混合型多属性决策问题的序关系求解方法

研究了包含实数型、区间型和风险型属性的混合型多属性决策问题,提出一种基于优先序关系的决策模型.并给出了具体求解方法和步骤说明,通过比较各属性下方案间的优劣程度,建立模糊互补判断矩阵,以排序向量为基础计算每个方案各属性下的Borda分,根据属性权重向量加权集结得到总排序向量,实现方案总体优劣的排序,该方法直观、概念明确,不需要对决策矩阵进行规范化,易于实际操作.最后以自动目标识别系统性能评估为例,进行了算例分析.     

A novel method for hybrid multiple attribute decision making

An approach based on 2-tuple is presented to solve the hybrid multiple attribute decision making problem with weight information unknown. First, transformation rules between linguistic variables and triangular fuzzy numbers, and distance between 2-tuple linguistics are defined, then the transformation method between 2-tuple linguistic and different forms of indicator values is given. Besides, according to grey incidence minimum deviation theory of positive ideal solution, the weights of indicators are determined, and then alternatives are ranked by 2-tuple linguistic weighting arithmetic average values. Finally, an illustrative example is given to demonstrate the procedure of the method and to compare with TOPSIS method to show the effectiveness and advantages of the presented method.     

基于分布式偏好关系的多属性决策方法及运用*

针对利用分布式偏好关系建模且考虑其一致性的多属性决策问题,提出了一种满足一致性的多属性决策方法。给定相邻方案间的分布式偏好关系,首先构建了基于等级得分值的等级合成规则并分析其性质,而后基于等级合成规则定义了分布式偏好关系矩阵的一致性判定准则,进而提出满足一致性的不同方案对间分布式偏好关系合成规则,最后以此规则为核心,设计多属性决策方法的流程,产生了满足一致性的决策结果。将提出的方法应用于芜湖市战略性新兴产业评估,验证了方法的应用性和有效性。     

A method for stochastic multiple criteria decision making based on dominance degrees

This paper proposes a method for solving the stochastic multiple criteria decision making (SMCDM) problem, where consequences of alternatives with respect to criteria are represented by random variables with probability distributions. Firstly, definitions and related analysis of dominance degree of one probability distribution over another are given. Then, by calculating the dominance degrees, the dominance degree matrix of alternative pairwise comparisons with respect to each criterion is built. Further, using PROMETHEE II method, an overall dominance degree matrix of alternative pairwise comparisons is constructed, and a net flow of each alternative is calculated. Based on the obtained net flows, a ranking of alternatives is determined. Finally, numerical examples for the three cases are given to illustrate the use of the proposed method.     

对方案有偏好的Vague集多属性决策方法的改进

针对属性权重未知且对方案有偏好的Vague集多属性决策问题,应用直觉模糊集的理论方法,建立了基于最小方差的多目标最优化模型。通过求解该模型,获得各属性的权重。此模型弥补了要瑞璞提出的线性规划模型求解属性权重为负的不足和缺陷。通过计算各方案综合值之间比较的可能度,给出了相应决策分析方法。进行了实例分析,说明了该方法的实用性和有效性。     

一种基于二元语义的混合型多属性决策方法

针对指标权重未知的混合型多属性决策问题,提出一种基于二元语义的决策方法.首先,定义了语言评价变量与三角模糊数的转化规则和二元语义之间的距离,给出了不同类型指标数据与二元语义的转化;然后,利用与正理想解灰色关联度偏差最小原理,确定了属性的指标权重,并利用二元语义加权算术平均值对方案进行排序;最后,通过应用案例说明了所提方法的决策步骤,并与TOPSIS方法进行了比较,表明了所提方法的有效性和优越性.     

A method based on stochastic dominance degrees for stochastic multiple criteria decision making

In this paper, a novel method based on the stochastic dominance degree (SDD) is proposed to solve a discrete stochastic multiple criteria decision-making (MCDM) problem. Firstly, a concept of stochastic dominance degree is introduced to describe the degree that one alternative dominates another when the SD relation for each pair of alternatives is determined, and a computation formula of the SDD is given. Then, by calculating SDDs, the SDD matrix on pairwise comparisons of alternatives with respect to each criterion is built. Furthermore, the SDD matrices with respect to all the criteria are aggregated into an overall SDD matrix using the simple additive weighting method. Based on the overall SDD matrix, an approach based on the idea of the PROMETHEE-II is developed to obtain the ranking result of alternatives. Finally, two numerical examples are used to illustrate the applicability and effectiveness of the proposed method.     

考虑准则依赖的风险型多准则决策新方法

为有效应对风险型多准则决策过程中准则依赖的问题,针对现有文献中完全理性和有限理性决策两种视角下准则独立假设的不足,应用DEMATEL方法分析决策准则之间的相互影响关系,得到准则依赖情境下的综合重要性权重,进而以备选方案状态均值为参照点,从前景理论出发,求解风险状态下备选方案的综合前景价值,作为决策依据。案例应用结果表明,所提方法在实践中是切实可行的。     

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。     

直觉模糊多属性决策的新方法

针对属性值以直觉模糊数形式给出的多属性决策中确定属性权重的问题,提出了一种直觉模糊数熵权的确定方法,依照传统权熵的确定方法的思路,通过一个公式求得直觉模糊熵;然后求得属性的信息熵;根据传统熵权确定公式得到属性权重,进而利用得分函数对方案进行排序;最后通过算例说明该方法的有效性和实用性。     

Grey relational analysis model for dynamic hybrid multiple attribute decision making

In this paper, the dynamic hybrid multiple attribute decision making problems, in which the decision information, provided by decision makers at different periods, is expressed in real numbers, interval numbers or linguistic labels (linguistic labels can be described by triangular fuzzy numbers), respectively, are investigated. The method first utilizes three different GRA (grey relational analysis (real-valued GRA, interval-valued GRA and fuzzy-valued GRA) to calculate the individual grey relational degree of each alternative to the positive and negative ideal alternatives based on the decision information expressed in real numbers, interval numbers and linguistic labels, respectively, provided by each decision maker at each period, and then adopt the concept of fuzzy membership grade and clustering to aggregate the grey relational degree of all the evaluated periods. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.     

