Generalized ordered weighted averaging operators based methods for MADM in intuitionistic fuzzy set setting

Multiattribute decision making（MADM） problems, in which the weights and ratings of alternatives are expressed with intuitionistic fuzzy（IF） sets, are investigated.Firstly, the relative degrees of membership and the relative degrees of non-membership are formulated as IF sets, the weights and values of alternatives on both qualitative and quantitative attributes may be expressed as IF sets in a unified way.Then a MADM method based on generalized ordered weighted averaging operators is proposed.The proposed method is illustrated with a numerical example.

Linear goal programming approach to obtaining the weights of intuitionistic fuzzy ordered weighted averaging operator

The multiple attribute decision making problems are studied, in which the information about attribute weights is partly known and the attribute values take the form of intuitionistic fuzzy numbers. The operational laws of intuitionistic fuzzy numbers are introduced, and the score function and accuracy function are presented to compare the intuitionistic fuzzy numbers. The intuitionistic fuzzy ordered weighted averaging （IFOWA） operator which is an extension of the well-known ordered weighted averaging （OWA） operator is investigated to aggregate the intuitionistic fuzzy information. In order to determine the weights of intuitionistic fuzzy ordered weighted averaging operator, a linear goal programming procedure is proposed for learning the weights from data. Finally, an example is illustrated to verify the effectiveness and practicability of the developed method.

Group Decision-Making Model of Renal Cancer Surgery Options Using Entropy Fuzzy Element Aczel-Alsina Weighted Aggregation Operators under the Environment of Fuzzy Multi-Sets

Since existing selection methods of surgical treatment schemes of renal cancer patients mainly depend on physicians’clinical experience and judgments,the surgical treatment options of renal cancer patients lack their scientifical and reasonable information expression and group decision-making model for renal cancer patients.Fuzzy multi-sets(FMSs)have a number of properties,which make them suitable for expressing the uncertain information of medical diagnoses and treatments in group decision-making(GDM)problems.To choose the most appropriate surgical treatment scheme for a patient with localized renal cell carcinoma(RCC)(T1 stage kidney tumor),this article needs to develop an effective GDM model based on the fuzzy multivalued evaluation information of the renal cancer patients.First,we propose a conversionmethod of transforming FMSs into entropy fuzzy sets(EFSs)based on the mean and Shannon entropy of a fuzzy sequence in FMS to reasonably simplify the information expression and operations of FMSs and define the score function of an entropy fuzzy element(EFE)for ranking EFEs.Second,we present the Aczel-Alsina t-norm and t-conorm operations of EFEs and the EFE Aczel-Alsina weighted arithmetic averaging(EFEAAWAA)and EFE Aczel-Alsina weighted geometric averaging(EFEAAWGA)operators.Third,we develop a multicriteria GDM model of renal cancer surgery options in the setting of FMSs.Finally,the proposed GDM model is applied to two clinical cases of renal cancer patients to choose the best surgical treatment scheme for a renal cancer patient in the setting of FMSs.The selected results of two clinical cases verify the efficiency and rationality of the proposed GDM model in the setting of FMSs.

Pythagorean Fuzzy Einstein Aggregation Operators with Z-Numbers:Application in Complex Decision Aid Systems

The primary goal of this research is to determine the optimal agricultural field selection that would most effectively support manufacturing producers in manufacturing production while accounting for unpredictability and reliability in their decision-making.The PFS is known to address the levels of participation and non-participation.To begin,we introduce the novel concept of a PFZN,which is a hybrid structure of Pythagorean fuzzy sets and the ZN.The PFZN is graded in terms of membership and non-membership,as well as reliability,which provides a strong advice in real-world decision support concerns.The PFZN is a useful tool for dealing with uncertainty in decision-aid problems.The PFZN is a practical way for dealing with such uncertainties in decision-aid problems.The list of aggregation operators:PFZN Einstein weighted averaging and PFZN Einstein weighted geometric,is established under the novel Pythagorean fuzzy ZNs.It is a more precise mathematical instrument for dealing with precision and uncertainty.The core of this research is to develop a numerical algorithmto tackle the uncertainty in real-life problems using PFZNs.To show the applicability and effectiveness of the proposed algorithm,we illustrate the numerical case study related to determining the optimal agricultural field.The main purpose of this work is to describe the extended EDAS approach,then compare the proposed methodology with many other methodologies now in use,and then demonstrate how the suggested methodology may be applied to real-world problems.In addition,the final ranking results that were obtained by the devised techniques weremore efficient and dependable in comparison to the results provided by other methods presented in the literature.

