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.     

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.     

模糊元图及其特性分析

模糊图已被广泛地应用于系统的分析与建模。然而现有的结构不适合于分析元素集之间的有向模糊关系。文中讨论了一种新的模糊图论结论－－模糊元图,它描述的是集合而非单个元素之间的有向关系,具有很强的图形化描述功能和形式化分析能力。文中着重分析了模糊元图的特性,尤其是其邻近矩阵的特性,这是模糊元图研究与应用的基础,模糊元图在系统建模和模糊规则管理方面有着广阔的应用前景。     

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.

     

Transformational approach to the development of software architectures on the basis of fuzzy graph models

An approach to the creation of software architectures is examined that is based on the model-oriented paradigm that opens up the way to the implementation of transformational evolution of software systems. The emphasis is on the formalization of fuzzy graphs, fuzzy graph models, and rules of their transformation. A theoretical categorical representation of fuzzy software architectures is developed, which allows one to manage the process of their transformations on the basis of making decisions in a fuzzy modeling space on the functionality of the target platform-specific system. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 139–150, September–October 2008.     

改进动态因果图与模糊推理融合故障诊断方法

在复杂的控制系统发生故障时,运维系统能保证对其进行快速、可靠的故障诊断尤为重要。针对复杂控制系统中控制信号多、信号关联性强、故障状态多、部件故障模式多的情况,提出一种改进动态因果图与模糊推理融合的故障诊断方法,利用改进动态因果图逻辑表达能力强,能因果互推的特点,构建多重（正向、反向、混合）模糊规则,有效克服了模糊逻辑推理中只能由因溯果而不能由果溯因的难题,同时,将动态因果图的动态特性引入到模糊规则的动态更新中,增强了模糊推理的实时性。最后,以某型装甲设备垂直力矩电机控制过程的故障诊断为应用背景,在自行研制的故障诊断平台中嵌入此法进行故障诊断测试,测试结果分析表明,此法能有效提高诊断效率,具有更高的准确性、先进性、适用性。     

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。     

Transformations of fuzzy graphs specified by <Emphasis Type="Italic">FD</Emphasis>-grammars

The categorical approach is proposed to formalize transformations of FD-graphs that consist of networks of distributed components whose nodes are specified by fuzzy graphs. Necessary and sufficient conditions are formally defined for FD-graph transformations that do not violate structure integrity and can be constructed componentwise. FD-grammars that generalize fuzzy graph grammars are proposed to describe the admissible transformations of FD-graphs. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 129–147, March–April 2007.     

基于图卷积神经网络的自注意力的融合节点分类框架

图神经网络因其强大的建模能力引起广泛关注, 常常被用来解决图上的节点分类任务. 现阶段常用的以图卷积神经网络 (graph convolutional network, GCN)为内核的模型解决此类问题, 但往往因为出现过拟合与过平滑而导致深层的节点嵌入表示效果并不好. 因此, 本文提出了一种基于GCN内核的结合残差连接与自注意力方法——GCNRN模型, 以提升GCN的泛化能力. 同时, 为了整合更深入的信息, 本文引入融合机制, 采用模糊积分融合多个分类器, 最终提高模型测试精度. 为了验证所提出方法的优越性, 本文采用ogbn-arxiv与常用的引文数据集进行了对比实验. GCNRN模型与多个以GCN为内核的现有模型相比, 节点分类准确率平均提高了2%, 且避免了传统的过拟合和过平滑现象. 此外, 实验结果表明, 增加了基于模糊积分的融合模块的多分类器模型比传统融合方法具有更好的分类效果.     

Bipolar fuzzy graphs

In this paper, we introduce the notion of bipolar fuzzy graphs, describe various methods of their construction, discuss the concept of isomorphisms of these graphs, and investigate some of their important properties. We then introduce the notion of strong bipolar fuzzy graphs and study some of their properties. We also discuss some propositions of self complementary and self weak complementary strong bipolar fuzzy graphs.     

