基于后悔理论的概率犹豫模糊双边匹配决策方法

针对概率犹豫模糊信息下准则具有期望水平的双边匹配决策问题,考虑双边主体后悔规避的心理行为特征,提出一种基于后悔理论的双边匹配决策方法.首先,定义概率犹豫模糊元的新兰氏距离和兰氏记分函数.然后,基于后悔理论提出一种准则具有期望水平的概率犹豫模糊双边匹配决策方法.该方法利用期望效用函数和概率犹豫模糊元兰氏记分函数构建双边主体的准则效用值矩阵;利用后悔-欣喜函数构建双边主体对于准则期望水平的后悔-欣喜值矩阵;依据后悔理论构建双边主体对于准则期望水平的感知价值矩阵.进一步,先利用离差最大化思想和概率犹豫模糊元新兰氏距离构建优化模型求解准则权重,再利用线性加权法构建双边主体的综合感知价值矩阵,利用极差变换法构建双边主体的满意度矩阵.在此基础上,基于满意度最大化,构建考虑双边匹配方案稳定性的多目标优化模型,并通过求解模型得到双边匹配结果.最后,通过算例分析表明了所提出匹配决策方法的有效性和实用性.     

考虑直觉模糊的多指标人岗双边匹配决策方法

针对现实生活中人岗双边匹配决策问题的特点,基于直觉模糊理论,构建了一种具有不同信息类型的人岗双向选择的多指标评价双边匹配决策模型,并提出了相应的决策方法。通过构造人岗双方匹配满意度计算规则,将包含直觉模糊偏好信息的人岗双边主体评价信息转化为匹配满意度;通过对所有标准下的满意度矩阵的集结,构造人岗双方的满意度矩阵。在此基础上,以人岗双方主体可接受最低水平为约束,构建了一个使双方主体满意度最大为目标的人岗双边匹配多目标决策优化模型。通过一个人岗双边匹配问题的案例证明了该方法的合理性。     

基于TODIM的直觉模糊双边公平满意匹配方法

针对直觉模糊偏好信息下的双边匹配问题,考虑匹配主体参照依赖和损失规避的心理行为,提出一种基于TODIM(TOmada de decis\ao interativa multicritério)的双边公平满意匹配方法.首先,对直觉模糊偏好信息下的双边匹配问题进行描述;然后,依据前景理论将双边主体的直觉模糊偏好信息转化为相对于参照点的收益或损失,在此基础上,依据TODIM法计算每个主体的总体优势度,构建满意度计算规则,建立双边公平满意匹配优化模型,求解模型并获得双边匹配解;最后,通过一个算例验证所提出方法的可行性和有效性.     

考虑直觉模糊偏好关系的双边稳定匹配及应用

针对现有双边匹配决策要求主体给出另一方全体偏好序信息的条件过于苛刻的问题, 提出一种新的匹配方法. 一方主体先两两比较另一方全体成员, 给出直觉模糊集形式的评价值并由全体成员评价值组成直觉模糊偏好关系; 然后, 通过改进的最小对数二乘法对其进行转化, 间接得到主体满意度; 进一步以双方主体满意度最大为目标, 同时考虑稳定匹配约束条件, 建立单目标优化模型并求解获得匹配方案; 最后, 通过算例分析表明了所提出方法的可操作性和有效性.

     

改进TOPSIS的多时刻融合直觉模糊威胁评估

针对防空作战中的目标威胁评估问题,提出一种新的多时刻融合直觉模糊数排序模型.首先,根据目标威胁属性的主、客观权重得到综合权重;然后,通过逼近理想解排序法衡量直觉模糊数信息量的大小,利用直觉模糊熵表征直觉模糊数信息的可靠性,并结合决策者的风险偏好构建基于信息量和不确定性的直觉模糊数排序模型,得出单时刻的目标威胁排序;最后,利用泊松分布逆形式构建时间序列权重,从而融合多个时刻的决策信息,得出最终的目标威胁排序.仿真结果表明,所提出的算法综合了多时刻的决策信息,并可根据决策者的风险偏好进行调整,灵活性强、可靠性高.     

