferroni 平均算子,并验证该算子的相关性质. 针对决策者及属性之间均存在关联作用且权重均未知的多属性群决策（Multi-attribute group decision making,MAGDM）问题,提出基于前景混合区间直觉梯形几何 Bonferroni （Prospect hybrid interval-valued intuitionistic trapezoidal fuzzy geometric Bonferroni,PHIITFGB）平均算子 的关联多属性群决策方法. 该方法首先通过依次定义IITFN 的前景效应、前景价值函数和前景价值,获取前景价值矩阵;其次,将前景价值矩阵转化为前景记分函数矩阵,并综合运用基于灰关联深度系数的客观属性权重极大 熵模型和基于2-可加模糊测度与Choquet 积分联合的决策者权重确定模型,获取决策者权重及属性权重;再次,利 用PHIITFGB 算子集结各决策者的方案评估信息,结合决策者权重即可获取相应于各方案的综合前景价值;最后,计算综合前景记分价值函数,基于IITFN 的序关系判别准则确定方案排序. 案例验证决策方法的有效性和可行性.     

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.     

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。