数集

Based on these operational laws, some aggregation operators, including pure interval-valued intuitionistic fuzzy weighted arithmetric averaging operator and pure interval-valued intuitionistic fuzzy ordered weighted averaging operator, are proposed.

论文摘要：对纯区间直觉模糊信息的集结算子进行了进一步研究，引入了区间直觉模糊数的一些运算法则、区间直觉模糊数的得分函数和精确函数，并基于这些运算法则，提出了一些新算子：纯区间直觉模糊数加权算术平均算子和纯区间直觉模糊数有序加权平均算子。

Regular Fractal Dimension Calculation is discussed by using Koch Curve and Cantor Ternary Set.Additivity of regular fractal dimension is discussed by continuation of Koch Curve with line and Cantor Ternary Set in vertical direction.CircumferenceArea,Variation,Grid and Radius methods of calculation statistical fractal dimension are introduced.

本文以科赫曲线与康托尔三分点集为例，讨论了有规分形维数的计算；以科赫曲线在垂直方向的两种拓展为例，讨论了有规分形维数的加和性；以周长—面积法、变量法、网络法与半径法为例，介绍了无规分形维数的计算方法。

On the fuzzy number valued mapping F:〓→〓, we put forward the definitions ofdirectional derivative, differential, gradient and subdifferential, and with the "cut method" byusing respectively the directional derivative and differential of two crisp functions that aredetermined by F, characterize the directional derivative and differential of F.

对于模糊映射F：〓→〓，提出了方向导数，微分，梯度及次微分的概念，并通过取截集，用由F所完全确定的通常函数的方向导数和微分分别刻划F的方向导数和微分。

The conceptions of the superiority, inferiority and equipollence position degrees of the interval grey number were defined, and it was proved that the sum of three position degrees for a certain interval grey number related to another grey number is 1, and that the relation set of the position degrees is a whole order set of the interval grey numbers.

运用灰色系统思想和系统工程的理论，揭示了人们在灰信息条件下的博弈心理与博弈决策规则；提出了区间灰数的优势、均势和劣势的概念；证明了与某一区间灰数相对的另一区间的各种灰数势之和为1，且灰数势大小关系的集合是一个全序集。

Consequently, a series of important topological indices such as σ-index(Merrifield-Simmons index), Clar number, the number of Kukule structures, and the first Herndon number are obtained.

给出了他们对应的独立集多项式和Clar覆盖多项式的简单显式表示，进而从中获得了一系列重要的拓扑指标：σ-指标(Merrifield-Simmons指标)，Clar数，Kekule结构数和第一Herndon数。

Course contents include the analysis of variance and covariance, multivariate analysis of variance and covariance, principle component, factor analysis, cluster analysis, discriminant analysis, canonical correlation analysis, multidimensional scaling, discrete choice model, and LISREL.

其主要内容包括变异数与共变异数分析、多变量变异数分析、主成份分析、因素分析、集群分析、区别分析、规则相关分析、多元尺度法、二元质量选择模型、及 LISREL 模型。

In chapter 6, we study the dimension of a code associated with a difference set and we also study how to construct Ramanujan graph by using difference sets, we obtain:(1) let q≡1 (mod 4) be a prime power, p be a prime such that p｜〓, then the p-rank of the quadratic residue partial difference set in the finite field GF is 〓.

在第六章中，我们研究差集对应的码的维数及用差集构造Ramanuian图，得到了：（1）设q≡1（mod 4）是素数幂，素数p｜〓，则GF中的二次剩余部分差集的p-秩是〓。

In recent years, set-valued optimization make much progress. In Chapter 5, based on Clarke tangent cone, we establish epiderivative of a class of set-valued maps and its properties. And furthermore, sufficiency optimization conditions of set-valued optimization are also obtained.

在第5章中，针对近几年发展起来的集值优化，基于Clarke切锥利用Epigraph建立了一类集值映射的Epi-导数并讨论它的一些性质，同时给出集值优化的充分的最优性条件。

The relationships between sub- and super-derivatives and Penot diferentials are dicussed as well.4. In recent years, set-valued optimization make much progress. In Chapter 5, based on Clarke tangent cone, we establish epiderivative of a class of set-valued maps and its properties.

在第5章中，针对近几年发展起来的集值优化，基于Clarke切锥利用Epigraph建立了一类集值映射的Epi-导数并讨论它的一些性质，同时给出集值优化的充分的最优性条件。

In this article, the author systematically summarizes current research and tendency of fuzzy rough set theory.

模糊粗糙集理论是解决数据集维数问题的有效工具，但基于模糊粗糙集的降维算法还不多。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。