Research On The Ranking Method Of Judgment Matrix And Compatibility

The problem of ranking method is an important problem in decision analysis,and it has a wide range of practical value.In real life,the company or the enterprise has to carry out a decision or a selection,how to sort the alternatives quickly and efficiently and then select and make decisions are particularly important.However,due to the alternatives in evaluation criteria and other aspects are the similar or the same,it is difficult to make measure and decisions,then these data are scaled and combined to form judgment matrices in a certain way.Among them,the ranking of complementary judgment matrix is the focus of experts in recent years,and its compatibility is the key problem to study the consistency of each expert group decision,its results of this study have a significant impact on the accuracy and appropriateness of the group selection problem,so it has important status for the study of compatibility problems.First of all,based on the multiplicative consistency definition and the additive consistency definition of complementary judgment matrices,this paper tries to propose a new function,and establishes optimization models respectively,corresponding to the two ordering formulas.Some of their properties are studied theoretically,and the feasibility and simplicity of this method are illustrated by simulation examples.Secondly,based on the preference information of the complementary judgment matrix in the group selection problem,two new analytical methods are proposed.Based on relative entropy and cosine similarity,two common metrics for evaluating the consistency of complementary judgment matrices are given.The compatibility and consistency problems are analyzed and studied in detail,and this paper gives the compatibility criteria and critical values.Finally,some simulation examples are given to show the suitability and actuality of the computing method proposed in this paper.