区间值强模糊图的运算性质

利用经典图和模糊图定义和性质,给出了区间值模糊关系、模糊变换以及区间值强模糊图的定义,相应地定义了区间值强模糊图弱直积、半直积运算,并且证明了其弱直积、半直积运算封闭的性质。     

半直觉模糊图与应用

将对象作顶点集,用直觉模糊数刻画对象间的相关性和不相关性表示成直觉模糊边;建立了半直觉模糊图模型。定义了半直觉模糊图的生成子图、度、路径、相关截图、序关系、最大生成树等概念。给出基于半直觉模糊图的聚类分析算法,分析了算法的复杂度。结合经典实例作了基于半直觉模糊图的聚类分析,结果显示基于半直觉模糊图的聚类分析算法复杂度低于一般直觉模糊聚类算法。高效实用且自动化程度高。     

模糊元图:一种构造模糊知识库的新方法

在分析了现有模糊图论结构的基础上,对模糊超图和模糊有向图进行扩充,提出一种新的图论结构－模糊元图,并将其应用于飞行器邦联诊断中的模糊知识库构造,实际应用表明,基于模糊元图的知识库具有很高的推理效率,并且便于规则的添加和删除。     

Database Skeleton and Its Application to Fuzzy Query Translation

This paper treats the problem of fuzzy query translation using the concept of database skeleton. An imprecise, or fuzzy, query is represented by a query graph, which can be analyzed for translatability with respect to a given database skeleton. The fuzzy query translation problem is formulated as a problem of converting a partially specified query graph into a completely specified query graph. This graph is then translated into a sequence of data manipulation commands, such as commands in relational algebra. Approaches to optimal fuzzy query translation are also described.     

Categorical approach to the construction of fuzzy graph grammars

The categorical approach is proposed to the formalization of fuzzy graph grammars obtained as a result of generalization of sequential graph grammars. This approach takes into consideration the basic types of fuzziness that arise in constructing categories of fuzzy objects and describing transformations of fuzzy graphs generated by fuzzy sets. All the problems of undecidability that are well known for Chomsky grammars are proved to hold true for fuzzy graph grammars. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 130–144, July–August 2006.     

Some remarks on fuzzy graphs

We show that a fuzzy group can be associated with a fuzzy graph in a natural way. Some properties of fuzzy graphs are considered and we introduce the notions of eccentricity and center. Our examples indicate that results from (crisp) graph theory do not always have analogs for fuzzy graphs.     

Node connectivity and arc connectivity of a fuzzy graph

The fuzzy graph approach is more powerful in cluster analysis than the usual graph - theoretic approach due to its ability to handle the strengths of arcs effectively. The concept of node-strength sequence is introduced and is studied in a complete fuzzy graph. Two new connectivity parameters in fuzzy graphs namely, fuzzy node connectivity (κ) and fuzzy arc connectivity (κ^′) are introduced and obtained the fuzzy analogue of Whitney’s theorem. Fuzzy node cut, fuzzy arc cut and fuzzy bond are defined. Fuzzy bond is a special type of a fuzzy bridge. It is proved that at least one of the end nodes of a fuzzy bond is a fuzzy cutnode. It is shown that κ=κ^′ for a fuzzy tree and it is the minimum of the strengths of its strong arcs. The relationships of the new parameters with already existing vertex and edge connectivity parameters are studied and is shown that the value of all these parameters are equal in a compete fuzzy graph. Also a new clustering technique based on fuzzy arc connectivity is introduced.     

基于模糊推理图的故障诊断

根据系统元件之间的连接结构构建故障诊断模糊推理图,通过对模糊推理图进行化简及模糊运算实现对系统的故障诊断。以观测点作为属性准则形成诊断矩阵,在推理图中按照原因-结果对进行连续推理,获得一个模糊诊断的优先级别排列,以减少故障的排查时间。     

区间值模糊图的分解性质

给出了区间值模糊图在笛卡尔积与合成运算下分解的充要条件,证明了区间值模糊图能够在并与联运算下分解。     

Types of arcs in a fuzzy graph

The concept of connectivity plays an important role in both theory and applications of fuzzy graphs. Depending on the strength of an arc, this paper classifies arcs of a fuzzy graph into three types namely α-strong, β-strong and δ-arcs. The advantage of this type of classification is that it helps in understanding the basic structure of a fuzzy graph completely. We analyze the relation between strong paths and strongest paths in a fuzzy graph and obtain characterizations for fuzzy bridges, fuzzy trees and fuzzy cycles using the concept of α-strong, β-strong and δ-arcs. An arc of a fuzzy tree is α-strong if and only if it is an arc of its unique maximum spanning tree. Also we identify different types of arcs in complete fuzzy graphs.     

