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1、個(gè)人資料整理 僅限學(xué)習(xí)使用汽車保險(xiǎn)問題的研究一)摘 要:利用某保險(xiǎn)公司在開展汽車保險(xiǎn)業(yè)務(wù)中所積累的具體數(shù)值資料,綜合分析影響續(xù)保率的因素、如承保車輛出現(xiàn)次數(shù),承保車輛年齡,承保車輛品牌,承保車輛的使用性質(zhì),承保車輛的銷售渠道,以及新車購(gòu)買價(jià)格的不同等因素,應(yīng)用數(shù)理統(tǒng)計(jì)與數(shù)學(xué)實(shí)驗(yàn)的方法,建立了一個(gè)汽車保險(xiǎn)的簡(jiǎn)單實(shí)用的數(shù)學(xué)模型,并根據(jù)相關(guān)數(shù)據(jù)的變動(dòng)提供了改進(jìn)模型的思路,該模型可為保險(xiǎn)公司開展汽車保險(xiǎn)業(yè)務(wù)提供較好的參考。關(guān)鍵詞: 汽車保險(xiǎn)。續(xù)保率,影響因素,數(shù)學(xué)模型1.問題重述近幾年,國(guó)內(nèi)汽車銷售市場(chǎng)異?;鸨?,銷售量屢創(chuàng)新高。車輪上的世界,保險(xiǎn)已經(jīng)與我們?nèi)缬半S形。汽車保險(xiǎn),簡(jiǎn)稱車險(xiǎn),是指對(duì)機(jī)動(dòng)車輛由

2、于自然災(zāi)害或意外事故所造成的人身傷亡或財(cái)產(chǎn)損失負(fù)賠償責(zé)任的一種商業(yè)保險(xiǎn)。汽車保險(xiǎn)是財(cái)產(chǎn)保險(xiǎn)中的主要險(xiǎn)種。自2006 年7 月1 日,交強(qiáng)險(xiǎn)實(shí)施以來,車險(xiǎn)與廣大車主間有了更加親密的關(guān)系。交強(qiáng)險(xiǎn),全稱機(jī)動(dòng)車交通事故責(zé)任強(qiáng)制保險(xiǎn),是我國(guó)首個(gè)由國(guó)家法律規(guī)定實(shí)行的強(qiáng)制保險(xiǎn)制度。交強(qiáng)險(xiǎn)的基本定義是:交強(qiáng)險(xiǎn)是由保險(xiǎn)公司對(duì)被保險(xiǎn)機(jī)動(dòng)車發(fā)生道路交通事故造成受害人不包括本車人員和被保險(xiǎn)人)的人身傷亡、財(cái)產(chǎn)損失,在責(zé)任限額內(nèi)予以賠償?shù)膹?qiáng)制性責(zé)任保險(xiǎn)。除了交強(qiáng)險(xiǎn),各個(gè)保險(xiǎn)公司有自己的商業(yè)車險(xiǎn)產(chǎn)品,種類繁多。在我國(guó)保險(xiǎn)業(yè),汽車保險(xiǎn)有著不可撼動(dòng)的地位。連續(xù)多年,汽車保險(xiǎn)穩(wěn)居國(guó)內(nèi)產(chǎn)險(xiǎn)業(yè)第一大險(xiǎn)種??梢哉f,對(duì)于財(cái)產(chǎn)保險(xiǎn)公司來

3、說,得車險(xiǎn)者得天下!2.問題分析評(píng)價(jià)一個(gè)保險(xiǎn)公司的綜合影響力時(shí),其市場(chǎng)份額具有舉足輕重的作用。近年來,由于越來越多的保險(xiǎn)公司涉足車險(xiǎn)市場(chǎng),使得車險(xiǎn)市場(chǎng)格局也發(fā)生了一些不容忽視的變化。當(dāng)新的保險(xiǎn)公司尋求自己的領(lǐng)地的時(shí)候,老的保險(xiǎn)公司要做的除了發(fā)展新的領(lǐng)地,還要保住自己原有的客戶。很多保險(xiǎn)公司開始關(guān)注續(xù)保率這個(gè)指標(biāo)。續(xù)保率就是當(dāng)年到期的客戶中續(xù)保客戶所占的比重。在續(xù)保數(shù)據(jù)中,我們發(fā)現(xiàn)承保車輛的使用性質(zhì),承保車輛的銷售渠道以及新車購(gòu)買價(jià)格的不同都會(huì)影響續(xù)保率。由具體數(shù)據(jù)可以看出:當(dāng)年到期車輛續(xù)保率和目標(biāo)客戶續(xù)保率的變化和幾種影響因素都有關(guān)。將不同時(shí)間的數(shù)據(jù)綜合列表,計(jì)算總體的平均值,并結(jié)合其對(duì)應(yīng)圖示

4、進(jìn)行分析。3合理假設(shè)一:將不同時(shí)間的數(shù)據(jù)綜合列表,分別計(jì)算各個(gè)影響因素下當(dāng)年到期車輛續(xù)保率和目標(biāo)客戶續(xù)保率變化的總體平均值。個(gè)人資料整理 僅限學(xué)習(xí)使用一)按照承保車輛出現(xiàn)次數(shù)統(tǒng)計(jì)1)2018 年 9 月-2018 年 3 月當(dāng)年到期車輛續(xù)保率及圖象201809201810201811201812201801201802201803出險(xiǎn) 0 次20.01%20.71%20.53%20.97%36.44%37.05%35.68%出險(xiǎn) 1 次29.38%29.93%29.96%30.51%41.73%42.82%42.12%出險(xiǎn) 2 次33.74%34.46%34.85%35.56%46.94%48

