【正文】 B， 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,G3,G4,G5,G6,G7),on the condition that it is plied with the consistency, and in accordance with the consistent ratio CR sorted from small to large, the top 5 expert judgment matrix is listed as follows : 11 2 1 / 2 5 6 6 1 / 21 / 2 1 1 / 4 3 5 6 1 / 22 4 1 6 7 8 21 / 5 1 / 3 1 / 6 1 3 4 1 / 31 / 6 1 / 5 1 / 7 1 / 3 1 2 1 / 61 / 6 1 / 6 1 / 8 1 / 4 1 / 2 1 1 / 72 2 1 / 2 3 6 7 1A????? ??????21 2 1 / 2 5 6 7 1 / 21 / 2 1 1 / 4 2 3 4 1 / 42 4 1 6 7 9 21 / 5 1 / 2 1 / 6 1 3 5 1 / 31 / 6 1 / 3 1 / 7 1 / 3 1 2 1 / 51 / 7 1 / 4 1 / 9 1 / 5 1 / 3 1 1 / 82 4 1 / 2 3 5 8 1A????? ?????? 13 31 3 1 / 2 5 6 5 1 / 21 / 3 1 1 / 5 2 5 3 1 / 42 5 1 8 9 5 1 / 21 / 5 1 / 2 1 / 8 1 4 2 1 / 51 / 6 1 / 5 1 / 9 1 / 4 1 1 / 3 1 / 81 / 5 1 / 3 1 / 5 1 / 2 3 1 1 / 72 4 2 5 8 7 1A????? ??????41 2 1 / 3 3 5 6 1 / 31 / 2 1 1 / 5 2 6 7 1 / 23 5 1 7 8 9 21 / 3 1 / 2 1 / 7 1 4 4 1 / 41 / 5 1 / 6 / 8 1 / 4 1 2 1 / 61 / 6 1 / 7 1 / 9 1 / 4 1 / 2 1 1 / 83 2 1 / 2 4 6 8 1A????? ??????51 3 1 / 2 4 5 7 21 / 3 1 1 / 5 2 4 7 22 5 1 6 8 9 41 / 4 1 / 2 1 / 6 1 3 5 1 / 21 / 5 1 / 4 1 / 8 1 / 3 1 4 1 / 31 / 7 1 / 7 1 / 9 1 / 5 1 / 4 1 1 / 61 / 2 1 / 2 1 / 4 2 3 6 1A???????0 6 4 10 6 10 126 0 6 4 14 22 204 6 0 10 10 18 1610 4 10 0 6 14 146 14 10 6 0 22 2210 22 18 14 22 0 1012 20 16 14 22 10 0E??? ?????? After calculating, the consistency ratios are: (, , , , )T Step2: Grade deviation matrix E is established as above. Step3: Choosing *ije According to the grade deviation matrix E, 6 elements with higher level of consistency are selected: * * * * * *13 24 12 23 45 15, , , , , ,e e e e e e and the undirected connected graph is produced. Figure1. Undirected Connected Graph (F1)Based on Grade deviation Matrix E Because it does not meet the requirements of undirected connected graph, V1V2V4V5, and V1V2V3 are all in the formation of loop, thus it is needed to follow the broken circle method. Firstly, the elements with larger grade deviation are replaced by adding the remained elements with smaller grade deviation. Omitting the detail processes, the undirected connected graphs Figure 2 and Figure 3 are obtained. 14 2 3 Based on Figure2, the elements selected correspondently from the judgment matrix A1A5 are: * * *1 2 1 3 2 4* * *1 6 4 5 6 7( 2 , 2 , 3 , 2 , 3 ) , ( 1 / 2 , 1 / 2 , 1 / 2 , 1 / 3 , 1 / 2 ) , ( 3 , 2 , 2 , 2 , 2 )( 6 , 7 , 5 , 6 , 7 ) , ( 3 , 3 , 4 , 4 , 3 ) , ( 1 / 7 , 1 / 8 , 1 / 7 , 1 / 8 , 1 / 6 )k k kk k ka a aa a a? ? ?? ? ? In accordance with the additive principle, it is: ? ?*12 2 2 3 2 3 / 5 12 / 5a ? ? ? ? ? ? ； ? ?*13 1 / 2 1 / 2 1 / 2 1 / 3 1 / 2 / 5 7 / 15a ? ? ? ? ? ? ；* ? ?*24 3 2 2 2 2 / 5 11 / 5a ? ? ? ? ? ? ； ? ?*16 6 7 5 6 7 / 5 31 / 5a ? ? ? ? ? ? ；* ? ?*45 3 3 4 4 3 / 5 17 / 5a ? ? ? ? ? ? ； ? ?*67 1 / 7 1 / 8 1 / 7 1 / 8 1 / 6 / 5 59 / 42 0a ? ? ? ? ? ? ；The results is listed as follows： * * * * * *12 13 24 16 45 6712 / 5 , 7 / 15 , 11 / 5 , 31 / 5 , 17 / 5 , 59 / 42 0a a a a a a? ? ? ? ? ? Therefore the initial matrix is established as below: 1 1 2 / 5 7 / 1 5 3 1 / 51 1 1 / 511 1 7 / 511 5 9 / 4 2 01A????? ????? 15 *1 12 / 5 7 / 15 132 / 25 224 4 / 125 31 / 15 182 9 / 210 05 / 12 1 7 / 36 11 / 5 187 / 25 31 / 12 182 9 / 504 015 / 7 36 / 7 1 396 / 35 673 2 93