一种基于多粒度语言偏好矩阵的多属性群决策方法

针对决策专家以多粒度语言偏好矩阵形式给出偏好信息的多属性群决策问题,提出一种基于二元语义一致化的多属性群决策方法.首先,构建一个基本语言偏好集作为多粒度语言一致化的参考集合;然后,采用基于二元语义的一致化处理方法将不同粒度的语言偏好信息均统一转化为相同粒度的二元语义形式,再通过二元语义的相关集结算子,对各决策专家给出的偏好信息进行集结并进行方案优选,得到满意结果;最后,通过算例说明了该方法的有效性.

     

基于相似度的多粒度不确定语言群决策方法

针对具有多粒度不确定语言评价信息的多属性群决策问题,提出了一种基于区间二元语义信息处理和矢量相似度的群决策方法,弥补了基于距离测度的决策方法易造成信息混淆的不足。该方法首先使用二元语义转换函数对多粒度区间语言评价信息进行一致化处理;然后通过建立使备选方案对正理想解相似度最大、负理想解相似度最小的最优化模型来获得相应的属性权重;最后利用区间二元语义的集结算子对评价信息进行加权集成,并通过优序数排序法实现对各方案的排序。实例分析说明了该方法的可行性和有效性。     

二元语义粗算子及其语言多属性决策中的应用

针对语言多属性决策,提出一种基于二元语言信息处理和粗糙集理论的求解方法。利用规范的语言评价信息建立决策信息表,提出了一种由属性依赖度和信息度来形成属性客观权重的方法,通过二元语义集成算子计算属性的主观权;根据决策者的偏好,将各属性的主客观权重信息集成,得到属性综合权重;将规范化的语言评价信息转化为二元语言形式,并与已有的信息集结算子合成,得到二语义粗算子;举例说明二元语义粗算子的应用。     

主客观权重集成及扩展VIKOR的多属性群决策方法

针对评价信息、属性权重均为不同粒度语言短语的多属性群决策问题,提出一种基于主客观权重集成及扩展多准则协调优化解（VIKOR）的多属性群决策方法。由基本语言评价集实现对多粒度语言评价矩阵的一致化,基于同一粒度的语言决策矩阵计算群体对属性的评价偏差,基于群体评价意见的一致性原则得到属性客观权重,通过二元语义加权算术平均（T-WAA）算子得到属性主观权重,从而集成主、客观权重求得属性综合权重。集结转化后的单个评价矩阵得到群体评价矩阵及其导出矩阵,由扩展VIKOR方法,根据群效用值、个体遗憾值及综合评价值分别对方案进行排序,获得折衷方案。算例分析表明该方法的有效性与可行性。     

基于云模型具有语言评价信息的多属性群决策研究

针对多属性群决策中具有语言评价信息偏好的表示与集结的关键问题．研究了基于云模型的决策专家个体偏好表示、偏好集结和方案优选方法．首先采用云模型表示决策者给出的自然语言评价信息,而属性和决策者权重大小则用云的语气运算表示;然后用浮动云进行偏好集结,根据云模型的相对距离进行方案的排序和优选．此方法可充分表达评价语言的模糊性和随机性,具有较大的客观性．     

基于重要度引导偏好识别修正的多粒度语言共识模型

研究多粒度语言偏好信息下的群体共识决策问题. 首先, 从个体和群体两个角度充分挖掘偏好信息下隐含的专家重要度信息, 基于个体一致度及个体与群体的相似度构建确定专家重要度的优化模型; 其次, 以专家重要度引导非共识偏好的识别和修正过程, 提出一种自适应的语言共识模型; 然后, 给出一种群决策方法, 确保在集结专家意见前群体达成一定程度的共识; 最后, 通过算例验证所提出方法的可行性和有效性.

