Multiple attribute group decision-making methods with unknown weights in intuitionistic fuzzy setting and interval-valued intuitionistic fuzzy setting

To better solve the corresponding multiple attribute group decision-making problem with unknown weights, multiple attribute group decision-making methods with completely unknown weights of decision-makers and incompletely known weights of attributes are proposed in intuitionistic fuzzy setting and interval-valued intuitionistic fuzzy setting. In the group decision-making method, two weight models are proposed based on the score function to determine the weights of both experts and attributes from the intuitionistic fuzzy decision matrices and the interval-valued intuitionistic fuzzy decision matrices. Then, overall evaluation formulas of weighted scores for each alternative are introduced in the intuitionistic fuzzy setting and the interval-valued intuitionistic fuzzy setting to obtain the ranking order of alternatives and the most desirable one(s). Finally, two numerical examples demonstrate the applicability and benefit of the proposed methods.     

大群体应急决策中考虑专家犹豫的不完全信息补值方法

针对特大突发事件应急决策中大群体专家存在偏好信息不完全的问题,提出了一种新的不完全偏好信息大群体应急决策方法.首先,利用TF-IDF（term frequency-inverse document frequency）算法对特大突发事件相关的微博大数据文本流进行关键词提取,获取事件属性及其权重;其次,根据专家给出的偏好信息计算专家的犹豫度,进而获得专家的权重;再次,根据不完全偏好信息矩阵进行属性关联测度和方案接近度测度,提出了基于属性关联和方案接近度的新的补值模型,获得完全偏好信息矩阵;然后,结合专家权重和属性权重进行信息集结和方案择优;最后,通过江西洪涝灾害事件验证所提方法的可行性和有效性.     

基于前景理论的犹豫二元语义灰关联群决策法

针对偏好信息为犹豫二元语义形式、专家权重和属性权重均完全未知的多属性群决策问题,基于前景理论和灰色关联分析法的思想,提出一种多属性群决策方法.首先,利用矩阵拉直运算和灰色关联分析法确定专家权重,利用偏差最大化法确定属性权重.其次,给出了两个犹豫二元语义元的比较方法,结合该比较方法确定各决策矩阵的正、负理想方案,并以此作为决策参考点.然后,根据前景理论和灰色关联系数确定犹豫二元语义环境下的前景价值函数,进而确定各方案的收益损失比值,并据此对候选方案进行排序.最后,将所提方法应用于一个投资决策算例,其结果表明了该方法的合理性和有效性.     

基于粗糙集和CBR的救灾口粮需求预测

救灾口粮预测所采用的方法多以专家经验判断为主,具有较大的随机性。为此,从灾害案例的特点出发,针对案例推理时存在效率低下和权重确定差异性较大的问题,结合粗糙集处理不确定知识的优点和案例推理的特点,提出一种方法,实现灾害应急救灾口粮需求预测,并通过洪涝灾害实例进行分析。结果表明该方法有利于减少主观影响,提高需求预测的准确率和效率。     

A multi-agent affective interactive MAGDM approach and its applications

Traditional multi-attribute group decision-making (MAGDM) methods focus on weights calculation of sub-attributes and experts' preferences, but lack the discussion on the decision-makers' affective interaction, and its influence on the decision preference and group consistency. To address this problem, the present study proposed a new multilayer affective computing model based on “personality–mood–emotion” pattern, under the multi-agent decision system framework. In addition, we introduced the group trending index and affection-preference incentive mechanism, which can help simulate MAGDM process and learn group experts' decision preferences. Further, we proposed a new multi-agent affective interactive MAGDM (MAAI-MAGDM) method, where we defined a novel group convergence index and an alternative decision entropy to explain the convergence process of decision and group consistency. Compared to the traditional MAGDM approaches, the proposed MAAI-MAGDM method fully considered the affective features of each expert, reduced the dependence on aggregation operators and weight analysis, alleviated the workload of group experts, and effectively reduced the complexity of decision-making calculation process. Finally, we verified that the proposed method can effectively assist the decision-making processes by employing two numerical cases.     

