F集值统计

汪培庄在文[1]中首次提出集值统计的概念,其理论基础是随机集落影理论,本文在文[1]的基础上,把随机集及其落影的概念加以扩充,给出F随机集及其落影的概念,进而提出F集值统计方法,同时,本文还讨论了K·Hirota提出的概率集与F随机集的关系.     

Numerical Characterizations of Covering Rough Sets Based on Evidence Theory

<正>Covering rough sets are improvements of traditional rough sets by considering cover of universe instead of partition.In this paper,we develop several measures based on evidence theory to characterize covering rough sets.First,we present belief and plausibility functions in covering information systems and study their properties.With these measures we characterize lower and upper approximation operators and attribute reductions in covering information systems and decision systems respectively.With these discussions we propose a basic framework of numerical characterizations of covering rough sets.     

Fuzzy Mathematics for Raw Silk Size Control

With photographing and experiments, this paper divides the cocoon layers into three categories according to their colors, establishes three-color membership function based on fuzzy mathematics, constructs fuzzy sets which satisfy the range of size control by using the ordinary set and attached frequency of threecolor cocoons combination, then achieves the ordinary sets of range of size control by choosing λ-cut. Under these ordinary sets, each end does duality relative level, then sets up relative matrix and overall sequence and finds the membership function to judge whether the size control is mormal.     

Interation of quasi-rational mapping

The more general ease of interation of quasi-rational mappings, including their Julia sets and quasi normal sets, is studied and some results corresponding to complex dynamics are obtained.     

基于随机集的复杂境况下多目标测量

在多传感器多目标融合系统中,多传感器所提供的信息常常不同类,难以融合,建立多传感器多目标的随机集观测模型可以解决统一融合问题.基于随机集理论,根据虚警及漏测的情况,给出了目标的信任测度及其全局密度.从单传感器单目标推广到多传感器多目标,建立了实用的多目标随机集测量模型,并根据实例证明了该模型的实用性和有效性.     

线性变换的不变子空间、Jordan标准形及二次型的主轴问题

本文用线性变换的不变子空间处理了 Jordan 标准形与二次型的主轴问题,期望能有利于《线性代数》的教与学.一、线性变换的不变子空间本节及下节中,我们设 S 为复数域 C 上的 n 维线性空间,S 上线性变换的集合记为L(S).定义设 A∈L(S)。S_1是 S 的子空间.称 S_1为 A 的不变子空间.如果对所有的α     

Dirichlet Form of Product of Variational Fractais

Much effort has gone into constructing Dirichlet forms to define Laplacians on self-similar sets.However, the results have only been successful on p. c.f. (post critical finite) fractals. We prove the existence of a Dirichlet form on a class of non- p. c.f. sets that are the product of variational fractals.     

时间序列系统的随机集建模与预测

介绍了随机集理论的基本数学概念.利用覆盖函数估计定义了一个模糊集,在此基础上将统计目标整合到基于规则的系统中.通过建模仿真,对有独立观测值的统计方法进行了很好的估计、预测和控制,提出了一种新的解决时间序列系统辨识的方法.实例结果表明,随机集是系统辨识的一个新的好方法.     

One Direction Rough Law Generation and Its Security Transmission

By using function one direction S-rough sets (function one direction singular rough sets),the concept of one direction rough law is proposed,where one direction rough law is the law pair {w(x)-,w(x)-} composed by w(x)-and w(x)-. If the attribute set {α-,α-} of function one direction S-rough sets changes,then one direction rough law {w(x)-,w(x)-} will change,too. By employing ellipse curves,the concept of one direction rough law security is presented,the security theorem of one direction rough law is proposed and the applications are given. One direction rough law security,which is generated by the intersection and penetration between function one direction S-rough sets and ellipse curves,is a new applied research direction of function S-rough sets.     

Security Steiner's Inequality on Layering Functions

The classical definition of Steiner symmetrizations of functions are defined according to the Steiner symmetrizations of function level sets and the layered representation of functions. In this paper, the definition is not only transformed into Steiner symmetrizations of one-dimensional parabolic functions, but also depends on the Steiner symmetrizations of the level sets of log-concave functions. To this end we prove Steiner’s inequality on layering functions in the space of log-concave functio...     

Fuzzy Sets and Rough Sets: a Comparison through an Extension of Obtulowicz's Category

<正>This paper is a purely mathematical one dealing with a common possible foundation of Fuzzy Set Theory and Rough Set Theory.It begins with a generalization of Obtulowicz's paper,rough sets and Heyting algebra valued sets,published in Bull.Polish Acad Sc.(math),198.In this paper Obtulowicz proposes a special subcategory of     

Hausdorff centered measure of certain linear Cantor sets

In this paper, we study the Hausdorff centered measure of certain linear Cantor sets. We establish the relationship between the Hausdorff centered measure of this set and the maximum centered density of the corresponding self-similar measure. From this relationship, the Hausdorff centered measure of certain sets is obtained. In particular, we consider the linear iterated function system consisting of three maps with the same contraction ratios. Under some technical restrictions, we determine the exact Hausdorff centered measure of its attractor.     