     

多粒度拓展语言层级群组DEMATEL改进方法*

决策试行与评价实验室方法(decision making trial and evaluation laboratory,DEMATEL)作为一种面向复杂社会经济系统问题的因素分析算法,近年来受到国内外学者的广泛关注。为解决DEMATEL方法在分析复杂不确定社会经济系统时,由于专家知识背景不同而导致的群组专家选择多粒度评价标度进行偏好信息判断的问题,引入二元语义模型表达群组专家的偏好判断信息,提出一种基于拓展语言层级模型的多粒度群组DEMATEL改进方法。改进方法先对群组专家给出的不同粒度评价信息构造二元语义直接影响矩阵,再利用拓展语言层级模型进行归一化处理,并通过二元语义集合算子进行群组信息的集成,进而运用DEMATEL方法进行系统因素的因果关系分析与决策。最后,将改进方法应用于中国汽车零部件再制造的内部障碍因素分析,案例应用结果表明,所提方法在实践中是切实可行的。     

基于双重语言信息联动的多阶段决策模型

研究双重语言信息联动下多阶段决策信息的动态集结方法. 考虑决策依据信息和专家偏好信息的自身特点, 设计基于双重语言信息融合的多阶段决策问题分析框架; 分析决策信息的动态变化特征, 以两类信息之间差异最小为原则构建规划模型群, 探寻阶段权重和各阶段下属性权重的具体表现; 设定决策者的信息偏好程度, 集结方案的动态综合绩效和专家判断结果, 在多阶段情形下实现候选方案的优选决策. 最后通过算例验证了所提出方法的科学性和适用性.     

基于双重语言信息联动的多阶段决策模型

研究双重语言信息联动下多阶段决策信息的动态集结方法.考虑决策依据信息和专家偏好信息的自身特点,设计基于双重语言信息融合的多阶段决策问题分析框架;分析决策信息的动态变化特征,以两类信息之间差异最小为原则构建规划模型群,探寻阶段权重和各阶段下属性权重的具体表现;设定决策者的信息偏好程度,集结方案的动态综合绩效和专家判断结果,在多阶段情形下实现候选方案的优选决策.最后通过算例验证了所提出方法的科学性和适用性.     

群决策中多阶段多元判断偏好的集结方法研究

研究群决策过程中决策者基干多个决策阶段、多种结构形式的判断偏好集结方法.基于互反判断偏好与互补判断偏好的转化公式,将多种类偏好的结构一致化;利用决策者判断偏好的一致性水平和与群体综合偏好偏差的距离,提出了确定决策者权重的方法;建立了基于决策先验信息的多阶段偏好集结的决策阶段赋权模型.根据各决策阶段的权重,将多阶段判断偏好集结成群体综合偏好.     

A web based consensus support system for group decision making problems and incomplete preferences

Reaching a high level of consensus among experts is critical in group decision making problems. Usually, it is the moderator task to assure that the consensus process is carried out properly and, if possible, to offer recommendations to the expert in order to change their opinions and narrow their differences.In this paper we present an implemented web based consensus support system that is able to help, or even replace, the moderator in a consensus process where experts are allowed to provide their preferences using one of many types (fuzzy, linguistic and multi-granular linguistic) of incomplete preference relations.This system is based on both consistency and consensus measures and it has been designed to provide advice to the experts to increase group consensus level while maintaining the individual consistency of each expert. The consistency measures are characterized by and computed using uninorm operators. When appropriate, the system also helps experts to reduce the incompleteness of their preference relations. The web interface allows to carry out distributed consensus processes and thus, experts do not necessarily need to physically meet together.     

Consensus reaching for group decision making with multi-granular unbalanced linguistic information: A bounded confidence and minimum adjustment-based approach

In group decision making problems, there exist the situations that decision makers may use unbalanced linguistic term sets that are not uniformly and symmetrically distributed to provide their linguistic assessments over alternatives. Moreover, due to the difference in knowledge and culture backgrounds, it is also possible that multi-granular linguistic term sets may also be used by decision makers. How to manage multi-granular unbalanced linguistic information in consensus-based group decision making has becoming an important topic in linguistic decision making. In this paper, we first revise Herrera’s unbalanced linguistic term sets and propose a simplified linguistic computational model to fuse multi-granular unbalanced linguistic terms. Afterwards, for multi-criteria group decision making problems with multi-granular unbalanced linguistic information, we develop two optimization models to generate adjustment advice for decision makers who have to change his/her opinions in consensus reaching process, which consider both the bounded confidence levels and minimum adjustment of decision makers’ linguistic assessments. Moreover, an algorithm is further proposed to help decision makers reach consensus in group decision making. Eventually, an application example for ERP system supplier selection and some simulation results are presented to illustrate and justify the consensus reaching algorithm.     

