THEOREMS OF INTERVAL FUZZY SET AND ITS OPERATION RULES

Although the concept of interval fuzzy set and its properties have been defined, its three theorems and their effectiveness are not proved. Therefore, the knowledge presentation and its operation rules of interval fuzzy set are studied firstly, and then the cut set of interval fuzzy set is proposed. Moreover, the decomposition theo- rem, the representation theorem and the extension theorem of interval fuzzy set are presented. Finally, examples are given to demonstrate that the classical fuzzy set is a special case of interval fuzzy set and interval fuzzy set is an effective expansion of the classical fuzzy set.

Bombieri's Theorem in Short Intervals

Under the assumption of sixth power large.sieve mean-value of Dirichlet L-function, we improve Bombieri＇s theorem in short intervals by virtue of the large sieve method and Heath-Brown＇s identity.

Interval Based Analysis of Bell’s Theorem

This paper introduces the concept and motivates the use of finite-interval based measures for physically realizable and measurable quantities, which we call -measures. We demonstrate the utility and power of -measures by illustrating their use in an interval-based analysis of a prototypical Bell’s inequality in the measurement of the polarization states of an entangled pair of photons. We show that the use of finite intervals in place of real-numbered values in the Bell inequality leads to reduced violations. We demonstrate that, under some conditions, an interval-based but otherwise classically calculated probability measure can be made to arbitrarily closely approximate its quantal counterpart. More generally, we claim by heuristic arguments and by formal analogy with finite-state machines that -measures can provide a more accurate model of both classical and quantal physical property values than point-like, real numbers—as originally proposed by Tuero Sunaga in 1958.

A Note on Robust Stability Analysis of Fractional Order Interval Systems by Minimum Argument Vertex and Edge Polynomials

By using power mapping(s =v^m),stability analysis of fractional order polynomials was simplified to the stability analysis of expanded degree integer order polynomials in the first Riemann sheet.However,more investigation is needed for revealing properties of power mapping and demonstration of conformity of Hurwitz stability under power mapping of fractional order characteristic polynomials.Contributions of this study have two folds: Firstly,this paper demonstrates conservation of root argument and magnitude relations under power mapping of characteristic polynomials and thus substantiates validity of Hurwitz stability under power mapping of fractional order characteristic polynomials.This also ensures implications of edge theorem for fractional order interval systems.Secondly,in control engineering point of view,numerical robust stability analysis approaches based on the consideration of minimum argument roots of edge and vertex polynomials are presented.For the computer-aided design of fractional order interval control systems,the minimum argument root principle is applied for a finite set of edge and vertex polynomials,which are sampled from parametric uncertainty box.Several illustrative examples are presented to discuss effectiveness of these approaches.

Robust stabilitv of neutral stochastic interval svstems

Although interval systems have received a great deal of attention, so far there is few work on neutral stochastic interval systems (NSIS) . The purpose of this paper is to initiate the study of NSIS. Using R^umikhin-type technique, a sufficient condition of exponential stability on NSIS is given. It is interesting that the NSIS changes into general stochastic interval system when the neutral item disappeared. So the results in this paper generalize some conclusions existed.

Traffic Flow Data Forecasting Based on Interval Type-2 Fuzzy Sets Theory

This paper proposes a long-term forecasting scheme and implementation method based on the interval type-2 fuzzy sets theory for traffic flow data. The type-2 fuzzy sets have advantages in modeling uncertainties because their membership functions are fuzzy. The scheme includes traffic flow data preprocessing module, type-2 fuzzification operation module and long-term traffic flow data forecasting output module, in which the Interval Approach acts as the core algorithm. The central limit theorem is adopted to convert point data of mass traffic flow in some time range into interval data of the same time range (also called confidence interval data) which is being used as the input of interval approach. The confidence interval data retain the uncertainty and randomness of traffic flow, meanwhile reduce the influence of noise from the detection data. The proposed scheme gets not only the traffic flow forecasting result but also can show the possible range of traffic flow variation with high precision using upper and lower limit forecasting result. The effectiveness of the proposed scheme is verified using the actual sample application. © 2014 Chinese Association of Automation.