考虑时间序列的动态大群体应急决策方法

针对专家权重和属性权重未知、阶段权重未知且与时间序列有关的动态大群体应急决策问题,提出一种考虑时间序列的动态大群体应急决策方法.首先,提出一个考虑区间直觉模糊数犹豫度的距离公式,定义区间直觉模糊数贴近度,综合考虑贴近度和相似度,用模糊聚类法对大群体专家偏好信息进行聚类;其次,基于现有区间直觉模糊熵公式的不足,提出一个新的区间直觉模糊熵公式,基于此公式考虑专家之间知识水平的差异和各个阶段偏好信息不具遗传性等特点,计算得出专家在不同属性下的权重和属性在各阶段下的权重;再次,考虑时间序列对各阶段权重的影响,构建相对熵模型,对阶段权重进行合理确定,进而利用加权平均算子得到整个决策过程中各方案的综合决策偏好;然后,利用区间直觉模糊数的得分函数和精确函数对方案进行排序,选出最优方案;最后,通过与以往文献的方法对比分析验证所提出方法的有效性和优越性.     

Consistency and consensus reaching process for group decision making based on complete interval distributed preference relations under social network analysis

Group decision-making (GDM) problems often consist of many indeterminacy factors in realistic situation. How to cope with consistency and consensus under uncertain circumstance are two critical issues in pairwise comparison based GDM problems. In this paper, we firstly propose the model of complete interval distributed preference relation (CIDPR) based on the concept of linguistic distribution with interval symbolic proportions, distribution linguistic preference relation (DLPR) and IDPR. Secondly, the additive consistency index of CIDPR is defined to measure the consistency level of expert's judgment, and an adjustment algorithm is proposed for converting inconsistent CIDPR to an acceptable consistent level. Thirdly, since trust relation is a critical factor in the generation of experts’ weights and the adjustment of experts’ opinions, consensus reaching process (CRP) is designed to take into account distributed linguistic trust relations under social network analysis (SNA). In the proposed adjustment mechanism, non-consensus individual should modify opinion towards his/her trusted and highly weighted expert. The advantage of the proposed inconsistent CIDPR adjustment model can maximally retain the information in the original distribution, while the CRP has a relatively fast convergent speed and good practicality. An illustrative example of strategic new product selection is conducted to demonstrate the applicability of the proposed method and its potential in supporting realistic GDM problems.     

基于判断矩阵的专家模糊核聚类组合赋权方法

研究群决策中专家赋权问题.实际决策问题中,由于客体信息自身存在的不完备性和不确定性以及人们描述过程中的模糊性,更适合采用模糊聚类的分析方法,为此提出一种基于判断矩阵的专家模糊核聚类赋权方法.该方法运用模糊核聚类理论对专家排序向量进行分类,根据分类结果、判断矩阵一致性和排序向量的熵对各专家进行组合赋权.算例表明,所提出的方法是可行且有效的.     

基于双层专家权重确定的风险型大群体决策

针对风险型大群体决策问题,考虑专家权重确定的复杂性,提出基于累积前景理论的决策信息处理和考虑双层专家权重确定的大群体决策方法.采用二元语义获取并表达专家的评价信息;基于累积前景理论计算方案的综合前景价值矩阵;采用双层专家权重确定方法,第1层利用聚类方法对大群体成员价值向量进行聚类,根据聚类结果确定聚集群权重, 第2层利用熵权法获得专家熵权,二者结合得到专家权重.通过确定专家权重和综合前景价值矩阵得出最终的决策结果.最后通过算例表明了所提出方法的可行性和有效性.     

Group decision making in medical system: An intuitionistic fuzzy soft set approach

In medical system, there may be many critical diseases, where experts do not have sufficient knowledge to handle those problems. For these cases, experts may provide their opinion only about certain aspects of the disease and remain silent for those unknown features. Feeling the need of prioritizing different experts based on their given information, this article uses a novel concept for assigning confident weights to different experts which are mainly based on their provided information. Experts provide their opinions about various symptoms using intuitionistic fuzzy soft matrix (IFSM). In this article, we propose an algorithmic approach based on intuitionistic fuzzy soft set (IFSS) which explores a particular disease reflecting the agreement of all experts. This approach is guided by the group decision making (GDM) model and uses cardinals of IFSS as novel concept. We have used choice matrix (CM) as an important parameter which is based on choice parameters of individual expert. This article has also validated the proposed approach using distance measurements and consents of the majority of experts. The effectiveness of the proposed approach is demonstrated using a suitable case study.     