Supplier selection with different risk preferences and attribute sets: An innovative study based on generalized linguistic term sets

Selecting the optimal supplier is crucial to the management of the company’s supply chain, which has received widespread attention from academia and business circles. Generally, a variety of suppliers and multiple attributes are usually involved in this selection proceeding which can be comparatively regarded as a linguistic multiple attribute group decision making (MAGDM) problem. However, common linguistic MAGDM problems may not take the following characteristics into consideration. Due to the limited knowledge, distinctive interests, and different semantic value expectations of decision makers (DMs), it is necessary for them to consider their diverse risk preferences and use multi-granular linguistic term sets (LTSs) to assess suppliers on individual attribute sets independently. Meanwhile, the complex decision environment may have influences on the integrity of the attribute weight information, such that it is always incompletely known. To deal with the afore-mentioned situations, this paper presents a procedure based on risk preferences and several attribute sets with incomplete weight information for choosing the desirable supplier. Firstly, a new multi-granular fuzzy linguistic transformation model is constructed to normalize linguistic domains of multi-granular generalized linguistic term sets (GLTSs). Multi-granular GLTSs are introduced to describe semantic values of multi-granular LTSs given by DMs with risk preferences. Secondly, according to the maximizing deviation method with incomplete attribute weight information, an optimization model is also established to determine attribute weight vectors of individual attribute sets. Thirdly, a novel method that comprises of the aforesaid models is presented to handle supplier selection problems with risk preferences and several attribute sets. Finally, an illustrative example on supplier selection and comparative analyses are provided to clarify the validity and feasibility of our proposed method. Significantly, the initiation of the proposed method and its application could afford to the theoretical development of linguistic MAGDM, as well as the practical expansion in the domain of supplier selection.     

基于相对熵和二元熵的多粒度直觉语言TODIM决策方法

针对评估信息为多粒度直觉语言集的决策问题,提出一种基于相对熵和二元熵的TODIM方法。该方法首先定义了直觉语言数的相对熵和二元熵,以度量决策信息的差异和不确定性;其次,构建了基于相对熵和二元熵的专家赋权模型,并建立了主观权重完全已知、部分已知和完全未知场景下的属性赋权模型;最后,为集结多粒度群体决策信息,提出了多粒度直觉语言加权算术平均(MIL-WAA)算子。算例分析表明,该方法能够较好地度量决策信息的不确定性和差异性,并考虑了决策者的有限理性行为,具有一定的合理性和有效性。     

On compatibility of uncertain additive linguistic preference relations based on the linguistic COWA operator

We develop a new compatibility for the uncertain additive linguistic preference relations and study its properties which are very suitable to deal with group decision making (GDM) problems involving uncertain additive linguistic preference relations. Based on the linguistic continuous ordered weighted averaging (LCOWA) operator, we present some concepts of the compatibility degree and compatibility index for the two uncertain additive linguistic preference relations. Then, we study some desirable properties including the property that the synthetic uncertain linguistic preference relation is of acceptable compatibility under the condition that uncertain additive linguistic preference relations given by experts are all of acceptable compatibility with the ideal uncertain linguistic preference relation, which provides a theoretic basis for the application of the uncertain additive linguistic preference relations in GDM. In order to determine the weights of experts, we construct an optimal model based on the criterion of minimizing the compatibility index in GDM. Finally, we propose a new approach based on the compatibility index and the expected additive linguistic preference relation to GDM and develop an application of the optimal weights approach compared with the equal weights approach where we analyze a GDM regarding the evaluation of schools in a university.     