Saddle Point Optimality Criteria of Interval Valued Non-Linear Programming Problem

The present paper aims to develop the Kuhn-Tucker and Fritz John criteria for saddle point optimality of interval-valued nonlinear programming problem.To achieve the study objective,we have proposed the definition of minimizer and maximizer of an interval-valued non-linear programming problem.Also,we have introduced the interval-valued Fritz-John and Kuhn Tucker saddle point problems.After that,we have established both the necessary and sufficient optimality conditions of an interval-valued non-linear minimization problem.Next,we have shown that both the saddle point conditions(Fritz-John and Kuhn-Tucker)are sufficient without any convexity requirements.Then with the convexity requirements,we have established that these saddle point optimality criteria are the necessary conditions for optimality of an interval-valued non-linear programming with real-valued constraints.Here,all the results are derived with the help of interval order relations.Finally,we illustrate all the results with the help of a numerical example.

电动缸举升伺服机构动力学建模与参数辨识

针对电动缸举升伺服机构动力学参数辨识困难的问题,本文提出了一种限定记忆区间的循环最小二乘辨识法,用于机构全行程内非线性模型、扰动参数的辨识拟合.首先,分析了机构完整模型的非线性参数成因,并提出了相应的简化模型;然后,分析了最小二乘法在平均位姿下的参数近似辨识特性,并提出了限定记忆区间的循环最小二乘法;最后,通过构造输入输出信号和选择辨识伺服环路,使得辨识过程不会超过机构的行程范围.实验结果表明:所提辨识法使得正弦速度和位移响应均方根误差相比最小二乘法分别下降了59.3%和84.2%.所提辨识法可给电动缸举升伺服机构的高精度动力学建模,控制器结合观测器的复合控制策略的实现提供参考.

实对称区间矩阵特征值确界的交错定理及其应用

本文将实对称矩阵特征值的交错定理推广到实对称区间矩阵,给出了实对称区间矩阵特征值确界的交错定理,并应用该定理构造了估计实对称三对角区间矩阵特征值界的算法.文中数值例子表明,本文所给算法与一些现有算法相比在使用范围、计算精度和计算量等方面都具有一定的优越性.

复区间矩阵的Gerschgorin圆盘定理及正则性条件

本文将矩阵特征值的Gerschgorin圆盘定理推广到复区间矩阵,给出复区间矩阵特征值的Gerschgorin圆盘区域,并证明所给复区间矩阵特征值的Gerschgorin圆盘区域包含于已有的复区间矩阵特征值的Gerschgorin方盘区域.最后,应用复区间矩阵特征值的Gerschgorin圆盘定理得到复区间矩阵正则的两个新的充分条件.

基于交易时间衰减的以太坊恶意地址检测方法

提出Trans-TAN模型,用于以太坊上的交易流向图中关联恶意地址的检测任务,模型改进基于Transformer模型的自注意力机制,根据以太坊地址的交易特点并受到牛顿冷却定理的启发,引入随时间交易的时间间隔衰减因素,同时融合以太坊地址间的相似度因素和交易金额因素。基于以上三方面,通过牛顿冷却定理的常微分方程解形式构建的地址关联矩阵,从而改进原有的自注意力矩阵。实验证明,Trans-TAN模型能够有效捕捉以太坊交易流向图过程中恶意节点地址的特征,在测试集中精准率(Precision)、召回率(Recall)和F 1指标优于传统的检测模型。

区间值模糊集合的分解定理

针对区间值模糊集合 ,给出了 8种截集的概念 ,讨论了其有关性质 ,并给出关于区间值模糊集合的分解定理 .

区间值模糊集合的表现定理

针对区间值模糊集合 ,给出了 2类区间值集合套的定义 ,得到了 2个区间值模糊集合的表现定理 .

