Deriving priority weights from intuitionistic multiplicative preference relations under group decision-making settings

The intuitionistic multiplicative preference relation (IMPR), which takes into account both the ratio degree to which an alternative is preferred to another and the ratio degree to which an alternative is non-preferred to another, is a useful tool for decision makers to elicit their preference information using Saaty’s 1–9 scale. In this paper, we focus on group decision making with IMPRs. First, we analyze the flaws of the consistency definition of an IMPR in previous work and then propose a new definition to overcome the flaws. On this basis, a linear programming-based algorithm is developed to check and improve the consistency of an IMPR. Second, we discuss the relationships between an IMPR and a normalized intuitionistic multiplicative weight vector and develop two approaches to group decision making based on complete and incomplete IMPRs, respectively. Based on the proposed algorithm and approaches, a general framework for group decision making with IMPRs is proposed. Finally, some numerical examples are provided to demonstrate the proposed approaches. The results show that the proposed approaches can deal with group decision-making problems with IMPRs effectively.     

基于累积共识贡献的不确定语言共识决策方法

针对不确定加型语言偏好信息下的群决策问题,提出一种基于累积共识贡献的自适应式语言共识决策方法。首先,将不确定加型语言偏好转化为不确定二元语义偏好,定义个体一致度与个体共识偏度,并利用它们构建确定专家初始权重的优化模型;然后,利用不确定二元语义的可能度构造集结模糊评价矩阵以及方案的集结群体偏好,提出专家累积共识贡献测度和群体共识测度,通过对拥有较少合作的专家权重进行惩罚让群体自适应地达成共识,无需强迫专家修改其观点,提出一种群体共识决策方法对方案排序择优。最后,通过一个算例说明方法的可行性和有效性。     

Ordinal regression revisited: Multiple criteria ranking using a set of additive value functions

We present a new method, called UTA^GMS, for multiple criteria ranking of alternatives from set A using a set of additive value functions which result from an ordinal regression. The preference information provided by the decision maker is a set of pairwise comparisons on a subset of alternatives A^R ⊆ A, called reference alternatives. The preference model built via ordinal regression is the set of all additive value functions compatible with the preference information. Using this model, one can define two relations in the set A: the necessary weak preference relation which holds for any two alternatives a, b from set A if and only if for all compatible value functions a is preferred to b, and the possible weak preference relation which holds for this pair if and only if for at least one compatible value function a is preferred to b. These relations establish a necessary and a possible ranking of alternatives from A, being, respectively, a partial preorder and a strongly complete relation. The UTA^GMS method is intended to be used interactively, with an increasing subset A^R and a progressive statement of pairwise comparisons. When no preference information is provided, the necessary weak preference relation is a weak dominance relation, and the possible weak preference relation is a complete relation. Every new pairwise comparison of reference alternatives, for which the dominance relation does not hold, is enriching the necessary relation and it is impoverishing the possible relation, so that they converge with the growth of the preference information. Distinguishing necessary and possible consequences of preference information on the complete set of actions, UTA^GMS answers questions of robustness analysis. Moreover, the method can support the decision maker when his/her preference statements cannot be represented in terms of an additive value function. The method is illustrated by an example solved using the UTA^GMS software. Some extensions of the method are also presented.     

A Direct Approach to Group Decision Making with Uncertain Additive Linguistic Preference Relations

In this paper, we study the group decision-making problem in which the preference information given by experts takes the form of uncertain additive linguistic preference relations. We define the concept of uncertain additive linguistic preference relation, and introduce a formula based on possibility measure for comparing two uncertain linguistic preference values. We introduce some aggregation operators such as the uncertain linguistic averaging (ULA) operator and uncertain linguistic weighted averaging (ULWA) operator, etc. Based on the ULA and ULWA operators, we develop a direct approach to group decision making with uncertain additive linguistic preference relations without loss of information. Finally, an illustrative numerical example is given to verify the developed approach.     