模糊聚类计算的最佳算法

给出模糊关系传递闭包在对应模糊图上的几何意义,并提出一个基于图连通分支计算的模糊聚类最佳算法.对任给的n个样本,新算法最坏情况下的时间复杂性函数T(n)满足O(n)≤T(n)≤O(n²).与经典的基于模糊传递闭包计算的模糊聚类算法的O(n³logn)计算时间相比,新算法至少降低了O(n相似文献   

A parallel fuzzy clustering algorithm for large graphs using Pregel

Large graphs are scale free and ubiquitous having irregular relationships. Clustering is used to find existent similar patterns in graphs and thus help in getting useful insights. In real-world, nodes may belong to more than one cluster thus, it is essential to analyze fuzzy cluster membership of nodes. Traditional centralized fuzzy clustering algorithms incur high communication cost and produce poor quality of clusters when used for large graphs. Thus, scalable solutions are obligatory to handle huge amount of data in less computational time with minimum disk access. In this paper, we proposed a parallel fuzzy clustering algorithm named ‘PGFC’ for handling scalable graph data. It will be advantageous from the viewpoint of expert systems to develop a clustering algorithm that can assure scalability along with better quality of clusters for handling large graphs.The algorithm is parallelized using bulk synchronous parallel (BSP) based Pregel model. The cluster centers are initialized using degree centrality measure, resulting in lesser number of iterations. The performance of PGFC is compared with other state of art clustering algorithms using synthetic graphs and real world networks. The experimental results reveal that the proposed PGFC scales up linearly to handle large graphs and produces better quality of clusters when compared to other graph clustering counterparts.     

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。     

A graph-based framework for sub-pixel image segmentation

Many image segmentation methods utilize graph structures for representing images, where the flexibility and generality of the abstract structure is beneficial. By using a fuzzy object representation, i.e., allowing partial belongingness of elements to image objects, the unavoidable loss of information when representing continuous structures by finite sets is significantly reduced, enabling feature estimates with sub-pixel precision.This work presents a framework for object representation based on fuzzy segmented graphs. Interpreting the edges as one-dimensional paths between the vertices of a graph, we extend the notion of a graph cut to that of a located cut, i.e., a cut with sub-edge precision. We describe a method for computing a located cut from a fuzzy segmentation of graph vertices. Further, the notion of vertex coverage segmentation is proposed as a graph theoretic equivalent to pixel coverage segmentations and a method for computing such a segmentation from a located cut is given. Utilizing the proposed framework, we demonstrate improved precision of area measurements of synthetic two-dimensional objects. We emphasize that although the experiments presented here are performed on two-dimensional images, the proposed framework is defined for general graphs and thus applicable to images of any dimension.     

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。     

Cycles and cocycles of fuzzy graphs

In this paper we show that if the fuzzy graph (σ,μ) is a cycle, then it is a fuzzy cycle if and only if (σ,μ) is not a fuzzy tree. We also examine the relationship between fuzzy bridges and cycles. We introduce and examine the concepts of chords, twigs, 1-chains with boundary zero, cycle vectors, coboundary, and cocycles for fuzzy graphs. We show that although the set of cycle vectors, fuzzy cycle vectors, cocycles, and fuzzy cocycles do not necessarily form vector spaces over the field Z₂ of integers modulo 2, they nearly do. Thisallows us to introduce the concepts of (fuzzy) cycle rank and (fuzzy) cocycle rank for fuzzy graphs in a meaningful way.     

基于KFCMSA的(k，l)加权社交网络匿名算法

图数据隐私保护的研究目前主要集中在简单图,适应范围有限。将权重图数据的隐私保护作为研究对象,可以改善权重图发布之后数据的可用性及有效性。针对在利用聚类匿名化方法处理社交网络数据时,需要增删大量的边和节点,造成严重的数据失真的问题进行了研究。提出了（k,l）加权社交网络匿名算法KFCMSA（联合k成员模糊聚类和模拟退火）,并利用改进的簇划分算法将权重社交网络聚类成不同的簇,对同一簇中节点的边权重进行泛化使节点满足l多样性。在实现k度匿名的同时有效减少了边的改变量,提高了数据的可用性,实现最优聚类的同时防止了同质性攻击。聚类质量实验和数据可用性分析表明该算法具有较高的性能优势和较高边保留率。     

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。     

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.