基于直觉模糊集的伯努利矩阵分解推荐算法

现有的基于矩阵分解的协同过滤推荐算法主要从定量的角度,利用用户的评分信息评估模型表现,而并未从定性的角度描述用户的不确定偏好信息.鉴于此,从用户偏好模糊概率的角度提出一种基于直觉模糊集的伯努利矩阵分解推荐算法为目标用户进行Top-n推荐.首先,根据用户偏好特征和直觉模糊集定义,将用户评分矩阵划分为隶属度矩阵、非隶属度矩阵和犹豫度矩阵;然后,借助伯努利矩阵分解模型对矩阵并行拟合,得到最优的潜在特征向量对,并将其内积按比例划分,从而获得目标用户对未评分项目偏好程度的直觉模糊数;最后,根据直觉模糊数排序规则确定最终推荐列表.在公开数据集上的实验结果显示,所提出方法在项目排序指标上均优于其对比方法,能够有效提高推荐质量.     

考虑时间序列的动态大群体应急决策方法

针对专家权重和属性权重未知、阶段权重未知且与时间序列有关的动态大群体应急决策问题,提出一种考虑时间序列的动态大群体应急决策方法.首先,提出一个考虑区间直觉模糊数犹豫度的距离公式,定义区间直觉模糊数贴近度,综合考虑贴近度和相似度,用模糊聚类法对大群体专家偏好信息进行聚类;其次,基于现有区间直觉模糊熵公式的不足,提出一个新的区间直觉模糊熵公式,基于此公式考虑专家之间知识水平的差异和各个阶段偏好信息不具遗传性等特点,计算得出专家在不同属性下的权重和属性在各阶段下的权重;再次,考虑时间序列对各阶段权重的影响,构建相对熵模型,对阶段权重进行合理确定,进而利用加权平均算子得到整个决策过程中各方案的综合决策偏好;然后,利用区间直觉模糊数的得分函数和精确函数对方案进行排序,选出最优方案;最后,通过与以往文献的方法对比分析验证所提出方法的有效性和优越性.     

属性权重完全未知的犹豫模糊双边匹配决策

针对基于犹豫模糊属性（HFV）信息且权重完全未知的双边匹配（TSM）问题,提出一种多属性匹配决策方法。首先,根据双方主体给出的犹豫模糊多属性评价值,通过最大化各属性之间的离差和从而确定属性权重;然后,由犹豫模糊有序加权平均算子集结多属性及权重信息获得双方的匹配度;进而建立一种基于匹配度的多目标优化模型,并使用极大极小法转化为单目标优化模型求解得到匹配方案;最后,进行实例分析和对比,所提方法得到目标函数值分别为1.689和1.575,且匹配解唯一。实验结果表明,所提方法可避免因主观确定目标函数权重而产生不唯一匹配解。     

多型异构数据下准则具有优先级别的双边匹配决策方法

针对多型异构数据下准则之间具有优先级别的双边匹配决策问题，提出了一种基于集对分析二元联系数和优先集结算子的双边匹配决策方法。首先，给出了一种将多型异构数据同构化为二元联系数的方法；其次，定义了二元联系数优先加权几何平均(BCNPWG)算子；然后，基于BCNPWG算子，提出了一种准则值为多型异构数据且准则之间具有优先级别的双边匹配决策方法。该方法先将多型异构数据匹配满意度矩阵转化为二元联系数匹配满意度矩阵，然后利用BCNPWG算子集结得到双方主体的综合匹配满意度矩阵；进一步地，以双方主体的综合匹配满意度总和最大为目标，构建二元联系数多目标匹配优化模型，并利用线性加权法及二元联系数的期望值和均方差将其转化为单目标匹配优化模型，进而通过求解该模型得到双边匹配结果。最后，通过一个算例说明了所提出匹配决策方法的可行性和有效性。     

考虑偏好信息的动态双边匹配决策方法

针对主体给出偏好信息的动态双边匹配问题,提出了一种匹配决策方法。给出了基于偏好信息的动态双边匹配问题的描述;依据广义优序法将双边主体给出的偏好信息转化为满意度;给出了指数衰减模型确定时序权重的方法,进而将满意度集成为综合满意度;在此基础上,通过建立并求解优化模型,得出最优匹配方案;以风险投资商与风险企业的匹配实例说明了所提决策方法的有效性和实用性。     

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.     

