The Axiomatic Definition And Application Of Several Kinds Of Grey Incidence Models

In view of the urgent need to study many nonlinear correlations with practical correlation backgrounds in real life and the axiomatic definition of grey incidence model under time series and panel data,on the basis of the classical grey incidence models,a new type of grey concave-convex incidence degree is constructed and its axiomatic definition and concrete examples are given,the problem of axiomatic definition of proximity and similarity incidence degree in panel data is also solved.Specific research contents include the following aspects:(1)For the time series,from the view of geometric point,the sequence which has the same convexity is a new correlation.By combining geometric and algebraic analysis,the absolute degree of concave and convex at the corresponding points is defined,and a new grey incidence degree of concave and convex reflecting this kind of correlation is given.(2)Further study its nature and significance,extract the common characteristic of the new grey incidence degree of concave and convex,that is,the incidence degree axiom.Through a concrete example,it is verified that the correlation degree of two sequences that have equal concave and convex are only 1 under this kind of incidence degree,which indicates that it depicts a new kind of correlation that the existing correlation coefficient and grey incidence degree can not describe,and points out that the new grey incidence degree of concave and convex should have a wide range of practical application background.(3)This paper also presents the axiomatic definition of grey similarity and proximity incidence degree based on panel data,which are two main types,meanwhile it attaches corresponding incidence degree models and proofs to prove the validity of the theorem.It also constructs a new initialization method of panel data,which verdicts their relational degree through the similarities and differences of the fluctuation near the average data.Then this paper emphasizes the resolution coefficient could be added to calculation of relational degree to improve the discrimination,and points out it should be dynamic and broadens its scope.Finally two corresponding examples of similarity and proximity incidence degree are given to prove the conclusion.