基于新型距离测度的概率语言多属性群决策方法

研究属性权重和专家权重均未知条件下的概率语言多属性群决策问题.首先,针对传统概率语言术语集距离测度的不足,提出改进的距离测度,并证明其性质和优越性.其次,基于新的距离公式,定义决策者的平均相似度,并结合专家之间的信任度矩阵计算每个属性下决策者的综合权重;构建基于相似-信任分析的群体共识调节模型,尽可能保留各属性下权威专家的意见;考虑到属性之间的相关性以及各个属性的重要程度,构建基于广义Choquet积分和离差最大化法的主客观综合赋权模型.随后,在新的距离测度的基础上,结合TODIM方法构建概率语言多属性群决策框架,实现对多个备选方案的排序.最后,以光伏电站的选址为例,验证所提出方法的有效性和合理性.     

一种结合主客观信息的多属性决策方法

研究了具有模糊偏好信息的模糊多属性决策问题．提出一种结合主观偏好信息与客观信息的综合特征向量方法．主观偏好信息由决策方案的模糊偏好互补矩阵和属性权重的两两比较互反矩阵组成，客观信息由客观决策矩阵组成．给出了求解模糊多属性决策问题的最小二乘偏差估计方法．通过建立二次规划模型决定属性权重向量，并对方案进行排序．最后，给出了使用该方法的数值例子．     

基于GRA-GCRITIC和改进加权双向投影的区间Fermatean模糊多属性群决策方法

针对司法案件决策环境的复杂性及评价信息的模糊性,提出一种基于GRA-GCRITIC（grey relational analysis-group criteria importance through intercriteria correlation）和改进加权双向投影的区间Fermatean模糊Hamacher-TODIM多属性群决策方法。首先考虑到各位专家对各评价方案下各指标评价信息的差异性,提出一种GRA-GCRITIC方法,该方法将灰色关联融入到CRITIC中,以确定指标综合权重比单一获取的指标权重更加客观可靠。其次,结合信任关系对加权双向投影法进行改进,兼顾主客观关系,利用专家个体与群体评价信息的隶属度及非隶属度矩阵间的相似度得到专家权重。最后,考虑到决策者的损失规避心理,将融合了Hamacher算子的TODIM方法拓展至区间Fermatean模糊环境中,通过具体算例可得到其综合优势度及排序,验证了所提方法的可行性及灵活性。     

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 consensus reaching model for 2-tuple linguistic multiple attribute group decision making with incomplete weight information

The aim of this paper is to put forward a consensus reaching method for multi-attribute group decision-making (MAGDM) problems with linguistic information, in which the weight information of experts and attributes is unknown. First, some basic concepts and operational laws of 2-tuple linguistic label are introduced. Then, a grey relational analysis method and a maximising deviation method are proposed to calculate the incomplete weight information of experts and attributes respectively. To eliminate the conflict in the group, a weight-updating model is employed to derive the weights of experts based on their contribution to the consensus reaching process. After conflict elimination, the final group preference can be obtained which will give the ranking of the alternatives. The model can effectively avoid information distortion which is occurred regularly in the linguistic information processing. Finally, an illustrative example is given to illustrate the application of the proposed method and comparative analysis with the existing methods are offered to show the advantages of the proposed method.     

考虑个体累积共识贡献的犹豫模糊语言自适应共识模型

针对犹豫模糊语言信息下的多属性群决策问题,提出一种基于个体累积共识贡献的自适应共识决策模型.首先,利用犹豫模糊语言得分函数,基于经典的信息熵和相对熵理论,综合考虑同一属性下不同方案间的信息差异,以及各方案分别与正理想方案和负理想方案的信息差异,构建确定属性权重的优化模型;然后,提出个体累积共识贡献测度和全局共识测度,利用全局共识度进行共识控制,依据个体累积共识贡献度对专家权重进行自适应修正,构建一种新的犹豫模糊语言自适应共识过程.该过程的特点是对拥有较少合作的非全共识专家执行专家权重惩罚,而且专家权重的更新引起属性权重的自适应更新,反过来又影响个体共识贡献的累积.最后通过一个应急医疗设施选址的共识决策例子表明方法的可行性和有效性.     

