Projection method for multiple criteria group decision making with incomplete weight information in linguistic setting

Multiple criteria group decision making (MCGDM) problems have become a very active research field over the last decade. Many practical problems are often characterized by MCGDM. The aim of this paper is to develop a new approach for MCGDM problems with incomplete weight information in linguistic setting based on the projection method. Firstly, to reflect the reality accurately, a method to determine the weights of decision makers in linguistic setting is proposed by calculating the degree of similarity between 2-tuple linguistic decision matrix given by each decision maker and the average 2-tuple linguistic decision matrix. By using the weights of decision makers, all individual 2-tuple linguistic decision matrices are aggregated into a collective one. Then, to determine the weight vector of criteria, we establish a non-linear optimization model based on the basic ideal of the projection method, i.e., the optimal alternative should have the largest projection on the 2-tuple linguistic positive ideal solution (TLPIS). Calculate the 2-tuple linguistic projection of each alternative on the TLPIS and rank all the alternatives according to the 2-tuple linguistic projection value. Finally, an illustrative example is given to demonstrate the calculation process of the proposed method, and the validity is verified by comparing the evaluation results of the proposed method with that of the technique for order preference by similarity to ideal solution (TOPSIS) method.     

A new methodology for fuzzy multi-attribute group decision making with multi-granularity and non-homogeneous information

The aim of this paper is to develop a new methodology for solving fuzzy multi-attribute group decision making problems with non-homogeneous information, including multi-granular linguistic term sets, fuzzy numbers, interval values and real numbers. In this methodology, different distances are defined to measure differences between alternatives and the ideal solution as well as the negative ideal solution. A relative closeness method is developed by introducing the multi-attribute ranking index based on the particular measure of closeness to the IS. The proposed method determines a compromise solution for the group, providing a maximum “group utility” for the “majority” and a minimum of an individual regret for the “opponent”. The implementation process, effectiveness and feasibility of the method proposed in this paper are illustrated with a real example of the missile weapon system design project selection.     

基于在线评价信息的概率语言多属性变权决策方法

针对电子商务网站中涌现的大量在线评价信息,本文提出一种基于在线评价信息的概率语言多属性变权决策方法,指导消费者的购买决策。在本文方法中,首先利用概率语言描述在线评价信息,构建概率语言决策矩阵,并重新定义了区间概率语言的得分函数;其次,利用变权方法处理决策矩阵,得出不同方案的各属性权重;再次,依据得出的属性权重,基于后悔理论,考虑决策者风险规避系数,求出各方案的综合感知效用值,并据此排序。最后,利用汽车之家网站提供的顾客在线评价信息,以一个汽车选择的实例说明了本文所提方法的合理性与实用性。     

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.     

A new method for multiple criteria group decision making with incomplete weight information under linguistic environment

A new method is proposed to solve multiple criteria group decision making (MCGDM) problems, in which both the criteria values and criteria weights take the form of linguistic information, and the information about linguistic criteria weights is partly known or completely unknown. Firstly, to get reasonable decision result, instead of assigning the same weight to the decision maker (DM) for all criteria, we propose a method to determine the weight of DM with respect to each criterion under linguistic environment by calculating the similarity degree between individual 2-tuple linguistic evaluation value and the mean given by all decision makers (DMs). Secondly, for the situations where the information about the criteria weights is partly known or completely unknown, we establish optimization models to determine the criteria weights by defining 2-tuple linguistic positive ideal solution (TL-PIS), 2-tuple linguistic right negative ideal solution (TL-RNIS) and 2-tuple linguistic left negative ideal solution (TL-LNIS) of the collective 2-tuple linguistic decision matrix. Thirdly, we propose a new method to solve MCGDM problems with partly known or completely unknown linguistic weight information. Finally, an illustrative example is given to demonstrate the calculation process of the proposed method.     

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。     

基于二元语义的犹豫模糊语言决策方法

当决策者在给出语言评价信息而表示出犹豫时,决策信息更适合用犹豫模糊语言术语集表达。为了减少语言决策过程中信息的丢失,得到较精准的评价结果,本文提出基于二元语义的犹豫模糊语言决策方法。首先定义了犹豫模糊二元语义集、犹豫模糊二元语义集的均值函数、方差函数及其集结算子,然后用集结算子求出各方案的综合评价值,通过犹豫模糊二元语义的均值函数和方差函数确定方案排序。最后通过实例说明了该方法的实用性和有效性。     

PROMETHEE-MD-2T method for project selection

Project selection is a real problem of multicriteria group decision making (MCGDM) where each decision maker expresses his/her preferences depending on the nature of the alternatives and on his/her own knowledge over them. Thus, information, as much quantitative as qualitative, coexists. The traditional methods of MCGDM developed for project selection usually discriminates in favour of quantitative information at the expense of qualitative information, and this is due to the capability to integrate this first type of information inside their procedure. In this article, two new multicriteria 2-tuple group decision methods called “Preference Ranking Organisation Method for Enrichment Evaluation Multi Decision maker 2-Tuple-I and II” (PROMETHEE-MD-2T-I and II) are presented. They are able to integrate inside their procedure both quantitative and qualitative information in an uncertain context. This has been performed by integrating a 2-tuple linguistic representation model dealing with non-homogeneous and imprecise information data made up by valued intervals, numerical and linguistic values into the aggregation operators of Promethee methods. Although they have been developed for project selection problems, these proposed methods can be applied to all kinds of decision-making problems with heterogeneous and multigranular information.     

A consensus reaching process in the context of non-uniform ordered qualitative scales

In this paper, we consider that a group of agents judge a set of alternatives by means of an ordered qualitative scale. The scale is not assumed to be uniform, i.e., the psychological distance between adjacent linguistic terms is not necessarily always the same. In this setting, we propose how to measure the consensus in each subset of at least two agents over each subset of alternatives. We introduce a consensus reaching process where some agents may be invited to change their assessments over some alternatives in order to increase the consensus. All the steps are managed in a purely ordinal way through ordinal proximity measures.     

基于不同粒度语言判断矩阵的群体一致性分析方法

针对群决策中基于不同粒度语言判断矩阵形式偏好信息的群体一致性问题,提出了一种分析方法。首先,给出有关不同粒度语言判断矩阵和二元语义等若干定义,通过转换函数将不同粒度语言判断矩阵一致化为由二元语义表示的判断矩阵;然后,通过定义专家与群偏好的偏差矩阵以及各专家的总体偏差指标,给出了专家群体一致性的判别方法及专家群体判断不一致的调整方法;最后,通过一个算例说明了该方法的有效性。