区间犹豫模糊ELECTRE多属性决策方法及应用

近年来,多属性决策问题一直是广大学者研究的重点,然而基于ELECTRE方法的区间犹豫模糊多属性决策问题的研究并不多见。因此,结合区间犹豫模糊集的信息表达优势和ELECTRE方法的思想,提出了一种区间犹豫模糊ELECTRE(IVHF ELECTRE)多属性决策新方法。首先构造了区间犹豫模糊决策矩阵,引入得分函数和可能度的概念,构造属性优势集和属性劣势集。然后通过设定阈值得到综合优先判定矩阵,从而得到各方案间的优先顺序。为了进一步得到各方案的整体排序,引入TOPSIS方法,通过计算各方案与正负理想点的相对距离来构造综合优先矩阵,从而得到各方案的总体排序。最后通过具体实例验证了该方法的可行性和合理性。     

Multiperson decision-making based on multiplicative preference relations

A multiperson decision-making problem, where the information about the alternatives provided by the experts can be presented by means of different preference representation structures (preference orderings, utility functions and multiplicative preference relations) is studied. Assuming the multiplicative preference relation as the uniform element of the preference representation, a multiplicative decision model based on fuzzy majority is presented to choose the best alternatives. In this decision model, several transformation functions are obtained to relate preference orderings and utility functions with multiplicative preference relations. The decision model uses the ordered weighted geometric operator to aggregate information and two choice degrees to rank the alternatives, quantifier guided dominance degree and quantifier guided non-dominance degree. The consistency of the model is analysed to prove that it acts coherently.     

权重信息未知对方案有偏好的vague集多指标决策

就指标权重未知,且对方案有偏好的vague集多指标决策问题,提出了通过使决策者的主观偏好值与属性值的相离度最小来建立最优化模型,从而获得指标的权重.通过将vague值转化为模糊值来建立模糊值矩阵,由模糊值矩阵按各指标对应值的大小对方案进行排序,形成多个线性序,进而由线性序来构造模糊优先矩阵,对其进行截割,得到最优方案.最后通过一个实例说明此方法的具体决策过程.     

A simulation-based test of stochastic multicriteria acceptability analysis using achievement functions

Stochastic multicriteria acceptability analysis using achievement functions (SMAA-A) is a preference model for discrete-choice decision making that inverts the traditional goal programming process by asking what combinations of aspirations are necessary to make each alternative the preferred one, rather than what alternative is preferred given a set of aspirations. In this paper, we test the ability of the model to discern good-performing alternatives from poorly-performing ones using a simulation study. Simulation results show that a suitably detailed construction of the acceptability index is particularly important, and that the resulting model can be fruitfully applied in the selection of a shortlist of alternatives from a larger set with only very limited decision maker involvement.     

Implausible alternatives in eliciting multi-attribute value functions

Many methods to elicit preference models in multi-attribute decision making rely on evaluations of a set of sample alternatives by decision makers. Using orthogonal design methods to create this set of alternatives might require respondents to evaluate unrealistic alternatives. In this paper, we perform an empirical study to analyze whether the presence of such implausible alternatives has an effect on the quality of utility elicitation. Using a new approach to measure consistency, we find that implausible alternatives in fact, have a positive effect on consistency of intra-attribute preference information and consistency with dominance, but do not affect inter-attribute preference information.     

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.     

模糊判断矩阵一致性逼近及排序方法

根据一致性模糊判断矩阵定义,提出了一种求取一致性判断矩阵及方案排序的新方法,该方法是通过建立一个线性目标规划模型来得到排序向量,并相应地得到逼近于决策偏好的一致性判断矩阵,最后给出了一个算例。     

Dominance-based fuzzy rough set analysis of uncertain and possibilistic data tables

In this paper, we propose a dominance-based fuzzy rough set approach for the decision analysis of a preference-ordered uncertain or possibilistic data table, which is comprised of a finite set of objects described by a finite set of criteria. The domains of the criteria may have ordinal properties that express preference scales. In the proposed approach, we first compute the degree of dominance between any two objects based on their imprecise evaluations with respect to each criterion. This results in a valued dominance relation on the universe. Then, we define the degree of adherence to the dominance principle by every pair of objects and the degree of consistency of each object. The consistency degrees of all objects are aggregated to derive the quality of the classification, which we use to define the reducts of a data table. In addition, the upward and downward unions of decision classes are fuzzy subsets of the universe. Thus, the lower and upper approximations of the decision classes based on the valued dominance relation are fuzzy rough sets. By using the lower approximations of the decision classes, we can derive two types of decision rules that can be applied to new decision cases.     

