【文章內(nèi)容簡介】 binations consistency improvement as well. The document [4] has studied on the optimization principle related with the convex coefficients of judgment matrix, and provided solution to the convex bination coefficients of judgment matrix. 10 Different matrix aggregation schemes will process the expert judgment data with discrepancy and aggregation results of judgment matrix are produced differently, therefore the weight and consistency after calculation are differential from another. While, in the process of matrix aggregation, the same aggregation schemes also present discrepantly in different judgment matrix aggregation. In the practice of solving problems, it is necessary to adopt different matrix aggregation methods and implement relevant verification and choice. This paper will investigate the feasibility and problems of matrix aggregation schemes that are initiated from graph theory and Hadamard convex binations, andrelevant verification, optimizing and choice have been made. 2 The Description of Matrix Aggregation Method The Solution of Matrix Aggregation Method Based on Graph Theory Matrix aggregation solution based on graph theory, is to set up a level deviation matrix E, and select more consistent factors from the different expert judgment matrix A(k), so as to construct a plete consistent judgment matrix A*. The detailed construction steps and explanation see document [1]. Step1: Setting up the expert judgment matrix with consistency A1Am； Step2: Setting up the grade deviation matrix in decisionmaking process *()ij n nEe? ， 1stij ij ijs t me a a? ? ???? Supported by colleges and universities natural science research project of Anhui Province, china (KJ2021Z054) 。Enterprise development special fund project of Anhui province china in 2021. sija represents that the expert ranked at s values the importance by paring indicator i with j. 11 ( 1 , 2 , 3 )8 110 ( 1 , 2 , 3 )sijsijsija k k mkak a k mk?????? ? ??? (2) Step3: Selecting (n1) elements *ije , which are got minimum value of grade deviation, meanwhile, require any one of (n1) elements is not given by the other (n2) elements。 Step4: From expert judgment matrix A1Am, choosing all the elements that locate in the same position of in *ije ,and recording as *kija ； Step5: Aggregating selected every group of *kija by using additive or multiplicative method, and recording the results as *ija ； Step6: Using additive synthesis to get *ija at (n1) and establishing prehensive judgment matrix A*, applying the method of summation to sort the schemes eventually. Matrix Aggregating Method Based on Hadamard Convex Combination For the aggregation of judgment matrix in group decision making, document [2] provides the concept of Hadamard convex binations, . if A1， A2， …..Am are judgment matrixes at number of m for the same problem, if it is ? ?10 , 1 ( 1 , 2 , 3 ) , 1mLL LLm?? ?? ? ??,let 1 1 2 2 3 3 mmA A A A A? ? ? ?? ? ? ? ? (3) 31 21 2 3 mmA A A A A?? ??? ? ? ? ? (4) Therefore, A is named as an added convex bination for A1， A2， …Am, and A is a Hadamard multiplicative convex bination. For the operators, ⊕ ,are defined as follows: If C=A⊕ B， so ij ij ijc a b??， if C=AB， we will get the results that ij ij ijc a b? On this basis, document [3] explained the basic theory for “addition ”and 12 “multiplication” convex binations of judgment matrix, it is believed that addition ”and “multiplication” convex binations of judgment matrix not only can eliminate the effects caused on subjective factors , but also can keep and improve consistency of judgment matrix, in the meanwhile the correspondent proving process was provided, therefore it is confirmed that “addition ”and “multiplication” convex binations of judgment matrix are two effective aggregating methods for judgment matrix in groups decision support system. 3 The Application of Matrix Aggregation Method The Application of Matrix Aggregation Based on Graph Theory Step1: According to the problem change in reality and environment, this paper will make certain adjustment on step1. The original document required the expert reconstructed judgment matrix when expert matrix cannot reach the consistency, on the contrary this paper argue that there are various difficulties exist in real practice for reconstructing judgment matrix. The paper claim that the expert data with inconsistency or less consistent could be ignored directly and to simplify the problem, as to the expert judgment matrix formed by evaluating the importance of index system G=(G1,G2,G