Einstein Weighted Geometric Operator for Pythagorean Fuzzy Hypersoft with Its Application in Material Selection

Hypersoft set theory is a most advanced form of soft set theory and an innovative mathematical tool for dealing with unclear complications.Pythagorean fuzzy hypersoft set(PFHSS)is the most influential and capable leeway of the hypersoft set(HSS)and Pythagorean fuzzy soft set(PFSS).It is also a general form of the intuitionistic fuzzy hypersoft set(IFHSS),which provides a better and more perfect assessment of the decision-making(DM)process.The fundamental objective of this work is to enrich the precision of decision-making.A novel mixed aggregation operator called Pythagorean fuzzy hypersoft Einstein weighted geometric(PFHSEWG)based on Einstein’s operational laws has been developed.Some necessary properties,such as idempotency,boundedness,and homogeneity,have been presented for the anticipated PFHSEWG operator.Multi-criteria decision-making(MCDM)plays an active role in dealing with the complications of manufacturing design for material selection.However,conventional methods of MCDM usually produce inconsistent results.Based on the proposed PFHSEWG operator,a robust MCDM procedure for material selection in manufacturing design is planned to address these inconveniences.The expected MCDM method for material selection(MS)of cryogenic storing vessels has been established in the real world.Significantly,the planned model for handling inaccurate data based on PFHSS is more operative and consistent.

WEIGHTED INEQUALITIES FOR THE GEOMETRIC MAXIMAL OPERATOR ON MARTINGALE SPACES

In this article, the authors introduce two operators-geometrical maximal operator Mo and the closely related limiting operator M0^＊, then they give sufficient conditions under which the equality M0=MM0^＊ holds, and characterize the equivalent relations between the weak or strong type weighted inequality and the property of W∞-weight or W∞^＊-weight for the geometrical maximal operator in the case of two-weight condition. What should be mentioned is that the new operator-the geometrical minimal operator is equal to the limitation of the minimal operator sequence, and the results for the minimal operator proved in [12] makes the proof elegant and evident.

Geometric Phase Gate Based on Both Displacement Operator and Squeezed Operators with a Superconducting Circuit Quantum Electrdynamics

We give the brief review on the related definition of the geometric phase independent of specific physical system based on the displacement opreator and the sqeezed operator, then show how the displacement operator and the squeezed operator can induce the general geometric phase. By means of the displacement operator and the squeezed operator concerning the circuit cavity mode state along a closed path in the phase space, we discuss specifically how to implement a two-qubit geometric phase gate in circuit quantum electrodynamics with both single photon interaction and two-photon interaction between the superconducting qubits and the circuit cavity modes. The experimental feasibility is discussed in detail.

Aggregation operators and CRITIC-VIKOR method for confidence complex q-rung orthopair normal fuzzy information and their applications

Supply chain management is an essential part of an organisation's sustainable programme.Understanding the concentration of natural environment,public,and economic influence and feasibility of your suppliers and purchasers is becoming progressively familiar as all industries are moving towards a massive sustainable potential.To handle such sort of developments in supply chain management the involvement of fuzzy settings and their generalisations is playing an important role.Keeping in mind this role,the aim of this study is to analyse the role and involvement of complex q-rung orthopair normal fuzzy(CQRONF)information in supply chain management.The major impact of this theory is to analyse the notion of confidence CQRONF weighted averaging,confidence CQRONF ordered weighted averaging,confidence CQRONF hybrid averaging,confidence CQRONF weighted geometric,confidence CQRONF ordered weighted geometric,confidence CQRONF hybrid geometric operators and try to diagnose various properties and results.Furthermore,with the help of the CRITIC and VIKOR models,we diagnosed the novel theory of the CQRONF-CRITIC-VIKOR model to check the sensitivity analysis of the initiated method.Moreover,in the availability of diagnosed operators,we constructed a multi-attribute decision-making tool for finding a beneficial sustainable supplier to handle complex dilemmas.Finally,the initiated operator's efficiency is proved by comparative analysis.

