【導(dǎo)讀】在分析和應(yīng)用兩種凸組合的阿達(dá)瑪基于矩陣聚合方案及圖論之后,本文將從。它通常涉及多個(gè)決策者,因此,多個(gè)判斷矩陣提供不同的決策者需要匯總,以便達(dá)到更合理的解決方案。領(lǐng)域中的矩陣聚合,李躍進(jìn)和郭欣榮利用連通的無(wú)向。通圖想出了一個(gè)互反判斷矩陣聚合方法。然而,劉欣和楊善麗基于判斷矩陣發(fā)展了。阿達(dá)瑪凸組合,提供了關(guān)于“添加法”和“乘法”凸組合一致性明顯改善的證據(jù)。同一聚合方案也存在不同的判斷矩陣不一致地聚合。在實(shí)踐中解決問(wèn)題,就必須采。本文將探討矩陣的可行性和存在。的問(wèn)題,從聚合方案啟動(dòng)圖論和阿達(dá)瑪凸組合,做出相關(guān)的驗(yàn)證、優(yōu)化和選擇。步驟1:建立一致性專家判斷矩陣1mAA；在此基礎(chǔ)上,文檔[3]解釋了“加法”和“乘法”凸組合的判斷矩陣的基本理論,法”凸組合判斷矩陣在群體決策支持系統(tǒng)中對(duì)判斷矩陣是兩個(gè)有效的聚合方法。判斷矩陣的重建。該報(bào)稱,專家數(shù)據(jù)不一致或不太一致可以忽略和簡(jiǎn)化問(wèn)題,專家判。得到無(wú)向連通圖。位偏差仍較小的元素。

　　

【正文】 .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。 the rationality of this abandon has been supported in corresponding documents. The document [5] believed that the integrated judgment matrix contributed by weighted arithmetic average method cannot extend the reciprocity of original judgment matrix, therefore, there is no consistency exists, but it will show clear randomness that arithmetic average method is used partially to maintain reciprocity, and then the new judgment matrix is constructed on a reciprocal basis. The document [6] by utilizing specific example also proved that the additive convex bination is not valid as well， however, it also believes that by using the simple geometric average, the generated matrices convert all the consistent and inconsistent information from expert judgments to a plete consistent positive reciprocal matrix, and also claim that it would be more reasonable to use weighted geometric average to get adjusted matrix by adopting weighted coefficients, which are generated on principle of consistency and rule of minority yield. Thus, this paper believed that the aggregation of judgment matrixes should be mutual proved and selected in variety of schemes to choose more consistent results. For aggregation of expert matrix A1， A2， A3， A4， A5, ? ? 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 ? are more reasonable to be selected as the weights of index system G= (G1, G2, G3, G4, G5, G6, G7). 5 Conclusion The calculation results of weights and indexes sorting getting from different schemes of matrix aggregation differ from each other, how to reduce this difference effectively and reach more reasonable results requires to adopt multiple aggregation methods in group decision making process, then selection and optimization must be done on the calculation results produced by those methods. This paper believes that the application 18 of multiple methods and optimization and selection in practice will benefit in improving rationality and consistency of matrix aggregation in group decision making process. Reference 1. Lv Yuejin, Guo Xinrong. An Effective Aggregation Method for Group AHP Judgment Matrix. Theory and Practice of Systems Engineering, 2021(7):132136. 2. Liu Xin, Yang Shanlin. Hadamard Convex Combinations of Judgment Matrix. Theory and Practice of Systems Engineering, 2021,20(4):8385. 3. Yang Shanlin, Liu Xinbao. Two Aggregation Method of Judgment Matrix in GDSS. Journal of Computers, 2021, 24(1):106111. 4. Yang Shanlin, Liu Xinbao. Research on optimizing principle of Convex Combination coefficients of Judgment Matrix. Theory and Practice of Systems Engineering, 2021,21(8):5052. 5. Xu Zeshui. A note in Document [1] and [2] for the Properties of Convex Combinations of Judgment Matrix. Theory and practice of Systems Engineering, 2021,21(1):139140. 6. Wang Jian, Huang Fenggang, Jin Shaoguang. Study on Adjustment Method for Consistency of Judgment Matrix in AHP. Theory and Practice of Systems Engineering, 2021(8):8591.