【正文】 / 7 584 7 / 294 025 / 132 5 / 11 35 / 396 1 17 / 5 155 / 132 182 9 / 110 88125 / 224 4 25 / 187 175 / 673 2 5 / 17 1 775 / 224 4 914 5 / 1884965 / 31 12 / 31 7 /A ?39 132 / 15 224 4 / 775 1 59 / 420210 0 / 182 9 504 0 / 182 9 294 0 / 548 7 110 88 / 182 9 188 496 / 914 5 420 / 59 1???????? Based on the reflexive principle, and principle that rows and columns are proportional to the others, the missing elements are filled in, hence a consistent judgment matrix A* is constructed. According to the calculation, it es to W= (, , , , , , )T Similarly, for Figure3, by using the same calculation processes, it es to W=（ ， ， ， ， ， ， )T The Application of Matrix Aggregation Based on Hadamard Convex Combination On the basis of foundational theory on Hadamard Convex Combination, expert matrix A1， A2， A3， A4， A5 above is selected according to consistent ratio, to take correspondent matrix aggregation. For the purposes of facilitating study, this paper set various expert judgment matrixes on equal weights, that is, let L?? (0 .2, 0 .2 , 0 .2 , 0 .2 , 0 .2 ) According to the calculation fromA ,it es 16 to ? ? 0 .2 0 0 , 0 .1 1 9 , 0 .3 6 2 , 0 .0 6 8 , 0 .0 3 5 , 0 .0 2 5 , 0 . 191 TW ? ,By using the square law, it es to CR=. Similarly, According to the calculation fromA ，TW = ( 0 .1 9 2 ,0 .1 1 2 ,0 .3 5 2 ,0 .0 6 7 , 0 .0 3 4 ,0 .0 2 6 , 0 .2 1 7 )By using the square law, it es to CR= 4 Selection and Optimization on Weighting the Results after Matrix Aggregation In summary, by using 4 different kinds of methods, 4 weight vectors are acquired as follows: ? ? T1 0 .2 0 0 , 0 .0 8 1 , 0 .4 1 9 , 0 .0 3 7 , 0 .0 1 1 , 0 .0 3 2 , 0 .2 20W ?? ? T2 0 .1 9 1 , 0 .0 8 0 , 0 .4 0 8 , 0 .0 3 6 , 0 .0 3 4 , 0 .0 3 1 , 0 .2 20W ?? ? T3 0 .2 0 0 , 0 .1 1 9 , 0 .3 6 2 , 0 .0 6 8 , 0 .0 3 5 , 0 .0 2 5 , 0 .1 91W ? ? ? T4 0 .1 9 2 , 0 .1 1 2 , 0 .3 5 2 , 0 .0 6 7 , 0 .0 3 4 , 0 .0 2 6 , 0 .2 17W ? It is could be seen by paring and analyzing the weight vectors listed above, the importance sorting list on the index system G=(G1,G2,G3,G4,G5,G6,G7) is shown as: ① G3G7G1G2G4G6G5； ② G3G7G1G2G4G5G6 ③ G3G1G7G2G4G5G6； ④ G3G7G1G2G4G5G6 Based on the sorting results above, the errors are focus on G1 and G7 which are listed in the second, third places, and the G5 and G6, in the sixth and seventh respectively. Accordingly and by bining with the 5 sorting results from above schemes, among the sorting results, ①②④ all have the outes G7G1 (G7 is more important than G1), while ③ has the contrary result: G1G7, which can also support that the sorting results ing from adding convex bination have significant difference from that of the other schemes, this result is attached with irrationality and should be removed. Meanwhile, in the results ①②④ , ② and ④ both show G5G6, only ① shows G6G5, so that ① should be removed likewise. Therefore this paper supposes that the 17 reasonable sorting scheme is: ? ? T0 .1 9 0 , 0 .0 8 9 , 0 .3 7 8 , 0 .0 5 5 , 0 .0 3 9 , 0 .0 2 9 , 0 .2 2 0W ? The abandon of sorting scheme ① and ③ is the discard of undirected connected graph and convex bination in this matrix aggregation essentially。 Optimization 1 Introduction As an effective method utilized in multiobjective and multifactor decision making, Analytic Hierarchy Process has been widely applied in many decision making aspects. It normally involves several decision makers, therefore, multiple judgment matrixes provided by different decision maker need to be aggregated so that to reach a more reasonable solution. In the field of matrix aggregation, Lv Yuejin and Guo Xinrong utilized the Connected Undirected Graph and its theories, by excluding the biased expert judgments, have e up with a reciprocal judgment matrix aggregation method which was oriented from the theory of mth power graph of simple undirected connected graph [1]. Nevertheless,Liu Xin and Yang Shanlin developed Hadamard convex bination based on judgment matrix [23], provided the evidence on “additive”and“multiplicative” convex 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 verificatio