基于几何矩特征与纹理度量的图像匹配算法

为提高多种几何内容变化下的特征点匹配准确度,引入双边滤波器,设计了几何矩特征耦合纹理度量的图像匹配算法。引入双边滤波器,对图像进行预处理,以去除图像中噪声,接着利用Hessian算子,准确检测图像特征。利用图像灰度信息,计算图像特征圆域内的几何矩,以形成鲁棒性较强的特征向量。通过平均梯度模型,对特征点邻域的纹理特征进行度量,并将其联合欧氏测量结果,对图像特征实施匹配。借助互相关模型,对匹配特征的相关程度进行测量,以检测特征点的匹配正确性,优化特征匹配结果。实验数据表明:较当前特征匹配方法而言,在多种几何内容变化下,所提技术具有更高的匹配准确度与鲁棒性。

服务失效状态为吸收状态及重试率为常数的M^([X])/M/1排队模型的主算子的谱分析

研究服务失效状态为吸收状态及重试率为常数的M^([X])/M/1排队模型的主算子在左半复平面中的谱.当顾客的到达率λ,服务员的服务率ν,顾客的重试率α和服务员的服务完成率b满足一定的条件时,证明了实部为-(λ+ν+b)的所有复数都不是该模型主算子的特征值;当λ,ν, α, b满足一定的条件时,证明了区间(-(λ+ν+b),0)中无穷多个点是该主算子的几何重数为1的特征值.

水力旋流器流场特征和分级分离性能研究综述

水力旋流器利用颗粒-颗粒或颗粒-流体在旋流流场中运动行为差异实现分级分离过程,被广泛地应用于化工、冶金、矿物加工和环保等行业。在实际运行中,由于操作条件不合理或设备结构条件限制,使颗粒分级或固液分离性能无法满足应用需求,本文分析了水力旋流器的流场特征,并总结了影响旋流器分离性能的关键因素。水力旋流器内部呈现复杂的多相流场,颗粒性质、料液性质、进料条件等操作参数和旋流器的几何结构会影响水力旋流器的分离性能,实际应用中可以通过优化运行条件和旋流器的几何结构,提高旋流器的分级分离性能。

Relationships among Three Multiplicities of a Differential Operator’s Eigenvalue

In this paper, the algebraic, geometric and analytic multiplicities of an eigenvalue for linear differential operators are defined and classified. The relationships among three multiplicities of an eigenvalue of the linear differential operator are given, and a fundamental fact that the algebraic, geometric and analytic multiplicities for any eigenvalue of self-adjoint differential operators are equal is proven.

Exact Inverse Operator on Field Equations

Differential equations of electromagnetic and similar physical fields are generally solved via antiderivative Green’s functions involving integration over a region and its boundary. Research on the Kasner metric reveals a variable boundary deemed inappropriate for standard anti-derivatives, suggesting the need for an alternative solution technique. In this work I derive such a solution and prove its existence, based on circulation equations in which the curl of the field is induced by source current density and possibly changes in associated fields. We present an anti-curl operator that is believed novel and we prove that it solves for the field without integration required.

Research on Normal Pythagorean Neutrosophic Set Choquet Integral Operator and Its Application

We first propose the normal Pythagorean neutrosophic set(NPNS)in this paper,which synthesizes the distribution of the incompleteness,indeterminacy,and inconsistency of the Pythagorean neutrosophic set(PNS)and normal fuzzy number.We also define some properties of NPNS.For solving the decision-making problem of the nonstrictly independent and interacting attributes,two kinds of NPNS Choquet integral operators are proposed.First,the NPNS Choquet integral average(NPNSCIA)operator and the NPNS Choquet integral geometric(NPNSCIG)operator are proposed.Then,their calculating formulas are derived,their properties are discussed,and an approach for solving the interacting multi-attribute decision making based on the NPNS is studied.Finally,the two kinds of operators are applied to validate the stability of the new 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.