对方案有偏好的Vague集互补判断矩阵决策法

研究指标权重信息未知且对方案有偏好的Vague集多属性决策问题。首先将决策信息和偏好信息的Vague值转化为模糊值,进一步将偏好信息转化为互补判断矩阵,从而建立目标规划模型,通过求解该模型得各指标的权重,并通过求解各方案综合属性值对方案进行排序和择优。最后给出算例。     

An interactive method for fuzzy multiple attribute group decision making

In this paper, we develop an interactive method for multiple attribute group decision making under fuzzy environment. The method can be used in situations where the information about attribute weights is partly known, the weights of decision makers are expressed in exact numerical values or triangular fuzzy numbers, and the attribute values are triangular fuzzy numbers. The method transforms fuzzy decision matrices into their expected decision matrices, constructs the corresponding normalized expected decision matrices by two simple formulas, and then aggregates these normalized expected decision matrices into a complex decision matrix. Moreover, the decision makers are asked to provide their preferences gradually in the course of interactions. By solving linear programming models, the method diminishes the given alternative set gradually, and finally finds the most preferred alternative. By using the method, the decision makers can provide and modify their preference information gradually in the process of decision making so as to make the decision result more reasonable. The method can not only reflect the importance of the given arguments and the ordered positions of the arguments, but also relieve the influence of unfair arguments on the decision result. Finally, a practical problem is used to illustrate the developed method.     

一种基于灰色关联度的多属性群决策方法

基于灰色关联度的思想提出了一种群决策方法。该方法根据各专家给出的决策矩阵,利用灰色关联度的思想确定专家权重,得出群决策矩阵,基于偏差最大化的思想计算属性权重,计算各方案的综合关联度,据此确定方案的排序。算例表明了利用此方法得出的方案综合关联度之间相对差距较大,提高了决策的科学性和有效性。指出了徐选华等人提出的算例中的错误,予以纠正。     

A novel aggregation method for Pythagorean fuzzy multiple attribute group decision making

As an extension of fuzzy set, a Pythagorean fuzzy set has recently been developed to model imprecise and ambiguous information in practical group decision‐making problems. The aim of this paper is to introduce a novel aggregation method for the Pythagorean fuzzy set and analyze possibilities for its application in solving multiple attribute decision‐making problems. More specifically, a new Pythagorean fuzzy aggregation operator called the Pythagorean fuzzy induced ordered weighted averaging‐weighted average (PFIOWAWA) operator is developed. This operator inherits main characteristics of both ordered weighted average operator and induced ordered weighted average to aggregate the Pythagorean fuzzy information. Some of main properties and particular cases of the PFIOWAWA operator are studied. A method based on the proposed operator for multiple attribute group decision making is developed. Finally, we present a numerical example of selection of research and development projects to illustrate applicability of the new approach in a multiple attribute group decision‐making problem.     

给出属性优先序的模糊多属性决策方法

研究属性值为模糊变量,已知属性优先序信息的模糊多属性决策问题。基于模糊变量的期望值、模糊变量之间的距离等概念,建立以极大化属性值的离差为目标的模糊期望值模型来确定各属性的权重;基于期望值算子,计算出各方案的期望效用值,从而获得各方案的排序;通过数值算例说明所提出方法的有效性。     

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。     

Vague集多属性决策的可能度法

给出了Vague集比较的可能度定义,并研究了其所具有的性质。针对属性权重已知和完全未知的Vague集多属性决策问题,应用最优点方案来建立最优化决策模型。应用Vague集间比较的可能度公式,提出了解决Vague集多属性决策问题的新方法。最后以应用实例对该方法进行说明和验证。     

A normal wiggly hesitant fuzzy MABAC method based on CCSD and prospect theory for multiple attribute decision making

Normal wiggly hesitant fuzzy set (NWHFS) is a new fuzzy information form to help decision makers (DMs) express their evaluations, which can further dig the potential uncertain information hidden in the original data given by the DMs. Firstly, we define a new distance measure and new operational laws of NWHFSs. Then, for the situation where attribute weights are completely unknown, we propose an extended CCSD method to produce them objectively, which comprehensively uses standard deviation (SD) and correlation coefficient (CC). What's more, we introduce the MABAC (multiattributive border approximation area comparison) method, which takes the distance between alternatives and the border approximation area (BAA) into consideration for handling the complex and uncertain decision‐making problems. Meanwhile, we combine the MABAC method with prospect theory (PT), which considers DMs' psychological behavior, and propose a new NWHF‐CCSD‐PT‐MABAC method to cope with the multi‐attribute decision making problems under normal wiggly hesitant fuzzy environment. Lastly, we illustrate the validity and advantages of the proposed method through an example of college book supplier selection.     

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.