区间值模糊集贴近度的构造及应用研究

贴近度是区间值模糊集接近程度的度量,是区间值模糊集常用的一种信息测度.针对区间值模糊集贴近度的构造进行研究,给出4种利用模糊集贴近度构造区间值模糊集贴近度的方法,并分析其性质.同时,利用所提出的构造方法,构建10种区间值模糊集贴近度的计算公式,并探讨区间值模糊集贴近度在模式识别、医疗诊断等领域的应用,并藉此验证构造的区间值模糊集贴近度公式的有效性.     

模糊集贴近度的一般表示形式

根据模糊集贴近度理论,研究了模糊集贴近度的各种一般表示形式,推广了常见的各种贴近度表示形式.     

基于区间数度量的区间值模糊集合的贴近度和模糊度的关系

给出了基于区间数度量的区间值模糊集合的贴近度和模糊度的概念,详细研究了区间值模糊集合的贴近度和模糊度之间的关系,并基于公理化定义,证明了它们二者之间的相互转化关系,最后,给出了若干公式来计算区间值模糊集合的贴近度和模糊度。     

直觉模糊集的单调贴近度及其与熵、包含度的关系

为了比较直觉模糊集贴近度之间的大小,定义并研究直觉模糊集的单调贴近度,探讨其性质,分析其与熵及包含度的关系,进而给出利用熵及包含度构造单调贴近度以及利用单调贴近度构造熵及包含度的方法.     

基于Hausdroff距离和L_p度量的直觉模糊集合贴近度的注记

针对Hung和Yang[3-4]给出的直觉模糊集合贴近度,本文指出并修正了一些直觉模糊集合贴近度的错误性质,并给出另外两个计算公式,这将有利于对直觉模糊集合的进一步研究.     

关于区间数贴近度的一般表示形式的研究

利用模糊集的贴近度理论,讨论了有关区间数贴近度的一般表示形式问题,得到了两种区间数贴近度的一般表示形式;并举例说明了根据区间数贴近度的一般表示形式可以构造多种贴近度公式.     

关于模糊数贴近度问题的研究

利用模糊集和区间数的贴近度理论,讨论了模糊数的贴近度问题.通过区间数与模糊数之间的关系,根据区间数贴近度的一般表示形式,给出了构造一些模糊数贴近度的具体计算公式的方法;并通过实例说明了所得到的贴近度公式的有效性和实用性,解决了常用贴近度公式所不能解决的问题.     

基于结构元理论的模糊数的贴近度

现有的计算贴近度的方法,都是建立在模糊集合的隶属函数基础之上的.在很多情况下,当隶属函数很难解析表达时,这时就很难用这些方法计算贴近度.为此,在结构元理论的基础上,提出并构造了模糊数的贴近度(称之为元贴近度).当隶属函数很难解析表达时,用其他方法无法得到的贴近度,此时,用元贴近度的方法往往可以得到,并且计算非常简捷.最后,通过一个模式识别例子,表明该方法的有效性.     

直觉模糊集信息系统属性约简算法

针对信息系统属性值是直觉模糊集的情况提出一种新的属性约简算法:首先定义各个属性值之间贴近度函数,计算出各个属性值的贴近度矩阵,定义了直觉模糊集信息系统的可区分矩阵,给出了其约简的判定定理,利用模糊聚类中的平方法求出其可区分矩阵的传递闭包,将其转化为等价矩阵,给定一个主观水平对其进行模糊聚类,将其转化为具有等价关系的信息系统并且进行约简,从而得到直觉模糊集信息系统的核心属性。给出了该算法的复杂度。最后通过一个算例表明这种方法的有效性和合理性。     

模糊粗糙集及粗糙模糊集的贴近度及其应用

本文研究了模糊粗糙集（FR集）及粗糙模糊集（RF集）的贴近度，是权衡两个FR集，两个RF集彼此糙近程度的一种标尺，进而研究了FR集，RF集的内积，外积，引进了FR集，RF集的格贴近度，并在此基础上提出一种新的属性约简的方法。     

基于模糊模式识别的动态联盟伙伴选择模型

在基于模糊模式识别的伙伴选择方法中,将TOPS IS方法借助于一个多属性决策问题的“理想解”和“负理想解”去排序的思想应用到其伙伴选择过程中,根据贴近度的公理化定义对TOPS IS方法作以修改,构造出“相对”贴近度,以此折衷地衡量动态联盟合作伙伴的优劣。避免了传统模糊模式识别单纯利用“绝对”贴近度所造成的结果均一化、可比性差的现象,从一定程度上减少了因贴近度选用的不同而造成的结果差异。从某种意义上来说,该种方法可以作为TOPS IS方法的拓展,是本文具有新意之处。     

