Analysis Of The Connectivity And The Stability Of Related Network Flows Of Intuitionistic Fuzzy Graphs

In the process of fuzzy network information system research and modeling,it is difficult to consider the structural processing of the system,including the establishment of hierarchical knowledge space structure,top-down acquisition of knowledge at different levels,and bottom-up synthesis of hierarchical fuzzy information,etc.Since fuzzy graph theory can describe and deal with the structural problems of information system well,especially in the analysis of fuzzy network information system,fuzzy data mining,image capture and network design,tree representation of fuzzy data structure,resource allocation and scheduling and other problems are closely related to fuzzy graph theory.Therefore,fuzzy graph theory and application of fuzzy graph theory to fuzzy information system analysis have been investigated.As a generalization of fuzzy graph,intuitionistic fuzzy graph allows the use of membership degree and non-membership degree to describe two aspects of fuzzy information under uncertain conditions,which makes the problem handling or structure analysis more comprehensive and delicate.In the study of fuzzy network information system,network connectivity has attracted more and more attention because of its importance and wide application in the investigation of network flow transmission,router problem and bandwidth allocation,connectivity and network stability.On the basis of intuitionistic fuzzy sets and intuitionistic fuzzy graphs,this thesis gives the definitions of connectivity status and cyclic connectivity index of intuitionistic fuzzy graphs,and discusses two kinds of parameters of connectedness of intuitionistic fuzzy graphs(the connectivity status and the cyclic connectivity index)and their characterization theorems.The connectivity status and status sequence of vertices are analyzed and the equivalent relation between connectivity index of fuzzy graph and connectivity status of intuitionistic fuzzy graph is discussed.Secondly,based on the concepts of cycle connectivity,cyclic connectivity index and average cyclic connectivity index,we discuss the vertex classification of intuitionistic fuzzy graph and the characterization of complete intuitionistic fuzzy graph,and find the condition that the connectivity index of complete intuitionistic fuzzy graph is equivalent to that of cyclic connectivity index.The influence and response of vertex increment and subtraction on the whole network system are discussed.As an application,the proposed two types of connectivity parameters are applied to the problem of network flow bandwidth allocation,the stability is analyzed,and the decision support for network designers is provided.