基于离差优化的信息不完全确定的多准则分类方法

提出一种准则权系数信息不完全确定且有训练集的多准则分类决策方法.该方法利用训练集的分类结果和准则权系数的不完全确定信息,基于类间离差最大和类离差最小构建非线性规划模型,再利用遗传算法求解所得优化模型,得到训练集中各方案在各准则下的效用值和准则权系数,通过插值得到方案集中方案在准则下的效用值,确定方案与各类间的离差,进而得到方案的分类.实例计算表明了该方法的有效性和可行性.     

一种信息不完全确定的多准则分类决策方法

针对准则权系数信息不完全确定和准则值信息不完全且有训练集的多准则分类决策问题，提出一种基于证据推理的分类方法，该方法在对训练集分类的基础上，结合不完全确定的准则权系数信息等建立非线性规划模型；然后利用遗传算法和单纯形法联合求解优化模型，得出准则权系数和分类效用阈值等参数，进而求出每一方案的效用值；最后与分类的效用阈值进行比较，得到方案集的分类．应用实例说明了该方法的有效性和可行性。     

一种供应商选择与评价模型

供应商的选择是决定企业成本及产品质量的重要因素,本文提出一种利用信息不完全的多准则层次分类方法来解决供应商选择评价问题,该方法利用训练集的分类和准则权系数的不完全信息,通过数学模型计算各准则的偏好值以及一致性指标,进而确定候选供应商是否属于所需分类,最后通过一个具体实例验证了该方法的有效性.     

信息不完全确定的多准则区间直觉模糊决策方法

提出了一种权系数信患不完全确定且准则值为区间直觉模糊集的多准则排序方法．该方法利用证据推理算法对准则进行集成。得到各方案的区间直觉模糊集，计算各方案与理想方案和负理想方案的距离。并结合不完全确定的权系数信息建立非线性规划模型。利用粒子群算法求解所得优化模型。得出最优准则权系数。通过比较方案的区间直觉模糊集与理想方案和负理想方案的距离，得到方案集的排序．最后的数值算例说明了该方法的有效性和可行性．     

一种信息不完全确定的多准则语言群决策方法

针对权系数信息不完全确定且方案的准则值为确定语言等级或位于两个连续语言等级之间，甚至缺失的群决策问题，提出一种群体语言决策方法．该方法利用证据推理算法得到方案属于各语言等级的信任度，利用二元语义对方案进行语言集结；然后结合决策者和准则权重的不完全确定信息及方案与理想方案的二元语义问的距离构建非线性规划模型．利用遗传算法求解所得模型，计算得到各方案的排序．实例计算表明了该方法的可行性和有效性．     

基于直觉梯形模糊数的信息不完全确定的多准则决策方法

针对权系数信息不完全确定和准则值为直觉梯形模糊数的多准则决策问题,提出一种基于直觉梯形模糊的信息不完全确定的多准则决策方法.该方法利用权系数的不完全确定信息,建立关于各方案综合直觉梯形模糊数与理想解和负理想解的Hamming距离的优化模型.通过求解优化模型可得到各准则的最优权系数,进而得到各方案与相对理想解的贴近度,再根据贴近度得到方案集的一个排序.实例分析表明了该方法的有效性和可行性.     

基于直觉模糊数的信息不完全的多准则规划方法

定义了直觉模糊数和直觉梯形模糊数及其期望值.针对权系数信息不完全确定和准则值为直觉梯形模糊数的多准则决策问题,提出了信息不完全确定的直觉梯形模糊多准则决策的规划方法.该方法利用权系数的不完全信息构造方案集综合期望值的最优线性规划模型,求解该模型得到各准则的最优权系数,进而得到各方案综合期望值的区间数.利用区间数可能度法对其进行比较,得到整个方案集的排序.实例分析说明了该方法的有效性和可行性.     

基于直觉梯形模糊数的信息不完全确定的多准则决策方法

针对权系数信息不完全确定和准则值为直觉梯形模糊数的多准则决策问题,提出一种基于直觉梯形模糊的信息不完全确定的多准则决策方法.该方法利用权系数的不完全确定信息,建立关于各方案综合直觉梯形模糊数与理想解和负理想解的Hamming距离的优化模型,通过求解优化模型可得到各准则的最优权系数,进而得到各方案与相对理想解的贴近度,再根据贴近度得到方案集的一个排序.实例分析表明了该方法的有效性和可行性.

     

基于直觉模糊数的信息不完全的多准则规划方法

定义了直觉模糊数和直觉梯形模糊数及其期望值 .针对权系数信息不完全确定和准则值为直觉梯形模糊数的多准则决策问题,提出了信息不完全确定的直觉梯形模糊多准则决策的规划方法 .该方法利用权系数的不完全信息构造方案集综合期望值的最优线性规划模型,求解该模型得到各准则的最优权系数,进而得到各方案综合期望值的区间数.利用区间数可能度法对其进行比较,得到整个方案集的排序. 实例分析说明了该方法的有效性和可行性.