Novel intuitionistic fuzzy soft multiple-attribute decision-making methods

An intuitionistic fuzzy soft set plays a significant role as a mathematical tool for mathematical modeling, system analysis and decision making. This mathematical tool gives more precision, flexibility and compatibility to the system when compared to systems that are designed using fuzzy graphs and fuzzy soft graphs. In this paper, we use intuitionistic fuzzy soft graphs and possibility intuitionistic fuzzy soft graphs for parameterized representation of a system involving some uncertainty. We present novel multiple-attribute decision-making methods based on an intuitionistic fuzzy soft graph and possibility intuitionistic fuzzy soft graph. We also present our methods as algorithms that are used in our applications.

     

Intuitionistic fuzzy MST clustering algorithms

In this paper, we investigate graph theory-based clustering techniques for Atanassov’s intuitionistic fuzzy sets (A-IFSs) and interval-valued intuitionistic fuzzy sets (IVIFSs). We start by introducing the concepts of graph, minimum spanning tree (MST), A-IFS, and intuitionistic fuzzy distance, and develop two intuitionistic fuzzy MST clustering algorithms ( and ). Then we extend Algorithm II for clustering IVIFSs, and show the effectiveness of our algorithms through some numerical experiments.     

模糊联盟图合作对策tau值

针对模糊环境下有限制的联盟合作情况,利用Choquet积分定义了模糊联盟图合作对策tau值,证明了其存在性和其他重要性质,讨论了其与模糊核心的关系,并给出凸模糊联盟图合作对策tau值的计算公式.最后通过一个算例表明了该tau值的有效性和合理性.研究发现,该tau值是传统tau值的拓展.     

基于随机Petri网的可修系统可用性模糊评价

结合模糊集理论和随机Petri网理论提出了一种可修系统可用性建模与分析的新方法——模糊随机Petri网方法。随机Petri网的状态可达图同构于连续时间马尔可夫链,由可达图可得到系统的稳定状态概率方程组。利用模糊代数理论解该模糊方程组即可得到系统转移概率和各种性能指标的模糊数,通过解模糊可得到系统的可用性指标值。文章进行了实例分析并与已有文献作比较,举例进行分析求解,结果表明该方法是可行的。     

模糊SDG故障诊断方法及其应用

基于SDG的故障诊断方法在使用过程中,由于阈值设定不合理会导致故障的误报或漏报。针对该问题展开研究,提出模糊SDG模型,建立五级SDG模型并引入参数模糊隶属度,提出相应的模糊推理算法。通过将模糊SDG模型及其推理方法应用于某常减压蒸馏装置进行故障诊断实例分析,验证了方法的有效性和可行性。     

犹豫模糊图及其在多属性决策中的应用*

犹豫模糊集作为定量描述犹豫不决的有效工具,通过同时处理不确定性信息中的犹豫性与模糊性,解决犹豫不决背景下的多属性决策问题.文中针对属性值为犹豫模糊数的多属性决策问题,研究基于模糊图论的相关模型与多属性决策方法.首先,提出犹豫模糊图的概念和部分常见运算规则.然后,构建基于犹豫模糊图的一般性多属性决策方法.最后,通过具体算例和对比性分析验证文中方法的合理性.     

A method for the analysis of Gaussian-like clusters

In this paper we are concerned with the analysis of Gaussian-like point clusters in an n-dimensional space. The method described uses the directed fuzzy graph obtained from the points by linking every point to its neighbors and assigning a measure of the local point density to each node of the graph. Next, the tops of the fuzzy graph are found and a subset of them selected as cluster centers. The rest of the points are then classified based on the selected tops.     

基于图割和模糊连接度的交互式舰船红外图像分割方法

针对舰船红外图像分割中的低对比度、边缘模糊和目标灰度不均匀问题, 提出了基于图割和模糊连接度的交互式图像分割方法. 交互方式为矩形笔刷, 选择目标和背景种子点. 分割方法为基于图割的图像分割方法, 引入模糊连接度来计算图割的似然能, 给出了模糊连接度权重的自动确定方法, 提出了基于直方图分解的高斯混合模型(Gaussian mixture model, GMM)成分个数和参数估计方法. 仿真结果表明, 新方法可实现各种复杂环境下舰船红外图像目标的有效分割.     

基于模糊理论和遗传算法的导弹故障诊断方法研究

研究了一种将有向图、模糊理论和遗传算法相结合的智能故障诊断方法。用有向图来构造系统模型,用模糊集来解决模型中的不确定性问题,用遗传算法来对可能的故障传播路径进行搜索。当被诊断的系统含有不可测量节点时,该方法仍然可以很好地进行诊断。将该方法应用于某大型导弹武器装备的故障诊断系统中,实践证明,该方法行之有效并可以大大提高故障诊断效率。