Fuzzy interval linguistic sets with applications in multi-attribute group decision making

Uncertain and hesitant information, widely existing in the real-world qualitative decision making problems, brings great challenges to decision makers. Hesitant fuzzy linguistic term sets(HFLTSs), an effective linguistic computational tool in modeling and eliciting such information, have hence aroused many scholars’ interests and some extensions have been introduced recently.However, these methods are based on the discrete linguistic term framework with the limited expression domain, which actually depict qualitative information using several single values. Therefore,it is hard to ensure the integrity of the semantics representation and the accuracy of the computation results. To deal with this problem, a semantics basis framework called complete linguistic term set(CLTS) is designed, which adopts a separation structure of linguistic scale and expression domain, enriching semantics representation of decision makers. On this basis the concept of fuzzy interval linguistic sets(FILSs) is put forward that employs the interval linguistic term with probability to increase the flexibility of eliciting and representing uncertain and hesitant qualitative information. For practical applications, a fuzzy interval linguistic technique for order preference by similarity to ideal solution(FILTOPSIS) method is developed to deal with multi-attribute group decision making(MAGDM) problems. Through the cases of movie and enterprise resource planning(ERP) system selection, the effectiveness and validity of the proposed method are illustrated.

An Evidence-Based CoCoSo Framework with Double Hierarchy Linguistic Data for Viable Selection of Hydrogen Storage Methods

Hydrogen is the new age alternative energy source to combat energy demand and climate change.Storage of hydrogen is vital for a nation’s growth.Works of literature provide different methods for storing the produced hydrogen,and the rational selection of a viable method is crucial for promoting sustainability and green practices.Typically,hydrogen storage is associated with diverse sustainable and circular economy(SCE)criteria.As a result,the authors consider the situation a multi-criteria decision-making(MCDM)problem.Studies infer that previous models for hydrogen storage method(HSM)selection(i)do not consider preferences in the natural language form;(ii)weights of experts are not methodically determined;(iii)hesitation of experts during criteria weight assessment is not effectively explored;and(iv)three-stage solution of a suitable selection of HSM is unexplored.Driven by these gaps,in this paper,authors put forward a new integrated framework,which considers double hierarchy linguistic information for rating,criteria importance through inter-criteria correlation(CRITIC)for expert weight calculation,evidence-based Bayesian method for criteria weight estimation,and combined compromise solution(CoCoSo)for ranking HSMs.The applicability of the developed framework is testified by using a case example of HSM selection in India.Sensitivity and comparative analysis reveal the merits and limitations of the developed framework.

Dynamic hesitant fuzzy linguistic group decision-making from a reliability perspective

A dynamic hesitant fuzzy linguistic group decisionmaking(DHFLGDM) problem is studied from the perspective of information reliability based on the theory of hesitant fuzzy linguistic term sets(HFLTSs). First, an approach is applied to transform the dynamic HFLTSs(DHFLTSs) into a set of proportional linguistic terms to eliminate the time dimension. Second, expert reliability is measured by considering both group similarity and degree of certainty, and an optimization method is employed to quantify the linguistic terms by maximizing the group similarity. Third, through computing the attribute stability as well as its reliability, a combination rule which considers both reliability and weight is proposed to aggregate the information, and then the aggregated grade values and degree of stability are used to make a selection. Finally,the application and feasibility of the proposed method are verified through a case study and method comparison.

Pythagorean Uncertain Linguistic Variable Hamy Mean Operator and Its Application to Multi-attribute Group Decision Making

Pythagorean fuzzy set(PFS) can provide more flexibility than intuitionistic fuzzy set(IFS) for handling uncertain information, and PFS has been increasingly used in multi-attribute decision making problems. This paper proposes a new multiattribute group decision making method based on Pythagorean uncertain linguistic variable Hamy mean(PULVHM) operator and VIKOR method. Firstly, we define operation rules and a new aggregation operator of Pythagorean uncertain linguistic variable(PULV) and explore some properties of the operator.Secondly, taking the decision makers' hesitation degree into account, a new score function is defined, and we further develop a new group decision making approach integrated with VIKOR method. Finally, an investment example is demonstrated to elaborate the validity of the proposed method. Sensibility analysis and comprehensive comparisons with another two methods are performed to show the stability and advantage of our method.

