Group decision-making based on heterogeneous preference relations with self-confidence

Preference relations are very useful to express decision makers’ preferences over alternatives in the process of group decision-making. However, the multiple self-confidence levels are not considered in existing preference relations. In this study, we define the preference relation with self-confidence by taking multiple self-confidence levels into consideration, and we call it the preference relation with self-confidence. Furthermore, we present a two-stage linear programming model for estimating the collective preference vector for the group decision-making based on heterogeneous preference relations with self-confidence. Finally, numerical examples are used to illustrate the two-stage linear programming model, and a comparative analysis is carried out to show how self-confidence levels influence on the group decision-making results.     

几种模糊传递关系的收敛性

本文对几种模糊传递关系进行比较 ,从一个侧面说明了用于构造偏好关系的模糊关系应是互逆关系 .文中证明了对任意的 n阶互逆传递模糊关系 R,必有 Rn=Rn+1 .     

Consistency analysis of triangular fuzzy reciprocal preference relations

In order to simulate the uncertainty associated with impression or vagueness, a decision maker may give her/his judgments by means of triangular fuzzy reciprocal preference relations in the process of decision making. The study of their consistency becomes a very important aspect to avoid a misleading solution. Based on the reciprocity property, this paper proposes a new definition of consistent triangular fuzzy reciprocal preference relations. The new definition is different from that reduced by consistent fuzzy reciprocal preference relations proposed by Buckley (1985). The properties of consistent triangular fuzzy reciprocal preference relations in the light of the new definition are studied in detail. In addition, the shortcomings of the proof procedure of the proposition given by Wang and Chen (2008) are pointed out. And the proposition is reproved by using the new definition of consistent triangular fuzzy reciprocal preference relations. Finally, using the (n − 1) restricted comparison ratios, a method for obtaining consistent triangular fuzzy reciprocal preference relations is proposed, and an algorithm is shown to make a consistent decision ranking. Numerical results are further calculated to illustrate the new definition and the obtained algorithm.     

A fuzzy preference relation in the vector maximum problem

A new approach to the compromise solution concept for the vector maximum problem is considered. It is assumed in this approach that one may specify a fuzzy preference relation in the alternative space reflecting the objective functions and the decision maker's preferences. The maximal nondominated alternative for this relation is proposed as a compromise solution to the initial problem. Properties of the compromise solution are analysed under different assumptions concerning the initial problem as well as the accepted fuzzy preference relation.     

Valued preference-based instantiation of argumentation frameworks with varied strength defeats

A Dung-style argumentation framework aims at representing conflicts among elements called arguments. The basic ingredients of this framework is a set of arguments and a Boolean abstract (i.e., its origin is not known) binary defeat relation. Preference-based argumentation frameworks are instantiations of Dung's framework in which the defeat relation is derived from an attack relation and a preference relation over the arguments. Recently, Dung's framework has been extended in order to consider the strength of the defeat relation, i.e., to quantify the degree to which an argument defeats another argument. In this paper, we instantiate this extended framework by a preference-based argumentation framework with a valued preference relation. As particular cases, the latter can be derived from a weight function over the arguments or a Boolean preference relation. We show under some reasonable conditions that there are “less situations” in which a defense between arguments holds with a valued preference relation compared to a Boolean preference relation. Finally, we provide some conditions that the valued preference relation shall satisfy when it is derived from a weight function.     

The w-reciprocity rule

Given a small number of choices, a matrix is a convenient way to represent a fuzzy preference relation. Usually, this matrix is reciprocal. The w-reciprocity rule is presented here as a way to relax the rigidity of the reciprocal assumption and to embody linguistic meanings for indifference and for the representation of the converse preference.     

考虑互惠偏好的闭环供应链系统合作机制研究

将互惠偏好引入到闭环供应链系统合作机制中,研究了由一个制造商,一个零售商和一个再制造商组成的三层闭环供应链,运用Stackelberg博弈理论分析了闭环供应链整体及各成员的最优决策问题,并对5种情形(决策模式)下的均衡结果进行比较分析.研究发现在考虑互惠偏好行为下,分散决策模式和局部联盟决策模式下的系统利润低于集中决策模式下的收益;新产品和再制造产品的销售量(零售价格)与制造商对零售商的互惠偏好系数呈正(负)相关,与零售商对制造商的互惠偏好系数呈负(正)相关;5种决策模式的供应链系统利润与制造商对零售商的互惠偏好系数呈正相关,与零售商对制造商的互惠偏好系数呈负相关.     