计及SOC自恢复的混合储能平抑风电功率波动控制

混合储能系统能够较好地应对复杂的风电波动,有效地提高电网的稳定性和安全性。在混合储能平抑风电功率波动的典型应用场景下,该文首先提出一种计及荷电状态(SOC)自恢复的混合储能平抑风电功率波动控制方法,在满足风电平抑需求的情况下,通过模型预测控制快速调节储能在平抑功率过程中的荷电状态,提高储能持续稳定运行能力;然后,为提高混合储能系统协调运行能力,设计了加权滑动平均(WMA)-模糊控制策略对超级电容和蓄电池功率进行动态分配;最后,结合实际风电功率数据,通过仿真验证了所提策略能有效平衡储能寿命和平抑风电波动的矛盾,能充分考虑两种储能设备的特性差异并提高功率分配的合理性。

智能电网用电异常诊断和调控策略

为了针对智能电网不同异常用电的原因制定分类调整方法,提出了基于二次根式函数电价调整和计算定界的策略,该策略基于自动过程控制和模糊综合评价进行监控、诊断及分类调整。首先,通过指数加权移动平均值作为自动过程控制的控制变量并确定上下界来监控用电量,建立监控模型;其次,用模糊综合评价法诊断异常用电原因;最后,根据不同原因制定分类调整策略,建立电价需求响应调整模型。算例仿真结果表明,提出的基于二次根式函数电价调整策略在调整频次、残差标准误差、全社会福利和电力公司利润等方面均优于线性函数调整。应用模糊综合评价方法能有效分析异常用电原因,制定分类调整策略能消除异常并获得平稳波动用电量。

Three methods for generating monotonic OWA operator weights with given orness level

Based on the properties of ordered weighted averaging (OWA) operator and regular increasing monotone (RIM) quantifier, three methods for generating monotonic OWA operator weights are proposed. They are geometric OWA operator weights, equidifferent OWA operator weights and the modified RIM quantifier OWA weights. Compared with most of the common OWA methods for generating weights, the methods proposed in this paper are more intuitive and efficient in computation. And as there are more than one solution in most cases, the decision maker can set some initial condition and chooses the appropriate solution in the real decision process, which increases the flexibility of decision making to some extent. All these three OWA methods for generating weights are illustrated by numerical examples.

基于WBS-RBS和PFWA算子的多式联运网络安全风险评估

为了能够评估多式联运网络中的安全风险,提出了一种基于工作分解结构-风险分解结构(WBS-RBS)和勾股模糊加权平均(PFWA)算子的安全风险评估方法。通过专家打分的勾股模糊数(PFLN)替代WBS-RBS的风险矩阵0-1赋值,从全阶段和分阶段两个过程分别对多式联运网络的安全风险排序值进行计算,从而得到安全风险评估结果。最后,以汽车零部件的铁-公-水联运过程为实例进行了验证,从整体上来看,转运区人员的作业不规范行为是整个运输过程中风险最大的因素;从作业的角度来看,转运区管理和安全防护设置管理的风险因素最高,存储区的布局管理则最低;从子风险的角度来看,人员安全意识淡薄和运输过程安全措施不完善导致的风险最高,存储设施引发的风险最低;从整体风险角度来看,5类风险因素按照平均风险值从大到小排序为人员风险、设施设备风险、环境风险、货物自身风险、运输管理风险。

基于新图模糊距离的EDAS决策方法及其应用

研究决策信息为图模糊集的多属性决策问题。首先,针对现有图模糊距离的不足,定义了含参数的弃权度的分配,同时结合一致性概念提出了反映决策者风险偏好的图模糊距离,通过数值算例将新图模糊距离与现有图模糊距离进行比较分析,验证其优越性。其次,针对属性权重,采用博弈论组合赋权法对熵权法确定的客观权重和决策者给出的主观权重进行组合优化。在此基础上,将新图模糊距离拓展到一种离平均方案距离的决策方法(EDAS),并运用新图模糊距离计算各方案与平均方案的正、负距离加权和,进而得到综合得分。最后,通过算例来验证所提决策方法的适用性和有效性。灵敏度与对比分析结果表明:决策者可以依据自身风险偏好调整参数的取值来满足不同的决策需求;所提方法相较于其他现有决策方法更具一般性与灵活性,所得排序结果更加合理。