A new preference scale mcdm method based on interval-valued intuitionistic fuzzy sets and the analytic hierarchy process

The intuitionistic fuzzy analytic hierarchy process (IF-AHP), in which intuitionistic fuzzy numbers are utilized in defining decision makers’ linguistic judgment, has been used to solve various multi-criteria decision-making problems. Previous theories have suggested that interval-valued intuitionistic fuzzy numbers (IVIFN) with hesitation degree can act as alternative fuzzy numbers that can handle vagueness and uncertainty. This paper proposes a new preference scale in the framework of the interval-valued intuitionistic fuzzy analytic hierarchy process (IVIF-AHP). The comparison matrix judgment is expressed in IVIFN with degree of hesitation. The proposed new preference scale concurrently considers the membership function, the non-membership function and the degree of hesitation of IVIFN. To define the weight entropy of the aggregated matrix of IVIFN, a modified interval-valued intuitionistic fuzzy weighted averaging is proposed, by considering the interval number of the hesitation degree. Three multi-criteria decision-making problems are used to test the proposed method. A comparison of the results is also presented to check the feasibility of the proposed method. It is shown that the ranking order of the proposed method is slightly different from that of the other two methods because of the inclusion of the hesitation degree in defining the preference scale.     

基于证据理论的偏好型直觉模糊群决策方法

针对直觉模糊多属性群决策问题,研究属性和专家权重的确定以及信息的集结方法.利用直觉模糊熵确定属性客观权重,并根据偏好信息确定合理的属性综合权重;在属性层面区分专家权重,将直觉模糊评价值作为Mass函数,构建证据冲突度模型确定专家权重,并利用犹豫度加以修正,避免综合支持度低而对方案排序影响大的专家权重过分削弱;采用证据理论集结决策信息,根据得分值进行方案排序.最后通过算例分析,验证了所提出方法的合理性和有效性.     

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.     

Aggregating decision information into Atanassov's intuitionistic fuzzy numbers for heterogeneous multi-attribute group decision making

The aim of this paper is to propose a new aggregation method to solve heterogeneous MAGDM problem which involves real numbers, interval numbers, triangular fuzzy numbers (TFNs), trapezoidal fuzzy numbers (TrFNs), linguistic values and Atanassov's intuitionistic fuzzy numbers (AIFNs). Firstly, motivated by the relative closeness of technique for order preference by similarity to ideal solution (TOPSIS), we propose a new general method for aggregating crisp values, TFNs, TrFNs and linguistic values into AIFNs. Thus all the group decision matrices for each alternative which involves heterogeneous information are transformed into an Atanassov's intuitionistic fuzzy decision matrix which only contains AIFNs. To determine the attribute weights, a multiple objective Atanassov's intuitionistic fuzzy programming model is constructed and solved by converting it into a linear program. Subsequently, comparison analyses demonstrate that the proposed aggregated technology can overcome the drawbacks of existing methods. An example about cloud computing service evaluation is given to verify the practicality and effectiveness of the proposed method.     

A rough set-based interval-valued intuitionistic fuzzy conceptual design decision approach with considering diverse customer preference distribution

Conceptual design evaluation plays a crucial role in new product development (NPD) and determines the quality of downstream design activities. Currently, most existing methods focus on fuzzy quantitative the evaluation information of multi-objectives in conceptual schemes selection. However, the above process ignores the various customers' preferences for each scheme under the evaluation objective, causing inconsistent preference weights in the various schemes, which cannot guarantee the market value of the optimal scheme. Furthermore, the ambiguous attitude from experts in the early design stage is not well taken into account. To this end, a conceptual scheme decision model with considering diverse customer preference distribution based on interval-valued intuitionistic fuzzy set (IVIFS) is proposed. The model is divided into three parts. Firstly, the initial decision matrix of multi-experts concerning the qualitative and quantitative design attributes is constructed based on intuitionistic fuzzy sets, and then the IFS decision matrix with interval boundaries is formed by using rough set technology. Secondly, the mapping model of design attribute to customer preference is constructed, and then the demand preference strategy implied by design attribute is judged. Thirdly, based on the demand preference strategy, the preferences’ weights for each scheme are calculated. Next, integrating the evaluation data with the same preference in the scheme, the comprehensive satisfaction of the scheme is obtained through IVIFS weighted aggregation operator, and then the optimal scheme is decided. Eventually, a case study of mobile phone form feature schemes is further employed to verify the proposed decision model, and results are sensitivity analyzed and compared.     

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.