The Dynamics of Closeness and Betweenness

Although both betweenness and closeness centrality are claimed to be important for the effectiveness of someone's network position, it has not been comprehensively studied which networks emerge if actors strive to optimize their centrality in the network in terms of betweenness and closeness. We study each of these centrality measures separately, but we also analyze what happens if actors value betweenness and closeness simultaneously. Network dynamics differ considerably in a scenario with either betweenness or closeness incentives compared with a scenario in which closeness and betweenness incentives are combined. There are not only more stable networks if actors’ betweenness and closeness are combined, but also these stable networks are less stylized.     

基于区间数贴近度的水环境质量评价模型研究

针对基于区间数的水环境质量评价问题,提出了基于区间数贴近度的水质评价模型.首先讨论了区间数贴近度的定义,给出了求贴近度的具体公式.然后给出了水质评价模型的一般步骤,并通过实例验证了模型计算方法简单且能较完整地反映水环境质量污染程度,是一种合理实用的评价方法.同时分析了评价指标因子的赋权法,给出了一种基于等权赋权法和指数赋权法的几何平均组合赋权法.     

具有多类评价信息的旅游景区游客满意度评价方法

针对多类型评价信息的旅游景区游客满意度评价问题,提出一种基于相对贴近度的评价方法。首先,建立旅游景区旅客满意度评价指标体系;其次,采用实数、区间数、三角模糊数、直觉模糊语言变量和直觉模糊数5种不同类型表示旅游进去的评价信息,提出各个旅游景区关于正理想解的相对贴近度计算方法;据此确定旅游景区满意度排序,并具体给出其评价步骤;最后,通过实例说明该方法的有效性和合理性。     

Bayes估计的进一步研究及其Pitman最优性

对线性模型参数,讨论了Bayes估计的Pitman最优性,将已有结果进行了改进,去掉了附加条件,证明了在Pitman准则下,Bayes估计一致优于最小二乘估计(LSE),在此基础上,提出了一种基于先验信息的方差分量估计,通过和基于LSE的方差分量估计作比较,证明了新估计是无偏估计且有更小的均方误差．最后,证明了在Pitman准则下生长曲线模型参数的Bayes估计优于最佳线性无偏估计．     

The topological defense in SIS epidemic models

The spreading of dangerous malware or faults in inter-dependent networks of electronics devices has raised deep concern, because from the ICT networks infections may propagate to other Critical Infrastructures producing the well-known domino or cascading effect. Researchers are attempting to develop a high level analysis of malware propagation discarding software details, in order to generalize to the maximum extent the defensive strategies. For example, it has been suggested that the maximum eigenvalue of the network adjacency matrix could act as a threshold for the malware’s spreading. This leads naturally to use the spectral graph theory to identify the most critical and influential nodes in technological networks. Many well-known graph parameters have been studied in the past years to accomplish the task. In this work, we test our AV11 algorithm showing that outperforms degree, closeness, betweenness centrality and the dynamical importance.     

Analysis of complex network performance and heuristic node removal strategies

Removing important nodes from complex networks is a great challenge in fighting against criminal organizations and preventing disease outbreaks. Six network performance metrics, including four new metrics, are applied to quantify networks’ diffusion speed, diffusion scale, homogeneity, and diameter. In order to efficiently identify nodes whose removal maximally destroys a network, i.e., minimizes network performance, ten structured heuristic node removal strategies are designed using different node centrality metrics including degree, betweenness, reciprocal closeness, complement-derived closeness, and eigenvector centrality. These strategies are applied to remove nodes from the September 11, 2001 hijackers’ network, and their performance are compared to that of a random strategy, which removes randomly selected nodes, and the locally optimal solution (LOS), which removes nodes to minimize network performance at each step. The computational complexity of the 11 strategies and LOS is also analyzed. Results show that the node removal strategies using degree and betweenness centralities are more efficient than other strategies.     

Metrics of algebraic closures in pattern recognition problems with two nonoverlapping classes

It is shown that, in the pattern recognition problem with two nonoverlapping classes, the matrices of estimates of the object closeness are described by a metric. The transition to the algebraic closure of the model of recognizing operators of finite degree corresponds to the application of a special transformation of this metric. It is proved that the minimal degree correct algorithm can be found as a polynomial of a special form. A simple criterion for testing classification implementations is obtained.