基于Fuzzy-AHP在子公司安全考核分级中的应用

为了便于集团公司对子公司的安全管理,提升子公司的安全管理水平,对安全管理薄弱的子公司进行有针对性的帮扶,因此对子公司实行安全考核级别的划分。传统安全考核级别的划分通常采用营业额的高低作为划分依据,子公司往往会重视生产而忽视安全隐患,不能反应子公司安全管理的真实水平。因此,本文借助于Fuzzy-AHP的原理和方法,选取子公司的7个共性指标作为分级依据,利用层次分析法确定分级指标的权重,利用模糊数学方法确定3级安全考核级别的分配比例,最后利用加权平均确定每家子公司的安全考核等级。结果表明,4家一级安全考核单位,6家二级安全考核单位,8家三级安全考核单位,说明Fuzzy-AHP运用于子公司的安全考核级别划分符合子公司的实际情况,具有指导意义。

优化模糊综合评价模型在水质评价中的应用

基于熵权法和层次分析法,并采用博弈论,将主客观权重相结合,确定了综合权重,优化了模糊综合评价模型的赋权过程,最后结合加权平均法,构建了水质评价优化模型。通过对案例中的水样进行评价,结果显示:7个采样点当中,Ⅱ类水和Ⅲ类水的采样点有4个,占比57.14%;Ⅳ类水的采样点有3个,占比42.86%。相较于单一熵权法赋权的模糊综合评价模型,优化后的评价模型综合考虑了主客观权重和评价因素对于整体水质影响,合理反映了水质特征,可为类似地区的水质评价工作提供参考。

基于OWA算子的模糊n-cell数排序方法

针对基于模糊n-cell数的多属性排序问题,提出了一种基于有序加权平均算子(OWA算子)的模糊n-cell数排序方法。该方法首先根据样本数据对评估对象的属性构造模糊n-cell数,其次根据均值将属性按照从大到小排列,然后选取合适的权重向量,应用OWA算子进行信息聚合得到综合模糊n-cell数,接着根据各分量均值得到排序结果。最后,将该方法运用到实例中,并与传统的均值方法进行了比较。结果表明该方法不仅灵活有效,可根据具体情况选择不同的OWA权重来消除部分不合理的情况,使结果更有说服力,还弥补了传统均值方法的不足。

基于对称差测度的Fuzzy度量

以测度空间(X,■,μ)为基础,以客观所需及Fuzzy集的分解定理为背景,从集合的对称差测度出发,建立了几种衡量X上的Fuzzy集之间的距离,并讨论了它们的基本性质。

基于WBS-RBS和IFWA算子的中欧班列多式联运安全风险评估

为保障中欧班列多式联运安全,首先选取工作分解结构-风险分解结构(WBS-RBS)法识别中欧班列多式联运全过程中的风险;其次,基于直觉模糊语言集改进传统WBS-RBS中的风险矩阵赋值算法,建立WBS-RBS直觉模糊风险矩阵;然后基于得分函数,结合投影法,融合专家信息,选取直觉模糊加权算术平均(IFWA)算子计算各类风险大小,并对其进行排序;最后,选取“郑州-阿拉山口-阿克套港-巴库港-斯图加特”线路进行案例分析,并从国际沟通、作业管理、技术操作、信息衔接等方面提出保障中欧班列多式联运安全运输的策略与建议。结果表明:阿拉山口口岸站进行票务交接时信息沟通程度、清关作业管理水平及斯图加特站进行基础作业时的社会秩序等是运输环节中较为明显的风险因素。

Entropy-based procedures for intuitionistic fuzzy multiple attribute decision making

The class of multiple attribute decision making （MADM） problems is studied, where the attribute values are intuitionistic fuzzy numbers, and the information about attribute weights is completely unknown. A score function is first used to calculate the score of each attribute value and a score matrix is constructed, and then it is transformed into a normalized score matrix. Based on the normalized score matrix, an entropy-based procedure is proposed to derive attribute weights. Furthermore, the additive weighted averaging operator is utilized to fuse all the normalized scores into the overall scores of alternatives, by which the ranking of all the given alternatives is obtained. This paper is concluded by extending the above results to interval-valued intuitionistic fuzzy set theory, and an illustrative example is also provided.

Interval-valued intuitionistic fuzzy aggregation operators

The notion of the interval-valued intuitionistic fuzzy set （IVIFS） is a generalization of that of the Atanassov＇s intuitionistic fuzzy set. The fundamental characteristic of IVIFS is that the values of its membership function and non-membership function are intervals rather than exact numbers. There are various averaging operators defined for IVlFSs. These operators are not monotone with respect to the total order of IVIFS, which is undesirable. This paper shows how such averaging operators can be represented by using additive generators of the product triangular norm, which simplifies and extends the existing constructions. Moreover, two new aggregation operators based on the t.ukasiewicz triangular norm are proposed, which are monotone with respect to the total order of IVIFS. Finally, an application of the interval-valued intuitionistic fuzzy weighted averaging operator is given to multiple criteria decision making.

