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.

Approach to obtaining weights of uncertain ordered weighted geometric averaging operator

The ordered weighted geometric averaging（OWGA） operator is extended to accommodate uncertain conditions where all input arguments take the forms of interval numbers. First, a possibility degree formula for the comparison between interval numbers is introduced. It is proved that the introduced formula is equivalent to the existing formulae, and also some desired properties of the possibility degree is presented. Secondly, the uncertain OWGA operator is investigated in which the associated weighting parameters cannot be specified, but value ranges can be obtained and the associated aggregated values of an uncertain OWGA operator are known. A linear objective-programming model is established; by solving this model, the associated weights vector of an uncertain OWGA operator can be determined, and also the estimated aggregated values of the alternatives can be obtained. Then the alternatives can be ranked by the comparison of the estimated aggregated values using the possibility degree formula. Finally, a numerical example is given to show the feasibility and effectiveness 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.

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.

基于博弈论组合赋权-云模型的消防员训练损伤风险评估

为降低消防员训练损伤发生率,从个人因素、环境因素和组织管理因素3个方面,提出包含19个指标的消防员训练损伤风险评估指标体系;采用Bonferroni有序加权平均算子(BON-OWA算子)修正层次分析法(AHP)的误差,获得各指标的主观权重;引用基于指标相关性的权重确定法(CRITIC)确定各指标的客观权重;基于博弈论组合赋权法确定各指标的组合权重;引入云模型理论,建立消防员训练损伤风险评估模型,并以河南省某消防救援大队消防员的训练为例,验证该模型的科学性。结果表明:训练装备的战技性能状况指标对消防员的训练损伤风险等级影响最大;该风险评估模型通过数据处理,可以确定消防员训练损伤风险等级;案例中,消防员在5种不同情景下的训练损伤风险等级均为一般风险,这与模糊综合评价法所得结果一致。

TFOWA算子及其在决策中的应用

研究了属性权重信息完全未知、属性值以梯形模糊数形式给出的多属性决策问题,给出了梯形模糊数决策矩阵的规范化公式.把有序加权平均(OWA)算子推广到所给定的数据信息均为梯形模糊数形式的不确定环境中,提出了一种梯形模糊有序加权平均(TFOWA)算子,给出了其在应用过程中的具体步骤,并提出了一种相应的集结决策信息的方法.TFOWA算子的特点是充分利用梯形模糊数的不确定性,因而更能反映客观事物的复杂性及人类思维的模糊性,从而使得决策更符合实际情况.最后通过算例说明了方法的可行性和有效性.

I-FIFOWA算子及其在群决策中的应用

对模糊数直觉模糊信息的集结算子进行了进一步研究,引入了模糊数直觉模糊的一些运算法则、模糊数直觉模糊的得分函数,并基于这些运算法则,提出了一些新算子:模糊数直觉模糊加权平均(FIFWA)算子、模糊数直觉模糊有序加权平均(FIFOWA)算子和诱导的模糊数直觉模糊有序加权平均(I-FIFOWA)算子,然后分析了它们的性质。针对属性权重和专家权重为实数,属性取值为模糊数直觉模糊数的多属性群决策问题,给出了一种基于FIFWA算子和I-FIFOWA算子的模糊数直觉模糊多属性群决策方法。最后,进行了实例分析,说明了该方法的实用性和有效性。

WSF:基于FOWA的Web服务选择算法

为了解决语言型数据无法用于计算的问题,提出了一种基于FOWA的Web服务选择算法.该算法分为两个部分:WSF-DF(defuzzification algorithm for WSF)基于多个用户对于Web服务的语言型评价,进行服务选择;WSF-Credibility(credi-bility test for WSF)用来查出可能存在的用户恶意评价并排除,从而提高Web服务选择结果的可信性.仿真结果表明,相比于其他Web服务选择算法,WSF算法考虑到了多个用户的评价意见,可以避免少数用户恶意评价带来的干扰,服务选择结果符合用户的真实意愿.

基于三维空间的新型配电网关键技术时空适应性评估

在新型电力系统发展的背景下,针对配电网规划建设和配电网关键技术在实际应用时与所处时空的适应能力、应用缺陷难定量化等问题,分析新型配电网关键技术的建设条件,提出一种基于电网满足度、时空资源度、成效改善度的三维立体空间的技术时空适应性评估模型.采用连续区间有序加权平均算子对层次分析法主观赋权进行改进,引入标准间冲突性相关性法构建的主客观组合赋权方法,解决了单一赋权法具有偏向性的问题.利用模糊综合评价法确定各指标隶属度,进而得到新型配电网关键技术评价等级.算例结果表明,所提方法能够量化配电网关键技术与所处时空的契合程度和双向辨识关键技术对于不同时空的适应性以及不同时空对于技术应用的满足度,揭示配电网关键技术的薄弱环节,有助于提升配电网投资效率与效益,更好地服务经济社会高质量发展.

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IOWA算子的空气质量组合预测

对空气质量指数进行预测,反映数据波动的趋势与规律,提出基于诱导有序加权平均(IOWA)算子的Prophet-EEMD-XGBoost模型。首先利用Prophet算法将数据分解为趋势项、季节项、节假日、误差项;然后集合经验模态分解EEMD将原始数据分为9项IMF以及残余分量。最后,利用XGBoost模型对各分量分别进行预测,预测结果利用MAE、MAPE、RMSE、RMSPE进行评价。结果表明,相较于一些单预测模型与其他组合预测模型,基于IOWA算子的Prophet-EEMD-XGBoost组合预测模型有更好的预测效果。

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。

Some OWA operator weights determination methods with RIM quantifier

Based on the quantifier guided method,an ordered weighted averaging(OWA)weights generating method under given orness level with regular increasing monotone(RIM)quantifiers is proposed.Then the RIM quantifier based OWA weights generating method is modified to make the generated weights be monotonic,which can be used to express the decision maker's consistent preference information.Finally,both of these weights generating methods are extended to their generic forms,so that they can generate the OWA weights for any ordinary elements set with any given aggregated value.

基于ITFOWA算子的多属性决策方法研究

将梯形模糊有序加权平均算子(TFOWA)扩充至诱导的梯形模糊有序加权平均(ITFOWA)算子情形.提出两梯形模糊数接近度概念,用其度量属性本身的重要性程度、并以属性值的接近度作为诱导变量,采用ITFOWA算子进行信息集结,得到一种新的基于诱导梯形模糊有序加权平均算子的多属性决策方法.

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.

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.

改进综合因子法的数控伺服刀架可靠性分配方法

针对可靠性分配过程中影响因素和专家打分的不确定性问题,提出一种将灰色关联理论、模糊集理论和有序加权平均算子结合的基于改进综合因子法的数控伺服刀架可靠性分配方法。综合考虑技术水平、重要度、复杂度、运行环境、维修性、费效比等多种影响因素,将各因素细化并分层,建立分层的综合因子评价模型,并给出评价标准。综合现场试验得到的统计数据,建立子系统的全局指标模型,得到每个子系统的全局指标,以故障率为分配指标将数控刀架系统的总体故障率分配到各子系统,实现数控伺服刀架的可靠性分配,得到的可靠度分配结果为驱动系统2.193×10-5、传动装置1.645×10-5、锁紧松开及定位装置2.547×10-5、刀盘信号装置盘1.345×10-5、密封与紧固装置4.589×10-5和连接线与连接界面4.544×10-5,与数控伺服刀架的工程实际情况相符。