A cumulative belief degree approach for group decision‐making problems with heterogeneous information

In some complex group decision‐making (GDM) problems, the information needing to be processed may be heterogeneous. This may involve consideration of objective and subjective criteria by experts who have their own particular set of criteria, their own preference format for assessing alternatives under these criteria, and who may themselves be assigned differing importance weights as experts. This paper presents a cumulative belief degree approach to cope with heterogeneous information in multiple attribute GDM problems. The proposed approach focuses to aggregate subjective expert assessments and objective criteria that are presented in various representation formats and scales. The methodology employs transformation formulae for several preference representation scales to belief structure, including 2‐tuple representation, classical fuzzy sets, hesitant fuzzy sets, and intuitionistic fuzzy sets. Aggregation formulae are proposed to combine expert criteria evaluations and find a collective preference. A consensus degree is calculated for measuring the agreement between the experts. An illustrative example is presented to clarify the steps of the methodology, and validity of the approach is assured through comparative analysis with the existing methods.     

Facilitating the use of multi-attribute utility theory in expert systems:an aid for identifying the right relative importance weights of attributes

In general, expert system applications to real cases involve making decisions, i.e. selecting a suitable action among a set of possible alternative actions. A well-known standard method for modelling decision problems is the so-called multi-attribute utility theory (MAUT), a method in which the alternatives are viewed in terms of their attributes. A set of attributes are identified and a specific value and a suitable relative importance weight are assigned to each attribute. However, it is not easy for the expert to quantify the relative importance weight of an attribute: this assignment entails a certain abstraction activity from the expert and, as is well known, experts have difficulty in providing their knowledge in abstract and general terms. In order to overcome this difficulty we propose a method for automatically inferring relative importance weights from a set of specific action sequences. An action sequence is a list in chronological order of the actions executed by the expert when facing specific cases of decision problems. Providing action sequences requires no other effort but remembering specific episodes, and this task is much easier for experts than having to directly provide precise numbers expressing relative importance weights. Moreover in many cases action sequences are already stored in suitable records. Consider, for example, the list of medical tests executed on a given patient, a list included in the patient clinical record stored in the clinical database of a hospital. On the basis of these considerations the proposed method should be useful for designers of expert systems which face problems of choosing the right action among a set of alternative actions.     

A multiple attributes decision making method using individual and collaborative attribute data in a fuzzy environment

Although multiple attribute decision making (MADM) problems with both individual attribute data of a single alternative and collaborative attribute data of pairwise alternatives exist in the real world, they have seldom been a focus of research. This paper proposes a MADM method using individual and collaborative attribute data in a fuzzy environment, in which experts use linguistic variables to express their opinions. In the method, first, the evaluation matrix of individual attributes date and the judgment matrix of collaborative attributes data are constructed. Then, the central dominance of one alternative outranking other all alternatives is defined for aggregating the collaborative data. From this, an integrated decision matrix incorporating individual and collaborative attribute data is constructed. Further, based on an extended TOPSIS, the fuzzy positive-ideal solution (FPIS) and the fuzzy negative-ideal solution (FNIS) are determined, and the relative closeness of each alternative to the FPIS and FNIS is calculated to determine the ranking order of all alternatives. Finally, two examples are used to illustrate the applicability of the proposed method.     

基于可能度矩阵的区间型多属性决策方法

研究了几组可能度公式之间的关系,提出一种基于可能度矩阵的区间型多属性决策(MADM)方法。对决策矩阵中各指标下的属性区间值两两比较并建立各指标的可能度矩阵,通过各个可能度矩阵的排序向量把属性值为区间数的决策矩阵转化为以精确数为测度的矩阵,把求解区间型多属性决策中指标权重的不确定性问题转化为确定性问题处理,随后利用区间数排序的可能度法获得最优方案。实验结果表明了所提方法的可行性和有效性。最后对多属性决策问题中由不确定性转化为确定性的求解策略及其可能产生的问题作了必要讨论。