区间值模糊集合的扩展原理

针对区间值模糊集合的分解定理和表现定理,给出了区间值模糊集合的极大、极小扩展原理,并讨论了其基本性质,进而提出了区间值模糊集合的一般扩展原理的公理化定义,给出了其相应的应用实例.

有界参数结构特征值的上下界定理

与方法近似性的结构特征值包含定理不同，给出参数近似性的结构的特征值上下界定理．在结构刚度矩阵和质量矩阵可以利用结构参数进行非员分解的条件下，通过区间分析，将特征值的上下界分解成两个广义特征值问题进行求解．结果可以看成是胡海昌教授的特征值质量包含定理和刚度包含定理在结构参数近似性特征值问题中的一种推广和应用．

MatriXX在IMRT剂量验证中的应用

目的:通过研究IMRT注量图的空间频率,分析在IMRT剂量验证时,Matrixx的取样间隔(探头间距)能否满足Nyquist采样定理。材料与方法:任意选取10例IMRT,其中鼻咽癌6例,肺癌4例。采用IBA公司的Matrixx进行调强剂量验证,每个电离室的测量值得到一系列离散采样信号。分别分析单个子野和整个测量平面的空间频率。①单个子野:从Pinnacle3 v8.0治疗计划系统中导出单个子野通量图。使用OmniPro I'mRT软件,从子野通量图取出一条离轴比曲线,Matlab对数据进行傅里叶变换处理,得出其最高空间频率fmax,比较分析不同子野宽度及其面积对fmax的影响。②测量平面:在TPS中导出整个测量平面的通量图,在X、Y方向上等间隔取出30条profile曲线,进行傅里叶变换,分析照射野的fmax。③选取1例IMRT,测量其剂量分布,多次移动探测面板,测量分布图,融合测量结果得到新矩阵,比较分析移动前、后Gamma值的变化。结果:①鼻咽癌子野面积2 cm2≤S≤5 cm2时,只有一个射野宽度w=2.9 cm的子野满足采样定理;子野面积5 cm2<S≤10 cm2时,不满足采样定理的射野宽度为:0.8 cm≤w≤2.6 cm。肺癌子野面积S>10 cm2时,其中仅有12%的子野不满足采样定理且子野宽度为:1.6 cm≤w≤2.5 cm。②6例鼻咽癌照射野的fmax符合采样定理比例分别为:80%、83%、76%、80%、80%、83%;4例肺癌的fmax符合采样定理的比例分别为:97%、97%、93%、93%。③移动后Gamma值变小。结论:使用MatriXX剂量验证时,当子野宽度小于2.6 cm时;S<5 cm2时绝大多数子野不满足采样定理,因此静态调强计划的最小子野面积不应过小。鼻咽癌和肺癌照射面的fmax符合采样定理的比例较高,因此MatriXX的7.6 mm的取样间隔适用临床要求。

广义区间动力系统稳定的充分条件

讨论了连续广义区间动力系统在系统矩阵为区间矩阵时的稳定性问题·根据Gershgorin圆盘定理,在假设广义区间动力系统满足系统矩阵A主对角线元素均为负区间数的约束条件下,给出了一个使广义区间动力系统正则、无脉冲膜且稳定的充分条件·针对系统对应的Gershgorin圆盘半径较大的情况做了进一步讨论,使上述充分条件能够适用于更一般的情况·举出实例说明了此方法的正确性,并给出了一个判别区间矩阵为非奇异的充分必要条件·

具p-Laplacian算子时滞微分方程边值问题解的存在唯一性

本文主要研究无穷区间上具有p-Laplacian算子的时滞微分方程边值问题解的存在性和唯一性,利用Schauder不动点定理得到解的存在性,由Banach压缩映射原理证明解的唯一性,并给出一个例子来说明主要结果的应用。

一类半无穷区间上分数阶非线性微分方程边值问题多个正解的存在性

考虑一类具有Caputo导数的分数阶非线性微分方程在半无穷区间上的边值问题,用Schauder不动点定理和Leggett-Williams不动点定理分别得到了该边值问题至少1个正解和至少3个正解的存在性定理.