捣固与打磨复合作业下有砟轨道几何不平顺预测模型

轨道几何不平顺的预测是铁路部门实现由周期修到状态修转化的基础,也是制定养修策略的关键。然而现有预测模型计算比较复杂且鲜有考虑捣固、打磨等复合作业对轨道不平顺的影响。为提升其运算效率与预测精度,考虑了不同作业区段的差异性,以有砟轨道几何不平顺恶化函数、捣固打磨作业下的恢复函数为研究对象,采用数值拟合等方法,形成了各区段特有的恶化矩阵,建立了捣固与打磨复合作业下的有砟轨道几何不平顺预测模型。利用京沪线相关里程数据进行预测分析,结果表明,所建立的模型有效,结果满足现场预测需求。

Region Analysis Approach for Constructing Solutions of Nonlinear Operator Equations(Dedicated to Professor You Zhaoyong for his 60th brithday)

Based on a variety of geometric observations for location of solutions, a general and unified region analysis framework for developing constructive solvability of nonlinear operator equations are proposed. Within this framework, the methods including interval, ball and ellipsoid methods can be studied in a unified way. The ball algorithm, as a typical example, is in particular analysed.

基于方差约束与几何不变特性的图像匹配算法

为解决较多图像匹配算法主要通过测量关键点之间的距离来实现特征匹配,忽略了图像的结构信息,使其存在较多的误匹配的问题,本文设计了方差约束耦合几何不变特性的图像匹配算法。借助于Forstner算子计算像素点的兴趣值,以检测图像的特征;计算图像的梯度信息,获取图像的方向值,并切割图像特征的圆形邻域,从而获取扇形子域;以图像的方向值为基础,通过计算扇形子域中的灰度不变矩,输出对应的特征向量;引入区域方差函数,获取图像的结构信息,将其加入至图像特征的匹配过程,以约束欧式距离的测量结果,实现图像特征匹配;最后利用匹配点间的几何不变特性,对匹配特征去伪求真,优化匹配结果。测试数据表明:相对于已有的匹配技术,在对无变换图像、缩放图像以及旋转图像匹配时,所提算法拥有更高的匹配准确度,分别达到了96.56%、95.38%和93.52%。

概率犹豫模糊集的再定义及其在群决策中的应用

为了更好地解决概率犹豫模糊集多属性群决策问题,构建了一种在不同维度下比较各方案综合属性值大小的决策模型.首先,以二维坐标形式给出概率犹豫模糊集(PHFS)中的隶属度和概率,并在此基础上建立概率犹豫模糊元(PHFE)的二维几何距离模型和二维离差程度系数模型;其次,对PHFS中的隶属度赋予相应的评审专家权重,并用三维坐标刻画隶属度、概率和评审专家权重,以此建立PHFE的三维几何距离模型和三维离差程度系数模型;再次,在二维与三维条件下分别计算2种维度下PHFE的综合值,并利用Maclaurin对称平均算子对以上2种维度下各个PHFE的综合值进行集结并排序;最后,利用实例对在2种维度下建立的算法进行了验证分析.结果显示所建立的算法均可对各方案进行有效地排序,但由于在三维视角下建立的决策模型能够反映评审专家的偏好问题,因此该模型的决策效果相对更好.

