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.

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.

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.

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.

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.

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。

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.

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.

Lanchester equation for cognitive domain using hesitant fuzzy linguistic terms sets

Intelligent wars can take place not only in the physical domain and information domain but also in the cognitive domain.The cognitive domain will become the key domain to win in the future intelligent war.A Lanchester equation considering cognitive domain is proposed to fit the development tendency intelligent wars in this paper.One party is considered to obtain the exponential enhancement advantage on combat forces in combat if it can gain an advantage in the cognitive domain over the other party according to the systemic advantage function.The operational effectiveness of the cognitive domain in war is considered to consist of a series of indicators.Hesitant fuzzy sets and linguistic term sets are powerful tools when evaluating indicators,hence the indicators are scored by experts using hesitant fuzzy linguistic terms sets here.A unique hesitant fuzzy hybrid arithmetical averaging operator is used to aggregate the evaluation.

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。

一种犹豫模糊集多属性群决策模型及应用

针对犹豫模糊集多属性群决策问题,从点坐标的角度出发设置了一类决策算法,更改了犹豫模糊集的表示方法,在此情形下建立了判断2个犹豫模糊元的大小比较规则与测度2个犹豫模糊元的距离模型,分别建立了计算决策专家客观权重、综合权重和属性的个体权重、整体权重以及综合权重的计算方法。在不同的决策专家权重类别与属性权重类别下,利用Maclaurin对称平均算子对犹豫模糊元进行集结以获取各方案的综合属性值进行排序。数值算例分析表明,利用点坐标建立的决策算法能够达到有效排序方案目的,同时,根据不同的决策专家权重类别与属性权重类别建立的9种决策模型得出的方案排序结果差异明显,说明决策专家权重类别与属性权重类别对决策结果的影响不容忽视,在具体的犹豫模糊集多属性群决策问题中,决策者应根据实际问题需要选择适当的决策模型,以更好地满足决策需求。

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.

改进二维云模型的信息工程监理风险评估

针对传统信息工程监理风险评估具有随机性与模糊性,提出了改进二维云模型的风险评估模型。通过三角模糊层次分析理论确定各风险因素权重,以可能性和严重度为基础变量,构建基于二维云模型的风险云图,在加权有序几何平均算子(order weighted geometric averaging operator,OWGA)的基础上引入情境参数,根据决策者的风险偏好优化各准则层风险云与云标尺的贴近度排序。经过实例仿真,表明所提模型可以在融合专家智慧的同时,避免定性云转换为定量值的损失,将风险以蕴含随机性和模糊性的形式可视化,经改进贴近度确定风险等级,验证了其有效性及优越性。

改进直觉模糊集TOPSIS在防波堤运营期健康状态评价中的应用

为了准确评价防波堤运营期健康状态的等级,建立了基于改进直觉模糊集逼近理想解排序法(Technique for Order Preference by Similarity to Ideal Solution,TOPSIS)的防波堤健康状态评价模型。首先,通过最小熵原理对多种组合权重方法进行最优化处理,以改进直觉模糊集TOPSIS法。其次,以安全性、适用性、耐久性3个维度建立防波堤运营期健康状态评价指标体系,该指标体系采用3个定性指标和8个定量指标进行表征。最后,将改进直觉模糊集TOPSIS模型应用到渤海基地港池护岸防波堤运营期健康状态评价中,并与改进前模型计算结果、实际情况进行对比分析。结果表明,改进模型计算结果与实际情况比较一致,优于改进前评价结果,为防波堤运营期健康状态评价提供了一种新的途径。

混合信息融合策略下共享电单车绿色回收供应商选择方法

共享电单车具有的速度快、舒适度高等特点使其拥有大量用户,运营商以过度投放策略来抢占市场先机进而引发了电单车故障率高、停放难且不规范等现实问题,增大了回收管理的难度。为此,研究了一种共享电单车绿色回收供应商选择方法,为回收管理提供决策支撑。首先,分析了共享电单车的回收需求特征,构建供应商评价指标体系,并引入区间直觉模糊集提出混合评价信息统一量化方法;其次,为集结群体评价信息,提出内嵌双参数的连续区间直觉模糊有序加权平均算子,并以群体一致性为目标构建了参数求解模型;然后,以所提算子为基础,提出用于解决回收供应商选择问题的群体决策方法;最后,通过共享电单车回收案例分析验证了所提方法的适用性与有效性。

基于改进SLIM方法的管制移交人误概率预测

基于模糊有序加权平均算子(Fuzzy Ordered Weighted Averaging Operator,FOWA)对成功似然指数法(Success Likelihood Index Methodology,SLIM)进行了改进,实现了对管制移交人误概率实施定量评估的目的。相比SLIM基本方法,改进方法可使评估过程更符合人的模糊判断特性,还能显著提升评估效率,在数据处理过程中及时过滤不良的判断信息。通过实际应用中的对比分析可知,虽然两种方法均能得出管制移交人误概率,但改进SLIM方法对专家知识的挖掘更充分。使用Delphi法对管制移交过程中的人误行为触发概率可能性进行排序,排序结果与改进SLIM方法一致度更高,由此验证了改进SLIM方法的优势与可行性。

T球面概率犹豫模糊集及在绿色创业企业绩效评估中的应用

基于T-球面模糊集(T-Spherical Fuzzy Sets,T-SFSs)和概率犹豫模糊集(Probabilistic Hesitant Fuzzy Sets,PHFSs)的性质,首先融合两者优点提出T-球面概率犹豫模糊集(T-Spherical Probabilistic Hesitant Fuzzy Sets,T-SPHFSs)概念,其能更准确地表达数据的模糊性和不确定性;然后,给出T-SPHFSs的运算法则和性质,提出T-球面概率犹豫模糊加权平均(T-Spherical Probabilistic Hesitant Fuzzy Weighted Averaging,T-SPHFWA)算子和T-球面概率犹豫模糊加权几何(T-Spherical Probabilistic Hesitant Fuzzy Weighted Geometric,T-SPHFWG)算子,并研究它们的幂等性、置换不变性、有界性和单调性等性质;最后,针对决策信息为T-球面概率犹豫模糊数的多属性决策问题,基于T-SPHFWA算子和T-SPHFWG算子构建多属性决策模型,通过绿色创业企业绩效评估算例证明决策方法的有效性与可行性。