MABAC method for multiple attribute group decision making under q-rung orthopair fuzzy environment

As the generalization of intuitionistic fuzzy set(IFS) and Pythagorean fuzzy set(PFS),the q-rung orthopair fuzzy set(q-ROFS) has emerged as a more meaningful and effective tool to solve multiple attribute group decision making(MAGDM) problems in management and scientific domains.The MABAC(multi-attributive border approximation area comparison) model,which handles the complex and uncertain decision making issues by computing the distance between each alternative and the bored approximation area(BAA),has been investigated by an increasing number of researchers more recent years.In our article,consider the conventional MABAC model and some fundamental theories of q-rung orthopair fuzzy set(q-ROFS),we shall introduce the q-rung orthopair fuzzy MABAC model to solve MADM problems.at first,we briefly review some basic theories related to q-ROFS and conventional MABAC model.Furthermore,the q-rung orthopair fuzzy MABAC model is built and the decision making steps are described.In the end,An actual MADM application has been given to testify this new model and some comparisons between this novel MABAC modeL and two q-ROFNs aggregation operators are provided to further demonstrate the merits of the q-rung orthopair fuzzy MABAC model.

Consensus intuitionistic fuzzy group decision-making method for aircraft cockpit display and control system evaluation

A novel group decision-making （GDM） method based on intuitionistic fuzzy sets （IFSs） is developed to evaluate the ergonomics of aircraft cockpit display and control system （ACDCS）. The GDM process with four steps is discussed. Firstly, approaches are proposed to transform four types of common judgement representations into a unified expression by the form of the IFS, and the features of unifications are analyzed. Then, the aggregation operator called the IFSs weighted averaging （IFSWA） operator is taken to synthesize decision-makers’ （DMs’） preferences by the form of the IFS. In this operator, the DM’s reliability weights factors are determined based on the distance measure between their preferences. Finally, an improved score function is used to rank alternatives and to get the best one. An illustrative example proves the proposed method is effective to valuate the ergonomics of the ACDCS.

Spherical Linear Diophantine Fuzzy Sets with Modeling Uncertainties in MCDM

The existing concepts of picture fuzzy sets(PFS),spherical fuzzy sets(SFSs),T-spherical fuzzy sets(T-SFSs)and neutrosophic sets(NSs)have numerous applications in decision-making problems,but they have various strict limitations for their satisfaction,dissatisfaction,abstain or refusal grades.To relax these strict constraints,we introduce the concept of spherical linearDiophantine fuzzy sets(SLDFSs)with the inclusion of reference or control parameters.A SLDFSwith parameterizations process is very helpful formodeling uncertainties in themulti-criteria decisionmaking(MCDM)process.SLDFSs can classify a physical systemwith the help of reference parameters.We discuss various real-life applications of SLDFSs towards digital image processing,network systems,vote casting,electrical engineering,medication,and selection of optimal choice.We show some drawbacks of operations of picture fuzzy sets and their corresponding aggregation operators.Some new operations on picture fuzzy sets are also introduced.Some fundamental operations on SLDFSs and different types of score functions of spherical linear Diophantine fuzzy numbers(SLDFNs)are proposed.New aggregation operators named spherical linear Diophantine fuzzy weighted geometric aggregation(SLDFWGA)and spherical linear Diophantine fuzzy weighted average aggregation(SLDFWAA)operators are developed for a robust MCDM approach.An application of the proposed methodology with SLDF information is illustrated.The comparison analysis of the final ranking is also given to demonstrate the validity,feasibility,and efficiency of the proposed MCDM approach.

我国中小商业银行竞争力的FWA评价分析

根据对现实竞争力和潜在竞争力的理解,建立了包括经营规模、经营质量、经营效率、业务结构和成长性等五个一级指标、16个二级指标的中小上市商业银行竞争力评价体系。选取11家上市的中小商业银行,包括部分股份制银行和城市商业银行,通过模糊权重平均方法进行实证研究。结果表明,中信银行、招商银行、民生银行是中小商业银行中处于领先地位的银行,宁波银行、南京银行等城市银行由于地域性的限制,综合竞争力仍不敌股份制银行,但在潜在竞争力上有一定优势。