三维视域下的概率犹豫模糊集及决策应用

在三维视角下定义了概率犹豫模糊集,并在此基础上设置了解决概率犹豫模糊集多属性群决策问题的两种算法.首先将隶属度、概率、决策专家权重看作以三维点坐标形式进行书写的三维变量,建立了计算概率犹豫模糊元的几何距离函数模型、离差程度函数模型以及概率犹豫模糊数的模糊值模型,然后在考虑概率犹豫模糊元的几何距离与离差程度两个因素的基础上计算属性权重.之后,利用加权的几何距离值与离差程度值计算概率犹豫模糊元的综合值,采用Maclaurin对称平均算子对概率犹豫模糊元的综合值进行集结进而对方案排序;计算概率犹豫模糊数的模糊值,以模糊值的上下确界分别作为区间数的右左端点,用区间数来近似表示概率犹豫模糊元的决策信息,同时,使用区间数的积型贴近度公式对各概率犹豫模糊元进行两两测度,通过比较属性的测度结果来鉴定各方案优劣.最后,将两种算法进行了实例验证,决策结果表明了算法的可行性.

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。

Mg-10Gd-3Y-0.5Zr合金在压缩变形中的滑移系激活规律和塑性变形不均匀性

为了定量和统计地了解高性能铸造Mg-10Gd-3Y-0.5Zr(质量分数,%,GW103)合金在室温单轴压缩变形中滑移系的激活规律和塑性变形不均匀性,对时效状态的该合金进行详细的滑移迹线分析和基于取向差的电子背散射衍射(EBSD)分析。在2%塑性应变后,根据鉴别的滑移迹线的相对比例,激活的滑移模式首先为基面滑移(73.3%),其次是柱面滑移(15.8%),然后是二级角锥面滑移(6.9%),最后是一级角锥面滑移(4%)。尽管大多数激活的滑移系表现出较大的施密特因子(m)值(>0.3),但值得注意的是,一些硬取向(m<0.1)的滑移系也被激活。对于大多数表现出极大几何必需位错(GND)密度的晶界,至少满足以下条件之一:晶界取向差角(GBMA)较大;相邻晶粒间特定滑移模式m_(max)之差较大。晶粒的塑性变形不均匀性(GND密度的大小/分布)与是否能观察到滑移迹线无关。晶内取向分布(GOS)和/或平均GND密度与m_(max)(对于特定滑移模式)没有明显的相关性。

双船联合举升多体协同作业系统横摇稳性评估

基于ADAMS平台,构建特定场景双船联合举升多体协同作业系统虚拟样机,对新型一体化拆解作业双船联合举升过程中待拆除组块横摇稳性进行预测与评估。构建了该系统拓扑模型,使用几何参数描述系统中上部组块横摇运动特征;通过虚拟样机仿真探究了双船不同耦合运动情况时上部组块最危险失稳状态,并分析了上部组块重心至连接点连线垂直距离与水平距离比值对横摇角度的影响规律。结果表明:物理模型试验数据驱动的虚拟样机技术可以有效评估该系统运动特征,与几何拓扑模型得到的上部组块横摇失稳角度理论公式计算结果吻合;双船同相位横摇与反相位垂荡耦合运动时对上部组块横摇稳性影响最大;待拆除上部组块横摇失稳时的极限纵横比可以作为复杂多体系统横摇稳性评估参数,为实际工程方案选择提供参考。

基于遗传-拟牛顿算法的机器人几何参数辨识

为提升工业机器人绝对定位精度,提出了一种遗传-拟牛顿算法来辨识机器人几何运动参数并进行机器人绝对定位误差补偿的联合算法。首先,利用MD-H方法建立机器人运动模型,并通过微分变化原理建立机器人各个关节误差转换到机器人末端误差模型;其次,通过激光跟踪仪测得KR16-2型机器人在指定工作空间50处采样点信息,通过传统遗传算法和遗传-拟牛顿联合算法分别对机器人几何参数进行辨识和比较,并在此算法中提出小区间生成初始种群的方式来提高迭代效率,通过算数交叉和动态变异完成新个体的生成,解决了传统遗传算法出现过早收敛问题。结果表明,此算法对机器人进行补偿后的精度分别提高71.28%和53.23%,直线制孔平均误差是0.45 mm,弧面制孔平均误差是0.42 mm,验证了联合算法的优越性和实用性。