区间Pythagorean犹豫模糊连续熵及灰色关联度的应用

区间Pythagorean犹豫模糊集,可以更加全面完整地描述决策者给出的决策结果,因此它是一个表示不确定现象的强有力的工具。针对模糊信息下的决策问题,提出了一种基于区间Pythagorean犹豫模糊连续熵的多属性决策方法。提出连续区间Pythagorean犹豫模糊有序加权平均（CIPHFOWA）算子,并提出了区间Pythagorean犹豫模糊连续熵,同时给出了属性权重完全未知和部分已知时的权重确定方法;提出了一种基于区间Pythagorean犹豫模糊连续熵-灰色关联度的多属性决策方法,并通过新型农村医疗制度完善情况评价案例说明该方法的可行性和有效性。     

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.     

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.     

Graded dominance interval-based fuzzy objective information systems

Dominance interval-based fuzzy objective information systems are generalized models of single-valued fuzzy information systems. By introducing a graded dominance relation to dominance interval-valued fuzzy objective information systems, we establish a graded dominance interval-valued rough set model (RSM), which is mainly based on replacing the indiscernibility relation in classical rough set theory with the graded dominance interval-valued relation. Furthermore, in order to simplify knowledge representation and extract nontrivial simpler graded dominance interval fuzzy decision rules, we propose two attribute reduction approaches to eliminate the redundant condition attributes that are not essential from the viewpoint of graded dominance interval-valued fuzzy decision rules. These results are helpful for decision-making analysis in dominance interval-valued fuzzy objective information systems.     

A method for multiple attribute decision making with incomplete weight information in linguistic setting

The aim of this paper is to investigate the multiple attribute decision making problems with linguistic information, in which the information about attribute weights is incompletely known, and the attribute values take the form of linguistic variables. We first introduce some approaches to obtaining the weight information of attributes, and then establish an optimization model based on the ideal point of attribute values, by which the attribute weights can be determined. For the special situations where the information about attribute weights is completely unknown, we establish another optimization model. By solving this model, we get a simple and exact formula, which can be used to determine the attribute weights. We utilize the numerical weighting linguistic average (NWLA) operator to aggregate the linguistic variables corresponding to each alternative, and then rank the alternatives by means of the aggregated linguistic information. Finally, the developed method is applied to the ranking and selection of propulsion/manoeuvring system of a double-ended passenger ferry.     

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。     

基于熵和相关系数的直觉模糊多属性决策方法

针对决策信息为直觉模糊信息且属性权重完全未知的多属性决策问题,提出了一种基于直觉模糊熵和得分函数的决策方法。为了准确度量直觉模糊集的直觉性和模糊性,首先提出了一种新的直觉模糊熵,并讨论其相关性质。其次为了减少不确定信息对决策的影响,结合直觉模糊熵建立规划模型,从而确定属性权重。 同时从隶属度,非隶属度和犹豫度三方面构建论域对象与理想对象之间相关系数,并在此基础上根据决策者的决策态度定义得分函数进而得到最优决策。 最后给出一种基于直觉模糊信息的多属性决策方法,并通过候选人评估实例验证了该方法的可行性和有效性。     

区间直觉模糊连续交叉熵及其多属性决策方法

在区间直觉模糊（IVIF）环境下,利用连续有序加权平均（COWA）算子定义了一种新的区间直觉模糊数间的交叉熵,即区间直觉模糊连续交叉熵。依据提出的区间直觉模糊连续交叉熵定义了直觉模糊数间的连续交叉熵距离。基于TOPSIS的思想得到备选方案与理想方案的加权距离,并且计算备选方案与理想方案的相对贴近度,依据相对贴近度选择最优方案。其中,针对属性权重信息不完全确定条件下的决策问题,提出了以区间直觉模糊连续交叉熵最大为准则的规划模型;针对属性权重信息完全未知的情况,根据交叉熵理论确定属性权重向量。实验结果验证了新的决策方法的可行性和有效性。     

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.     

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.

     

基于可信度的基本不确定区间犹豫模糊广义TODIM应急群决策方法

针对应急决策环境所存在的信息不完备、认知不足等问题,区间犹豫模糊集能充分表达决策者在信息评价时的犹豫性和模糊性,但随着研究的深入,发现其存在无法保证信息质量的缺陷.为此,提出更符合实际决策需求、信息表达更加灵活的基本不确定区间犹豫模糊集,其为包含区间犹豫模糊集和确定度的二维信息集.在此基础上,定义基本不确定区间犹豫模糊加权平均算子、犹豫度及可信度,提出基于可信度的专家权重调整方法和属性权重确定方法,充分考虑了决策专家提供评价信息的可靠程度.最后,将广义TODIM方法拓展到基本不确定区间犹豫模糊环境,通过应急决策案例验证所提方法的可行性,并利用灵敏度分析和对比分析验证该方法的稳定性和有效性.     