Medical Waste Treatment Station Selection Based on Linguistic q-Rung Orthopair Fuzzy Numbers

During the COVID-19 outbreak,the use of single-use medical supplies increased significantly.It is essential to select suitable sites for establishing medical waste treatment stations.It is a big challenge to solve the medical waste treatment station selection problem due to some conflicting factors.This paper proposes a multi-attribute decision-making(MADM)method based on the partitioned Maclaurin symmetric mean(PMSM)operator.For the medical waste treatment station selection problem,the factors or attributes(these two terms can be interchanged.)in the same clusters are closely related,and the attributes in different clusters have no relationships.The partitioned Maclaurin symmetric mean function(PMSMF)can handle these complex attribute relationships.Hence,we extend the PMSM operator to process the linguistic q-rung orthopair fuzzy numbers(Lq-ROFNs)and propose the linguistic q-rung orthopair fuzzy partitioned Maclaurin symmetric mean(Lq-ROFPMSM)operator and its weighted form(Lq-ROFWPMSM).To reduce the negative impact of unreasonable data on the final output results,we propose the linguistic q-rung orthopair fuzzy partitioned dual Maclaurin symmetric mean(Lq-ROFPDMSM)operator and its weighted form(Lq-ROFWPDMSM).We also discuss the characteristics and typical examples of the above operators.A novel MADM method uses the Lq-ROFWPMSM operator and the Lq-ROFWPDMSM operator to solve the medical waste treatment station selection problem.Finally,the usability and superiority of the proposed method are verified by comparing it with previous methods.

考虑对称交互熵的对偶犹豫模糊企业环境行为决策模型分析

顺应绿色新发展理念,建设高质量生态文明,提升企业环境治理能力现代化水平,企业环境行为指标已逐渐被纳入投资者考量范围。本文针对第三方国际环境审计平台对企业环境行为评价的问题,研究面向对偶犹豫模糊评价信息的聚类方法。首先,定义对偶犹豫模糊相对熵与对称交互熵,并基于信息论角度提出一个新的对偶犹豫模糊相似度公式;然后,构造相似系数矩阵,并基于编网聚类方法对对偶犹豫模糊集进行聚类。最后,以不同指标权重下评价企业环境行为优劣程度为例进行计算,并与使用传统相关系数聚类方法所得结果进行对比,说明在考虑决策者提供的信息量较大的情况下,本文方法概念清晰、计算简单、分辨率高,是一种更加灵活、全面的多层次评价方法,为完善企业环境评价系统的构建提供了一种新思路。

基于FDHHFLTS-BN的海底管道泄漏失效风险定量分析

为预防海底油气管道泄漏失效事故,提出基于自由双层次犹豫模糊语言术语集(FDHHFLTS)和贝叶斯网络(BN)的FDHHFLTS-BN风险分析方法,用于分析海底油气管道泄漏失效事故概率及事故的关键风险因素。将故障树模型转换为BN结构,由专家根据FDHHFLTS评估基本事件发生可能性;采用最佳最差法(BWM)确定专家权重,结合相似性聚合方法(SAM)聚合专家意见;依据构建的BN模型,正向推理得到事故发生概率,反向推理得到后验概率,并进行敏感性分析。将该方法应用于实例分析,结果表明:分析段海底管道泄漏事故的概率值为P=6.20×10^(-3);焊缝施工缺陷、材料施工缺陷和渔具作用等为事故发生的关键因素;与传统方法对比分析结果证明,所提方法在确定海底管道风险方面具有一定的优势。

Warhead power assessment based on double hierarchy hesitant fuzzy linguistic term sets theory and gained and lost dominance score method