On consistency measures of linguistic preference relations

Inspired by the concept of deviation measure between two linguistic preference relations, this paper further defines the deviation measure of a linguistic preference relation to the set of consistent linguistic preference relations. Based on this, we present a consistency index of linguistic preference relations and develop a consistency measure method for linguistic preference relations. This method is performed to ensure that the decision maker is being neither random nor illogical in his or her pairwise comparisons using the linguistic label set. Using this consistency measure, we discuss how to deal with inconsistency in linguistic preference relations, and also investigate the consistency properties of collective linguistic preference relations. These results are of vital importance for group decision making with linguistic preference relations.     

A new method for ranking fuzzy numbers and its application to group decision making

In this paper, a new method for comparing fuzzy numbers based on a fuzzy probabilistic preference relation is introduced. The ranking order of fuzzy numbers with the weighted confidence level is derived from the pairwise comparison matrix based on 0.5-transitivity of the fuzzy probabilistic preference relation. The main difference between the proposed method and existing ones is that the comparison result between two fuzzy numbers is expressed as a fuzzy set instead of a crisp one. As such, the ranking order of n fuzzy numbers provides more information on the uncertainty level of the comparison. Illustrated by comparative examples, the proposed method overcomes certain unreasonable (due to the violation of the inequality properties) and indiscriminative problems exhibited by some existing methods. More importantly, the proposed method is able to provide decision makers with the probability of making errors when a crisp ranking order is obtained. The proposed method is also able to provide a probability-based explanation for conflicts among the comparison results provided by some existing methods using a proper ranking order, which ensures that ties of alternatives can be broken.     

Aggregation of fuzzy preference relations to multicriteria decision making

Weighted aggregation of fuzzy preference relations on the set of alternatives by several criteria in decision-making problems is considered. Pairwise comparisons with respect to importance of the criteria are given in fuzzy preference relation as well. The aggregation procedure uses the composition between each two relations of the alternatives. The membership function of the newly constructed fuzzy preference relation includes t-norms and t-conorms to take into account the relation between the criteria importance. Properties of the composition and new relation, giving a possibility to make a consistent choice or to rank the alternatives, are proved. An illustrative numerical study and comparative examples are presented.     

Derivation of intuitionistic fuzzy weights based on intuitionistic fuzzy preference relations

This paper proposes linear goal programming models for deriving intuitionistic fuzzy weights from intuitionistic fuzzy preference relations. Novel definitions are put forward to define additive consistency and weak transitivity for intuitionistic fuzzy preference relations, followed by a study of their corresponding properties. For any given normalized intuitionistic fuzzy weight vector, a transformation formula is furnished to convert the weights into a consistent intuitionistic fuzzy preference relation. For any intuitionistic fuzzy preference relation, a linear goal programming model is developed to obtain its intuitionistic fuzzy weights by minimizing its deviation from the converted consistent intuitionistic fuzzy preference relation. This approach is then extended to group decision-making situations. Three numerical examples are provided to illustrate the validity and applicability of the proposed models.     

基于序数偏差融合度的动态匹配决策方法

针对具有不确定偏好序信息的动态匹配决策问题,提出了一种决策方法。首先,给出了序数偏差的相关描述;然后,把在同一时刻的不同方案间或同一方案在不同时刻间的序数偏差关系作为证据,并通过证据组合求出双边序数偏差融合度;在此基础上,构建了优化模型,获得双边匹配方案。最后,通过一个算例说明了该方法的可行性和有效性。     

偏好信息为模糊互反判断矩阵的模糊多属性决策法

研究只有部分权重信息且决策者对方案的偏好信息以模糊互反判断矩阵形式给出的模糊多属性决策问题。提出了一种基于目标规划模型的模糊多属性决策方法。该法首先基于模糊互反判断矩阵，利用转换函数将决策信息一致化，建立了一个目标规划模型．通过求解该模型确定属性的权重，然后运用加性加权法求出各方案的模糊综合属性值，并利用已有的三角模糊数排序公式求得决策方案的排序。文章最后把该法应用于解决风险投资领域中的项目评估问题。     

Group decision making based on intuitionistic multiplicative aggregation operators

Preference relations are the most common techniques to express decision maker’s preference information over alternatives or criteria. To consistent with the law of diminishing marginal utility, we use the asymmetrical scale instead of the symmetrical one to express the information in intuitionistic fuzzy preference relations, and introduce a new kind of preference relation called the intuitionistic multiplicative preference relation, which contains two parts of information describing the intensity degrees that an alternative is or not priority to another. Some basic operations are introduced, based on which, an aggregation principle is proposed to aggregate the intuitionistic multiplicative preference information, the desirable properties and special cases are further discussed. Choquet Integral and power average are also applied to the aggregation principle to produce the aggregation operators to reflect the correlations of the intuitionistic multiplicative preference information. Finally, a method is given to deal with the group decision making based on intuitionistic multiplicative preference relations.     