Probabilistic linguistic vector-term set and its application in group decision making with multi-granular linguistic information

With the rapid information explosion and sharing, recommender systems (RS) play an auxiliary role in assisting the Internet users to make decision especially in the e-service platform. Normally, the information in this process is related to opinions and preferences, which are usually expressed through a qualitative way such as linguistic evaluation terms (LETs). However, the LETs may come from different sources such as experts, users, etc., which makes the linguistic evaluation scales (LESs) used in this process probably be different due to their different backgrounds and levels of knowledge. The diversity and flexibility of these LESs determine the quality of information, and further affect the effectiveness of a RS. In this paper, we focus on improving the accuracy of the multi-granular linguistic recommender system by supporting customers to find out the most eligible items according their own preferences. We first propose the probabilistic linguistic vector-term sets (PLVTSs) to promote the application of multi-granular linguistic information. Based on the PLVTSs, we then develop a novel algorithm to tackle multi-attribute group decision making (MAGDM) problems with multiple LESs. Furthermore, the effectiveness of the PLVTSs is validated by an illustration of personalized hospital selection-recommender problem. Finally, we point out some possible research directions regrading to the PLVTSs.     

Multi-granular linguistic distribution evidential reasoning method for renewable energy project risk assessment

Nowadays, renewable energy projects have constantly been emphasized and the assessment of potential risks has been considered as an indispensable activity prior to implementation of projects.To carry out a reasonable assessment, multi-granular linguistic distribution assessments (LDAs), an effective and uncertainty representation tool, are adopted to express and quantify opinions based on personalized individual linguistic term sets. Specifically, this study develops a novel uncertain multiple criteria decision making approach, named multi-granular linguistic evidential reasoning method, which can handle incomplete and personalized preferences. A novel comparison method for LDAs is first put forward based on numerical characteristics, namely an expectation value and central moment. To fuse the multi-granular LDAs, a lossless transformation technique is further introduced and some of itsessential properties are discussed. Finally, a case study on renewable energy project risk assessment is discussed to verify the feasibility of the proposed method. Besides, sensitivity analysis is conducted to investigate the sequencing stability and comparative analysis is included to highlight the superiority of the proposed method.     

二元语义处理不同偏好评价信息的群决策方法

针对具有序关系值、效用值、互反判断矩阵、互补判断矩阵、区间模糊数、三角模糊数六种不同偏好评价信息的群决策问题,根据偏好信息的实际意义,通过转换函数将不同偏好信息一致化为二元语义判断矩阵形式,阐明转化方法的合理性与有效性,采用二元语义加权算术平均（T-WAA）算子集结转化后的二元语义判断矩阵,得到群体二元语义判断矩阵,基于二元语义有序加权平均（T-OWA）算子计算某方案优于其他所有方案的整体偏好程度,从而对方案排序择优。算例分析表明该群决策方法的有效性与合理性。     

Multiplicative consistency-based decision support system for incomplete linguistic preference relations

The experts may have difficulty in expressing all their preferences over alternatives or criteria, and produce the incomplete linguistic preference relation. Consistency plays an important role in estimating unknown values from an incomplete linguistic preference relation. Many methods have been developed to obtain a complete linguistic preference relation based on additive consistency, but some unreasonable values may be produced in the estimation process. To overcome this issue, we propose a new characterisation about multiplicative consistency of the linguistic preference relation, present an algorithm to estimate missing values from an incomplete linguistic preference relation, and establish a decision support system for aiding the experts to complete their linguistic preference relations in a more consistent way. Some examples are also given to illustrate the proposed methods.     

The induced linguistic continuous ordered weighted geometric operator and its application to group decision making

In this paper, based on the induced linguistic ordered weighted geometric (ILOWG) operator and the linguistic continuous ordered weighted geometric (LCOWG) operator, we develop the induced linguistic continuous ordered weighted geometric (ILCOWG) operator, which is very suitable for group decision making (GDM) problems taking the form of uncertain multiplicative linguistic preference relations. We also present the consistency of uncertain multiplicative linguistic preference relation and study some properties of the ILCOWG operator. Then we propose the relative consensus degree ILCOWG (RCD-ILCOWG) operator, which can be used as the order-inducing variable to induce the ordering of the arguments before aggregation. In order to determine the weights of experts in group decision making (GDM), we define a new distance measure based on the LCOWG operator and develop a nonlinear model on the basis of the criterion of minimizing the distance of the uncertain multiplicative linguistic preference relations. Finally, we analyze the applicability of the new approach in a financial GDM problem concerning the selection of investments.