Warhead power assessment of the anti-ship missile plays a vital role in determining the optimal design of missile, thus having important strategic research significance. However, in the assessment process, expert’s judgement will directly affect the assessment accuracy. In addition,there are many criteria involved in the missile design alternatives. Some criteria with poor performance may be compensated by other criteria with excellent performance, and then it is impossible to find the truly optimal alternative. Aimed at solving these problems, this paper proposes a synthetical assessment process based on fuzzy hesitant linguistic term set and the Gained and Lost Dominance Score(GLDS) method. In order to improve the assessment accuracy of experts and solve the problem that experts generate different opinions, combined with the advantages of fuzzy hesitant sets and linguistic term sets, the double hierarchy hesitant fuzzy linguistic term sets are used in this paper to improve the accuracy of expert’s judgement. In order to effectively combine expert’s experience with the data of criteria, the evidence theory and entropy weight method are used to transfer the expert’s judgement to the weight. In order to avoid selecting defective alternative of missile design, the GLDS is used to fuse expert information and criteria information. Sensitivity analysis shows that the assessment process has sensitivity to some extent. However, when the fluctuation of expert’s assessment makes the fluctuation of θ in the range of-5% to 5%, the impact on the results is not quite conspicuous. The analysis of calculation result and comparative analysis show that the assessment process proposed in this paper is accurate enough, has great advantage in selecting the current and potential optimal alternative of missile design, and avoids the alternatives with low criteria performance that cannot be compensated by other criteria being selected.

数据驱动的犹豫模糊语言信息策略优先权排序方法

数据挖掘使得决策者获取信息更为方便有效。本文在冲突分析图模型理论框架下,首先基于数据对冲突策略进行挖掘,实现了冲突策略的合理构建。其次,考虑到现实冲突中决策者对某策略的选择更多表现为一种被选择的可能性,将犹豫模糊语言信息和冲突分析图模型理论进行有效交叉融合,采用犹豫模糊语言信息进行评估,并基于粗糙集思想对犹豫模糊语义评价信息进行集结以代表这种可能性;进一步地,提出一种新的基于犹豫模糊语言信息的冲突分析图模型策略优先权排序法。最后,对沭河跨境水污染进行建模分析,对沭河水污染治理提出建议,并且就状态排序结果对比了新旧两种方法,结果验证本文提出方法的合理性。

WPLTS多属性群决策问题的点坐标解法

为了解决加权概率语言术语集(WPLTS)多属性群决策问题,将该问题转换为加权概率犹豫模糊集(WPHFS)多属性群决策问题,并从点坐标的角度出发建立了解决WPHFS多属性群决策问题的一种算法.首先,将WPHFS中的隶属度、概率、专家权重以点坐标形式刻画,在此基础上提出了加权概率犹豫模糊元(WPHFE)的相关运算;其次,分别建立了计算决策专家综合权重以及属性综合权重的计算模型;最后,采用Maclaurin对称平均算子集结WPHFE以获取每个方案的综合属性值.决策结果表明,WPLTS多属性群决策算法不仅可行,而且可以从多个角度来客观地分析方案的排序问题,为精准地确定最优方案提供了一种有效路径.

基于HFLTS中融合专家权重的群决策模型

针对犹豫模糊语言术语集多属性群决策(HFLTSMAGDM)问题,从平面坐标的角度出发建立了一类决策模型.在犹豫模糊语言术语集(HFLTS)中添加决策专家权重,进而构建一种加权的犹豫模糊语言术语集(WHFLTS);将WHFLTS转换为加权的区间值犹豫模糊集(WIVHFS),并对WIVHFS中的区间数(IN)进行测度,把IN的测度结果与其对应的决策专家权重以平面点坐标形式进行描述,在此基础上建立了2个犹豫模糊元(HFE)的大小比较规则及度量2个HFE的距离模型;分别定义了计算属性的整体权重、个体权重以及综合权重的计算方法,在属性的不同权重类别下皆采用Maclaurin对称平均算子集结HFE以获取各方案的综合属性值.案例分析表明,将WHFLTS转换为加权的犹豫模糊集并以平面坐标形式书写而建立的决策算法是可行的,且决策模型具有很好的稳定性.