Eigenvector method,consistency test and inconsistency repairing for an incomplete fuzzy preference relation

In this paper, we extend the eigenvector method (EM) to priority for an incomplete fuzzy preference relation. We give a reasonable definition of multiplicative consistency for an incomplete fuzzy preference relation. We also give an approach to judge whether an incomplete fuzzy relation is acceptable or not. We develop the acceptable consistency ratio for an incomplete multiplicative fuzzy preference relation, which is simple and similar to Saaty’s consistency ratio (CR) for the multiplicative preference relation. If the incomplete fuzzy preference relation is not of acceptable consistency, we define a criterion to find the unusual and false element (UFE) in the preference relation, and present an algorithm to repair an inconsistent fuzzy preference relation until its consistency is satisfied with the consistency ratio. As a result, our improvement method cannot only satisfy the consistency requirement, but also preserve the initial preference information as much as possible. Finally, an example is illustrated to show that our method is simple, efficiency, and can be performed on computer easily.     

基于OWGA算子的偏好信息集结法及其在群决策中的应用

研究了决策者的偏好信息以不同形式给出的群决策问题。首先，利用不同偏好信息之间的转换公式，将偏好次序型、效用值型、互反判断矩阵型三种偏好信息一致化为模糊互补判断矩阵型的偏好信息；其次。利用加权几何平均（OWGA）算子对一致化后的决策信息进行集结。再对方案的加权几何平均优势度进行综合集结，并以此进行方案的排序，提出了基于OWGA算子的群决策方法，该方法具有操作简便和计算量少的特点。最后。通过实例说明方法的可行性和实用性。     

The vetoers in a simple game with ordinal preferences

We consider a core of a simple game with ordinal preferences on a set of alternative outcomes Ω. When a player's strict preference relation takes any logically possible form of acyclic binary relation on Ω, necessary conditions for a simple game to have a nonempty core are given. If Ω is a finite set, the conditions are also sufficient. Further some related results are obtained.     

加型一致性毕达哥拉斯模糊偏好关系

在模糊偏好关系两种等价的加型一致性概念基础上,通过简单的数学证明,分析了区间值模糊偏好关系、直觉模糊偏好关系的相应的两种加型一致性并不是等价的.然后,在加型一致性直觉模糊偏好关系的启发下,构造了可以与毕达哥拉斯模糊偏好关系相互转换的两个区间值模糊偏好关系,并利用它们的加型一致性,定义了加型一致性毕达哥拉斯模糊偏好关系,并分析了其与杨艺等定义的加型一致性毕达哥拉斯模糊偏好关系的关系.其次,研究了加型一致性毕达哥拉斯模糊偏好关系的性质以及毕达哥拉斯模糊偏好关系的满意一致性,并给出满意一致性毕达哥拉斯模糊偏好关系下的方案优劣排序算法.最后,通过两个计算实例说明了排序算法可行有效.     

区间直觉模糊判断矩阵群决策中的逆判问题

研究了区间直觉模糊判断矩阵的群决策问题.定义了两种区间直觉模糊集相似度公式,给出两种与决策群体意见一致性程度最高的理想区间直觉模糊判断矩阵构造优化方法.利用矩阵对不同专家判断矩阵中相同位置元素的一致性进行分析,并对不同专家的判断信息进行整体相似程度分析,最后通过算例说明了该方法的有效性和实用性.     

Interval weight generation approaches for reciprocal relations

In this paper, we propose methods to derive interval weight vectors from reciprocal relations for reflecting the inconsistency when decision makers provide preferences over alternatives (or criteria). Several goal programming models are established to minimize the inconsistency based on multiplicative and additive consistency, respectively. Especially, if we obtain a crisp weight vector from a reciprocal relation, then it is consistent. Then, we extend the proposed methods to incomplete reciprocal relations and interval reciprocal relations and develop the corresponding models to derive interval weight vectors. Several examples are also given to compare the developed methods with the existing ones.