Graphene-immobilized flower-like Ni_3S_2 nanoflakes as a stable binder-free anode material for sodium-ion batteries

A binder-free Ni_3S_2 electrode was prepared directly on a graphene-coated Ni foam(G/Ni) substrate through surface sulfiding of substrate using thiourea as the sulfur source in this work. The Ni_3S_2 showed a flower-like morphology and was uniformly distributed on the G/Ni surface. The flower-like Ni_3S_2 was composed of cross-arrayed nanoflakes with a diameter and a thickness of 1-2 μm and ~50 nm, respectively. The free space in the flowers and the thin feature of Ni_3S_2 buffered the volume changes and relieved mechanical strain during repeated cycling. The intimate contact with the Ni substrate and the fixing effect of graphene maintained the structural stability of the Ni_3S_2 electrode during cycling. The G/Ni-supported Ni_3S_2 maintained a reversible capacity of 250 mAh·g~(-1) after 100 cycles at 50 mAh~(-1), demonstrating the good cycling stability as a result of the unique microstructure of this electrode material.     

A method of combining SE-tree to compute all minimal hitting sets

In model-based diagnosis, the candidate diagnostic results are generally characterized by all minimal hitting sets for the collection of all conflict sets. In this paper, a new method is proposed to judge a hitting set by the number of conflict sets corresponding to components, and the computing procedure is formalized by combining revised SE-tree (set enumeration tree) with closed nodes to generate all minimal hitting sets. Results show that because closed nodes are added into SE-tree, the search efficiency is highly improved. Furthermore, the proposed method is easy to be understood and implemented. Compared with other effective algorithms with completeness in some experimental tests, the diagnosis efficiency of our proposed method is higher, particularly for single- and double-fault diagnosis.     

Improvement and Parallelism of k-Means Clustering Algorithm

The k-means clustering algorithm is one of the most commonly used algorithms for clustering analysis. The traditional k-means algorithm is, however, inefficient while working on large numbers of data sets and improving the algorithm efficiency remains a problem. This paper focuses on the efficiency issues of cluster algorithms. A refined initial cluster centers method is designed to reduce the number of iterative procedures in the algorithm. A parallel k-means algorithm is also studied for the problem of the operation limitation of a single processor machine when given huge data sets. The analytical results demonstrate that these improvements can greatly enhance the efficiency of the k-means algorithm, i.e., allow the grouping of a large number of data sets more accurately and more quickly. The analysis has theoretical and practical importance for work on the improvement and parallelism of cluster algorithms.     

Rough Sets and Three Valued Connectives Extended Abstract

<正>1 Introduction In[5]we investigated the significance of some truth-functional three valued logics of ill-known sets described by pairs of disjoint(or pairs of nested) subsets.In particular,we referred to the case of rough sets showing that if from a mathematical standpoint we obtain sound results,the interpretation with respect to     

基于随机集的可能性测度

利用随机集定义了一种粗糙近似算子，并给出了这种近似算子的性质，当随机集是全序随机集时，这种近似算子与可能性测度之间存在密切的关系。     

Distributed heterogeneous inspecting system and its middleware-based solution

There are many cases when an organization needs to monitor the data and operations of its super-vised departments, especially those departments which are not owned by this organization and are managed by their own information systems. Distributed Heterogeneous Inspecting System (DHIS) is the system an organization uses to monitor its supervised departments by inspecting their information systems. In DHIS, the inspected systems are generally distributed, heterogeneous, and constructed by different companies. DHIS has three key processes-abstracting core data sets and core operation sets, collecting these sets, and inspecting these collected sets. In this paper, we present the concept and mathematical definition of DHIS, a metadata method for solving the interoperability, a security strategy for data transferring, and a middleware-based solution of DHIS. We also describe an example of the inspecting system at WENZHOU custom.     

On σ—colleetionwise normality and collctionwise normality

In we have introduced the classes of quasi—paracompact and strictlyquasi—para compact spaces,each of which contains metacpmpact andsubparacompact spaces.In the same paper,we have also defined theσ—collectionwise normality as follows:a topological space S is σ—colle-ctionwise normal if every discrete collection of closed sets of S admitsa σ—disjoint collection of open sets(?),such that     

Enhanced dielectric properties of polypropylene based composite using Bi2S3 nanorod filler

A novel two-phase composite system using polypropylene(PP) as matrix and semiconductor bismuth sulfide(Bi_2S_3) as filler,was prepared by a simple process.Surfactant KH550 was chosen to modify the interface between inorganic fillers and organic PP matrix.The variations of dielectric properties of the Bi_2S_3/PP composites with the volume fraction of Bi_2S_3,frequency and temperature were discussed.The results reveal a percolative behavior of the composites with the threshold of 0.08.The composite is demo...