基于云模型的船舶建造项目后评价

为提高船舶建造项目后评价中专家评价信息融合结果的准确性,建立一种基于云模型的船舶建造项目综合效果评价方法。采用偏差熵模型计算专家的一致性判断矩阵,再通过模糊层次分析法(fuzzy analytic hierarchy process,FAHP)确定指标权重;基于犹豫模糊语言术语集和云模型特征参数,量化评价信息的模糊性和不确定性,建立船舶建造项目综合效果评价云模型,通过云模型计算得到云图即可评价船舶建造项目的综合效果。分析表明:偏差熵模型可用于计算专家对一致性意见的贡献度,提高指标权重计算的准确性;基于犹豫模糊语言术语集的云模型评价方法能兼顾评价信息的模糊性和不确定性,减少专家经验差异对评价结果的影响,适用于船舶建造项目的综合效果评价。

基于犹豫模糊语言决策信息的被执行人聚类算法

针对法院“执行难”现状,将模糊聚类分析方法应用于司法执行领域,聚类的数据类型拓展为犹豫模糊语言信息,构建了一套完整的被执行人隐匿财产行为评估体系。通过估测被执行人隐匿财产的量化概率,为执行法官确定查控重点提供了决策支持。对当前的犹豫模糊语言距离测度存在的局限性进行了分析,给出了犹豫模糊语言犹豫度的定义和新的犹豫模糊语言距离计算方法。采用离差最大化思想确定最优属性权重,提出了一种基于离差最大化的犹豫模糊语言凝聚式层次聚类算法。犹豫模糊语言决策信息环境下的被执行人聚类分析算例验证了评估体系和聚类算法的有效性。

新型对偶犹豫模糊集距离测度及其多属性决策方法

对偶犹豫模糊集为处理复杂问题的不确定性提供了有效手段,其距离测度是一重要衡量指标。针对现有距离测度的局限性,本文定义了对偶犹豫模糊集的犹豫度,给出了基于犹豫度偏差以及隶属度与非隶属度完全偏差的对偶犹豫模糊集距离测度。新距离测度从3个信息维度来衡量距离偏差,更全面客观地体现出数据信息,弥补了传统距离测度可能无法识别的不足。最后结合TOPSIS决策思想给出决策步骤,并应用于航空公司服务质量评价,验证了新距离测度的有效性和合理性。

犹豫模糊语言距离测度及其在多属性决策中的应用

针对现有犹豫模糊语言距离测度存在不满足直递性、改变了原始决策信息、忽略了犹豫度差异等方面的问题,提出了一系列更为合理的新型犹豫模糊语言距离测度方法。首先,对现有犹豫模糊语言距离测度的局限性进行了枚举和分析。其次,给出了犹豫模糊语言犹豫度的定义,分别提出了犹豫模糊语言集的Euclidean距离、Hamming距离、Hamming-Hausdorff距离、Euclidean-Hausdorff距离以及它们的广义形式、加权形式和广义加权形式等一系列新型犹豫模糊语言距离测度,并对新型犹豫模糊语言距离测度的相关性质和定理进行了证明。在此基础上,提出了一种基于新型犹豫模糊语言距离测度和离差最大化的多属性决策方法。最后,通过具体算例和对比分析验证了新型犹豫模糊语言距离测度和多属性决策方法的可行性和有效性。

DUAL HESITANT FUZZY INFORMATION AGGREGATION WITH EINSTEIN T-CONORM AND T-NORM

Dual hesitant fuzzy set （DHFS） is a new generalization of fuzzy set （FS） consisting of two parts （i.e., the membership hesitancy function and the non-membership hesitancy fimction）, which confronts several different possible values indicating the epistemic degrees whether certainty or uncertainty. It encompasses fuzzy set （FS）, intuitionistic fuzzy set （IFS）, and hesitant fuzzy set （HFS） so that it can handle uncertain information more flexibly in the process of decision making. In this paper, we propose some new operations on dual hesitant fuzzy sets based on Einstein t-eonorm and t-norm, study their properties and relationships and then give some dual hesitant fuzzy aggregation operators, which can be considered as the generalizations of some existing ones under fuzzy, intuitionistic fuzzy and hesitant fuzzy environments. Finally, a decision making algorithm under dual hesitant fuzzy environment is given based on the proposed aggregation operators and a numerical example is used to demonstrate the effectiveness of the method.