Another potential shortcoming of AHP

In the last twenty years many features of Saaty’s Analytical Hierarchy Process (AHP) have been criticised, especially the additive hierarchical composition of conventional AHP, which leads to the possibility of occurrence of the Rank Reversal phenomenon (adding an irrelevant alternative may cause a reversal in the ranking at the top). In this paper we show another feature of AHP which may be, and in many application contexts will inneed be, an even stronger shortcoming of the method. It consists in the fact that the addition of indifferent criteria (for which all alternatives perform equally) causes a significant alteration of the aggregated priorities of alternatives, with important consequences. In hierarchies with four or more levels, rank reversal may happen. Since in almost all applications of AHP the set of criteria is not fixed ex-ante but is variable and is constructed in accordance with reasons of relevance and simplicity, almost all applications of AHP are potentially flawed.     

基于最大满意度的区间混合判断矩阵排序方法

区间混合判断矩阵对表达决策者的判断信息很有帮助,然而区间混合判断矩阵尚未引起学者的足够重视.定义了一致性乘型区间混合判断矩阵和一致性加型区间混合判断矩阵,并基于最大满意度的思想,提出了求解区间混合判断矩阵的乘型和加型最大满意度模型和一致性指标,分析讨论了最大满意度模型的优点,最后通过算例验证了该模型的正确性和适用性,具有一定的理论和实际应用价值.     

基于二元联系数距离的不确定语言多属性决策模型

研究了属性权重范围已知,方案主观偏好值为语言变量,决策信息为不确定语言决策矩阵的多属性决策问题.在给出不确定语言变量转换为二元联系数的公式以及二元联系数距离公式的基础上,将方案主观偏好语言评价值转换为二元联系数,将不确定语言决策矩阵转换为二元联系数决策矩阵,从而得到方案的二元联系数综合属性值,通过最小化方案的二元联系数综合属性值和主观偏好值之间距离,建立多目标优化模型,并将其转换为一个单目标规划模型计算出属性权重.然后,通过对方案的二元联系数综合属性值进行不确定性分析,得到各方案的排序总数,利用排序总数对方案进行排序择优.应用实例表明该决策方法可行有效.     

A robust additive consistency-based method for decision making with triangular fuzzy reciprocal preference relations

To express uncertain information in decision making, triangular fuzzy reciprocal preference relations (TFRPRs) might be adopted by decision makers. Considering consistency of this type of preference relations, this paper defines a new additive consistency concept, which can be seen as an extension of that for reciprocal preference relations. Then, a simple method to calculate the triangular fuzzy priority weight vector is introduced. When TFRPRs are inconsistent, a linear goal programming framework to derive the completely additive consistent TFRPRs is provided. Meanwhile, an improved linear goal programming model is constructed to estimate the missing values in an incomplete TFRPR that can address the situation where ignored objects exist. After that, an algorithm for decision making with TFRPRs is presented. Finally, numerical examples and comparison analysis are offered.     

Multi-criteria semantic dominance: A linguistic decision aiding technique based on incomplete preference information

A linguistic decision aiding technique for multi-criteria decision is presented. We define a relation between alternatives as multi-criteria semantic dominance (MCSD). It adopts the similar ideal of the stochastic dominance by utilizing the partial information of the decision maker’s preference, which is only ordinal or partially cardinal. The MCSD rules based on three typical types of semanteme functions are introduced and proven. By using these rules, all the alternatives under consideration are divided into two mutually exclusive sets called efficient set and inefficient set. The decision maker who has such a semanteme function will never choose the alternative from the corresponding inefficient set as the optimal one. In such a way, when we analyze the linguistic decision information, the inherent fuzziness of preference can be handled and several controversial operations of the linguistic terms can be avoided. An example is also provided to illustrate the procedure of the proposed method.     

Some models for deriving the priority weights from interval fuzzy preference relations

Interval fuzzy preference relation is a useful tool to express decision maker’s uncertain preference information. How to derive the priority weights from an interval fuzzy preference relation is an interesting and important issue in decision making with interval fuzzy preference relation(s). In this paper, some new concepts such as additive consistent interval fuzzy preference relation, multiplicative consistent interval fuzzy preference relation, etc., are defined. Some simple and practical linear programming models for deriving the priority weights from various interval fuzzy preference relations are established, and two numerical examples are provided to illustrate the developed models.     

基于方案贴近度和满意度的交互式不确定多属性决策方法

针对属性权重信息部分确知且对方案有偏好的不确定多属性决策问题,提出一种基于方案贴近度和满意度的交互式决策方法.方法首先利用已知的客观信息和决策者的主观要求建立单目标规划模型,其次通过对方案满意度和综合度的给定与修正来实现人机交互决策.最后,通过实例说明模型及方法的可行性和有效性.     

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.