Dominance Matrix Of Hypergraph And Its Application

As to the rapid prototyping of the Internet,the scale into various networks is becoming larger and larger,resulting in more and more complex structural information.The ability of graph theory to solve practical problems is greatly limited,but the hypergraph theory can be used to solve this problem.The hypergraph can be regarded as a kind of finite subset system,which can describe complex information relations of the form of set,matrix and graph.Dominance matrix also plays an important role in information representation.It represents the good and bad relationship between objects in the form of set.In real life,the information relationship between advantageous relationship is everywhere,such as the transfer station selected in the subway line.Therefore,the dominant matrix of the hypergraph is defined in hypergraphs,which is the dominant matrix of hypergraphs.It is combined with acyclic axiom for Graham reduction.The result of reduction is a acyclic hypergraph or a cyclic hypergraph.Fuzzy hypergraph is a fuzzy extension of hypergraphs,and its fuzzy information also has the characteristics of advantage.In fuzzy hypergraph,a fuzzy set-valued advantage matrix with advantage relationship and expressed by set value is defined.Since decision makers will hesitate on the problem of fuzzy information,from the perspective of transforming fuzziness into certainty,the fuzzy set-valued dominance matrix can be transformed into the dominance matrix of hypergraphs.This thesis studies the concept of the hypergraph theory from the perspective of dominance matrix,and the formed circular hypergraph is to evaluate whether the task has high feasibility,and the formed acyclic hypergraph can make decisions on fuzzy information.The specific work of this thesis is as follows:(1)On the problem of determining cyclic hypergraphs,it is proved that the dominance matrix of hypergraphs can provide a new tool for the study of the hypergraph theory.The dominance matrix of the hypergraph is defined,the relationship between the dominance matrices of different hypergraphs is deduced,and the reduction results of different types of dominance matrices are discussed.Then some properties of acyclic and cyclic hypergraphs are mined.The subway routes of six cities are represented by hypergraphs as an example,and their dominance matrices are reduced.The final results are all cyclic.Thus,considering the factors affecting the proportion of the cyclic hypergraph,the simulation experiment shows that the more transfer stations,the greater the probability of the final cyclic hypergraph,which proves that the cyclic hypergraph can evaluate the rationality of subway route planning.(2)In order to explore the acyclic property of classical hypergraph in fuzzy hypergraph,the fuzzy set-valued dominance matrix of fuzzy hypergraph is defined,its properties are studied,and the dominance matrix of hypergraph is extended to fuzzy hypergraph.When the ? value changes,the occurrence rate of the cyclic hypergraph and the acyclic hypergraph is statistically analyzed.Finally,an example is given to help decision makers choose computer models.