基于改进模糊熵和证据推理的多属性决策方法

针对证据推理方法框架下属性权重难以获取的问题,提出一种基于改进模糊熵和证据推理的多属性决策方法。首先,定义证据推理信度决策矩阵框架下的三角函数模糊熵公式,并证明了其满足熵的四个公理化定义。其次,所提方法能够同时处理属性权重完全未知和属性权重信息部分已知两种情况：当属性权重完全未知时,基于信度框架下的改进模糊熵和熵权法的基本思想计算属性权重;当属性权重信息部分已知时,定义加权模糊熵,建立期望模糊熵最小的线性规划模型求解最优属性权重。最后,利用证据推理算法融合方案属性值,结合期望效用理论得到方案排序结果。通过实例计算,并与传统模糊熵计算方法进行比较分析,验证了所提方法能够更加充分地反映原始决策信息,更具客观性和一般性。     

区间犹豫模糊三角相似度及其多属性群决策

构建了区间犹豫模糊三角相似度公式,并且研究了区间犹豫模糊环境下属性权重信息完全未知的多属性群决策方法。首先基于正弦三角函数构造了区间犹豫模糊三角相似度公式,并证明其满足区间犹豫模糊相似度公理化定义的四个条件;接着给出了区间犹豫模糊交叉熵的公理性定义,同时研究了区间犹豫模糊相似度和区间犹豫模糊交叉熵的关系;最后基于区间犹豫模糊三角相似度,提出了在属性权重信息完全未知条件下的区间犹豫模糊多属性群决策方法,并用实例验证该方法的可行性和有效性。     

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.

     

Attribute weights determination models for consensus maximization in multiple attribute group decision-making

Multiple attribute group decision making (MAGDM) is an important research field of decision science. A critical aspect of MAGDM is to determine the weights of attributes. In this paper, we study the MAGDM problem in which the attributes are given in real numbers or interval numbers, and the information about attribute weights is completely unknown or partially known. We first get the group opinion by fusing all individual opinion with each decision-makers' importance and introduce the deviation variable of each individual opinion and the group opinion. Then, we develop a quadratic programming model by means of minimizing the sum of all the deviation values, and a simple and straightforward formula for determining attribute weights can be derived from solving the developed models. We also establish a generalized model for solving MAGDM problems with partial weight information on attributes. In addition, we establish some similar models for MAGDM with interval attribute values. At last, we apply our models to a practical problem of a military unit purchasing new artillery weapons.     

考虑信任度的Pythagorean模糊两阶段交互多属性群决策方法

针对属性值为Pythagorean模糊语言,属性权重未知且考虑群体一致性和决策者属性偏好不确定性的决策问题,探讨了一种考虑信任度的两阶段交互多属性群决策方法.首先,考虑决策者偏好,将属性集分为必选属性集和可选属性集;其次,构建两阶段交互机制以确保必选属性集的群体一致性达到阈值,第一阶段以提升群体共识水平为目标进行交互,第二阶段以降低冲突水平为目标进行交互;再次,同时考虑交互的积累稳定性和积累影响因子以确定必选属性集下的决策者权重,并依据信任度确定可选属性集下的决策者权重;最后,用距离熵确定属性权重,并用VIKOR法选出最优方案.算例分析表明,该方法能够较好地解决考虑共识和冲突水平的多属性群决策问题.     

模糊语言下的梯形模糊数心态指标群决策方法

在模糊语言下,提出了梯形模糊数心态指标的群决策方法。在属性权系数和决策者权系数信息都不完全的情况下,引入心态指标,将模糊语言的梯形模糊数决策矩阵转化为带心态指标的决策矩阵;利用决策的不完全信息构造Fuzzy线性规划,分别求解出属性权重和决策者权重;对决策者的心态指标进行集成得到群体风险态度,模糊集成群体风险态度与方案的群体评价值,得到整个方案集的排序。选取实例说明该方法的有效性、可行性和可操作性。     

Possibilistic programming approach for fuzzy multidimensional analysis of preference in group decision making

Multiple attribute decision making (MADM) problems are the most encountered problems in decision making. Fuzziness is inherent in decision making process and linguistic variables are well suited to assessing an alternative on qualitative attributes using fuzzy rating. A few techniques in MADM assess the weights of attributes based on preference information on alternatives. But they are not practical any more when the set of all paired comparison judgments from decision makers (DMs) on attributes are not crisp and also we have to deal with fuzzy decision matrix. This paper investigates the generation of a possibilistic model for multidimensional analysis of preference (LINMAP). The model assesses the fuzzy weights as well as locating the ideal solution with fuzzy decision making preference on attributes and fuzzy decision matrix. All of the information is assumed as triangular fuzzy numbers (TFNs). This method is developed in group decision making environments and formulates the problem as a possibilistic programming with multiple objectives.     

区间直觉模糊信息下的双向投影决策模型

研究权重完全未知、评价信息为区间直觉模糊数的多准则决策问题. 考虑犹豫度影响, 给出备选方案与正理想方案、负理想方案形成的向量表达方式, 提出一种针对区间直觉模糊信息的向量投影测度方法; 构建基于方案投影总偏差最小的非线性规划准则权重确定模型; 给出基于方案投影的相对贴近度测算公式, 并以此对方案进行排序. 最后通过算例对比分析表明了所提出方法的有效性和可行性.

     

考虑属性权重优化的犹豫模糊多属性决策方法

针对属性权重完全未知的犹豫模糊多属性决策问题, 提出一种属性权重多目标优化方法. 首先, 根据属性值的均值、方差以及属性间的关联度建立属性权重确定模型; 然后, 利用方案与犹豫模糊正理想点的相似度对方案进行排序; 最后, 通过算例分析表明了所提出方法的有效性和可行性.