     

基于WC-OWA算子的随机多准则决策方法

针对准则权重信息不完全确定且准则值为正态分布随机变量的多准则决策问题，提出一种基于WC—OWA算子的多准则决策方法．该方法根据正态分布3σ原则，将正态分布准则值转化为区间数．并利用连续区间有序加权平均算子集结区间数，通过方案贴近度和加权的连续区间有序加权平均算子建立非线性规划模型，利用遗传算法对模型进行求解，得到准则的最优权系数，进而确定方案的排序．实例分析表明了所提出方法的有效性和可行性．     

Interval-valued intuitionistic fuzzy mathematical programming method for hybrid multi-criteria group decision making with interval-valued intuitionistic fuzzy truth degrees

As an important component of group decision making, the hybrid multi-criteria group decision making (MCGDM) is very complex and interesting in real applications. The purpose of this paper is to develop a novel interval-valued intuitionistic fuzzy (IVIF) mathematical programming method for hybrid MCGDM considering alternative comparisons with hesitancy degrees. The subjective preference relations between alternatives given by each decision maker (DM) are formulated as an IVIF set (IVIFS). The IVIFSs, intuitionistic fuzzy sets (IFSs), trapezoidal fuzzy numbers (TrFNs), linguistic variables, intervals and real numbers are used to represent the multiple types of criteria values. The information of criteria weights is incomplete. The IVIFS-type consistency and inconsistency indices are defined through considering the fuzzy positive and negative ideal solutions simultaneously. To determine the criteria weights, we construct a novel bi-objective IVIF mathematical programming of minimizing the inconsistency index and meanwhile maximizing the consistency index, which is solved by the technically developed linear goal programming approach. The individual ranking order of alternatives furnished by each DM is subsequently obtained according to the comprehensive relative closeness degrees of alternatives to the fuzzy positive ideal solution. The collective ranking order of alternatives is derived through establishing a new multi-objective assignment model. A real example of critical infrastructure evaluation is provided to demonstrate the applicability and effectiveness of this method.     

对方案有偏好的直觉模糊多属性决策方法

对属性权重信息不完全、属性值和决策者对方案的偏好信息均以直觉模糊数表示的多属性决策问题提出一种决策方法。首先根据决策者对方案的偏好信息建立多目标规划模型,求出属性权重,接着利用觉模糊加权算术平均算子求出方案的综合属性值,由直觉模糊数的得分函数和精确函数确定方案的排序,最后通过实例证明了该方法的实用性和有效性。     

区间值模糊随机多准则决策方法

针对不完全信息的区间值模糊随机多准则决策问题,提出了两种求解方法。第一种方法利用离差最大化构建区间参数线性规划,通过区间数运算法则和定位规划求得最优准则权重向量、状态集结值区间决策矩阵与期望值区间决策矩阵,根据决策者风险偏好水平得到各方案的期望集结值从而确定排序。第二种方法将区间值模糊数决策矩阵转化为直觉模糊数决策矩阵,利用不完全的准则权重,通过规划模型求解,获取各方案在各自然状态下的加权记分函数值与加权精确函数值的区间,利用不完全的状态概率,得到各方案的记分函数期望值与精确函数期望值的区间,根据决策者风险偏好水平,求得各方案的记分函数与精确函数的期望集结值,进而确定方案的排序结果。算例分析验证了两种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.     

基于模糊熵和证据推理的语言?? 数多准则决策方法

定义了语言??数及其模糊熵, 提出了基于模糊熵和证据推理的多准则决策方法, 以解决准则权系数信息不完全确定的语言??数多准则决策问题. 所提方法通过建立基于语言??数模糊熵的线性规划模型来得到准则的最优权系数, 利用证据推理算法确定方案的综合准则值, 进而得出最优方案. 最后通过实例验证了所提出方法的有效性和可行性.

     

Learning criteria weights of an optimistic Electre Tri sorting rule

Multiple criteria sorting methods assign alternatives to predefined ordered categories taking multiple criteria into consideration. The Electre Tri method compares alternatives to several profiles separating the categories. Based on such comparisons, each alternative is assigned to the lowest (resp. highest) category for which it is at least as good as the lower profile (resp. is strictly preferred by the higher profile) of the category, and the corresponding assignment rule is called pessimistic (resp. optimistic). We propose algorithms for eliciting the criteria weights and majority threshold in a version of the optimistic Electre Tri rule, which raises additional difficulties w.r.t. the pessimistic rule. We also describe an algorithm that computes robust alternatives׳ assignments from assignment examples. These algorithms proceed by solving mixed integer programs. Several numerical experiments are conducted to test the proposed algorithms on the following issues: learning ability of the algorithm to reproduce the DM׳s preference, robustness analysis and ability to identify conflicting preference information in case of inconsistencies in the learning set. Experiments show that eliciting the criteria weights in an accurate way requires quite a number of assignment examples. Furthermore, considering more criteria increases the information requirement. The present empirical study allows us to draw some lessons in view of practical applications of Electre Tri using the optimistic rule.