基于直觉支持度的对偶犹豫模糊粗糙集模型

支持直觉模糊集多属性决策虽考虑了备选方案的固有属性值评价,也关注如经济能力等决策方的自身支持程度,有效避免了多属性决策中模糊元被均值化的情形,然而面向解决更复杂的现实决策问题时仍显不足。论文将支持度扩展为直觉模糊形式表示,为此提出了直觉支持度对偶犹豫模糊集模型,给出其定义和得分函数。后将粗糙集引入到直觉支持度对偶犹豫模糊环境,构造直觉支持度的对偶犹豫模糊粗糙集模型,定义集合及其上下近似,后讨论该模型的一些性质,并对上下近似集合进行函数拟合,由得分结果排序进行决策。通过对舰船动力系统供应商选择的实例验证了该模型有效性。

概率对偶犹豫模糊集的距离测度及其在疾病诊断中的应用

概率对偶犹豫模糊集由于能够同时表达随机性与模糊性而被广为关注,而距离测度在模式识别、医疗诊断、多属性决策等诸多可以使用概率对偶犹豫模糊集进行建模的研究领域中起着至关重要的作用。但目前已有的概率对偶犹豫模糊集的距离依然存在一定的缺陷,因此,首先定义了概率对偶犹豫模糊元隶属度和非隶属度的上界、下界、均值、标准差与犹豫度,从不同侧面来反映其隶属度与非隶属度的取值信息;其次,基于以上所定义的5个指标提出了两个概率对偶犹豫模糊元之间的标准汉明距离、标准欧氏距离、标准广义距离及其加权形式,并且证明了所提出的新的概率对偶犹豫模糊距离及其加权形式均满足三角不等式;同时我们还研究了两个概率犹豫模糊集之间的标准汉明距离、标准欧氏距离、标准广义距离及其加权形式。最后,通过一个医疗诊断的例子说明提出的距离测度的有效性与实用性。

基于DOWA算子的模糊决策环境下绿色供应商选择方法

针对模糊环境下的绿色供应商选择问题,利用DOWA算子提出了一种属性值为区间对偶犹豫模糊不确定语言变量的多属性决策方法.给出了区间对偶犹豫模糊不确定语言变量的运算法则及排序方法,定义了依赖型区间对偶犹豫模糊不确定语言有序加权平均算子的概念并探讨其相关性质.该算子的特点是对不正确的或者有偏差的评价值赋予较小的权重,而对与靠近均值的评价值赋予更多的权重,从而削弱不公平性对评价结果的影响.利用该算子构建犹豫模糊环境下的多属性决策模型,并将其应用于绿色供应商选择问题中,验证该方法的可行性和有效性.

Prioritizing real estate enterprises based on credit risk assessment:an integrated multi‑criteria group decision support framework

Credit risk assessment involves conducting a fair review and evaluation of an assessed subject’s solvency and creditworthiness.In the context of real estate enterprises,credit risk assessment provides a basis for banks and other financial institutions to choose suitable investment objects.Additionally,it encourages real estate enterprises to abide by market norms and provide reliable information for the standardized management of the real estate industry.However,Chinese real estate companies are hesitant to disclose their actual operating data due to privacy concerns,making subjective evalu-ation approaches inevitable,occupying important roles in accomplishing Chinese real estate enterprise credit risk assessment tasks.To improve the normative and reliability of credit risk assessment for Chinese real estate enterprises,this study proposes an integrated multi-criteria group decision-making approach.First,a credit risk assessment index for Chinese real estate enterprises is established.Then,the proposed framework combines proportional hesitant fuzzy linguistic term sets and preference ranking organization method for enrichment evaluation II methods.This approach is suitable for processing large amounts of data with high uncertainty,which is often the case in credit risk assessment tasks of Chinese real estate enterprises involving massive subjec-tive evaluation information.Finally,the proposed model is validated through a case study accompanied by sensitivity and comparative analyses to verify its rationality and feasibility.This study contributes to the research on credit assessment for Chinese real estate enterprises and provides a revised paradigm for real estate enterprise credit risk assessment.