5、.08%48.02%出險(xiǎn) 3 次32.68%34.00%34.11%34.77%42.03%42.62%44.65%出險(xiǎn) 4 次32.73%34.08%34.40%35.44%42.45%42.08%42.50%出險(xiǎn) 5 次32.72%33.13%34.36%34.96%17.65%18.18%35.29%出險(xiǎn) 5 次33.49%34.07%34.42%34.68%37.21%40.18%43.27%以上出險(xiǎn)次數(shù)23.22%23.88%23.78%24.27%38.26%38.99%37.88%平均值平均值27.34%35.21%40.24%37.84%37.67%29.47%36.76%30

6、.04%34.32%60.00%20100950.00%20101040.00%20101130.00%20.00%20101210.00%2011010.00%201102201103平均值2)2018 年 9 月-2018 年 3 月目標(biāo)客戶續(xù)保率及圖像201809201810201811201812201801201802201803出險(xiǎn) 0 次20.17%20.89%20.87%21.26%36.53%37.13%35.80%出險(xiǎn) 1 次33.39%34.31%34.86%35.58%43.53%44.55%44.92%出險(xiǎn) 2 次出險(xiǎn) 3 次出險(xiǎn) 4 次出險(xiǎn) 5 次出險(xiǎn) 5 次以上出

7、險(xiǎn)次數(shù)21.28%22.00%22.03%22.46%37.21%37.84%36.66%平均值平均值27.52%38.73%0.00%0.00%0.00%0.00%0.00%28.50%31.58%個(gè)人資料整理 僅限學(xué)習(xí)使用50.00%20100940.00%20101030.00%20.00%20101110.00%2010120.00)按照承保車輛年齡統(tǒng)計(jì)1)2018 年 9 月-2018 年 3 月當(dāng)年到期車輛續(xù)保率及圖象2018092018102018112018122018012018022018030-1 年24.83%25.22%25.0

8、6%25.84%37.27%37.76%37.81%1-2 年27.45%29.08%28.81%29.22%44.77%46.28%45.35%2-3 年21.64%22.24%22.19%22.37%37.09%39.03%37.22%3-4 年21.16%21.95%21.86%21.71%35.31%36.85%35.34%4-5 年18.50%18.42%18.34%18.70%33.68%32.78%29.00%5-6 年17.23%17.82%18.00%18.34%38.24%38.21%37.24%6-7 年18.01%18.45%18.74%18.96%43.78%39.2

9、2%36.39%7-8 年19.66%20.07%20.06%20.14%36.84%32.49%34.41%8-9 年18.92%19.80%20.24%20.21%28.00%26.42%26.85%9-10 年16.47%17.12%16.82%17.71%35.71%33.87%25.36%10 年以16.51%16.49%16.41%16.76%18.52%25.48%25.65%上車齡23.22%23.88%23.78%24.27%38.26%38.99%37.88%平均值平均值30.54%35.85%28.83%27.74%24.20%26.44%27.65%26.24%22.9

10、2%23.29%19.40%30.04%26.93%50.00%45.00%20100940.00%35.00%20101030.00%20101125.00%20.00%20101215.00%20110110.00%2011025.00%0.00%201103平均值2)2018 年 9 月-2018 年 3 月目標(biāo)客戶續(xù)保率及圖像2018092018102018112018122018012018022018030-1 年21.95%22.35%21.95%22.48%35.30%35.52%35.62%平均值27.88%個(gè)人資料整理 僅限學(xué)習(xí)使用1-2 年25.79%27.71%28.0

11、3%28.74%45.00%45.89%44.48%2-3 年20.69%21.28%21.56%21.90%35.79%38.36%37.00%3-4 年20.37%21.23%21.50%21.25%35.19%36.53%34.54%4-5 年17.56%17.47%17.45%17.92%33.65%32.76%29.40%5-6 年16.62%17.16%17.42%17.85%36.26%36.90%35.89%6-7 年17.10%17.48%18.01%18.11%43.69%40.06%36.35%7-8 年18.86%19.07%19.20%19.27%36.07%30.9

12、4%32.70%8-9 年18.77%19.52%19.79%19.86%28.17%27.84%26.83%9-10 年16.01%16.52%16.39%17.44%35.71%34.43%26.32%10 年以16.44%16.48%16.62%17.03%18.00%24.83%25.35%上車齡21.28%22.00%22.03%22.46%37.21%37.84%36.66%平均值35.09%28.08%27.23%23.74%25.45%27.26%25.16%22.97%23.26%19.25%28.50%26.16%50.00%20100940.00%20101030.00%

13、20101120.00%20101210.00%2011010.00%201102201103平均值三)按照承保車輛品牌統(tǒng)計(jì)東南50.00%42.86%23.13%50.00%50.00%50.00%東風(fēng)悅達(dá)53.79%51.72%44.32%58.48%55.34%53.79%起亞江鈴37.30%36.52%27.01%25.00%27.78%37.30%上海通用41.19%38.31%32.49%36.57%38.63%41.19%雪佛蘭吉利31.35%30.12%18.63%32.41%34.32%31.35%昌河27.48%26.83%19.51%25.53%29.41%27.48%海

14、南馬自50.00%42.11%33.78%72.73%53.33%50.00%達(dá)長(zhǎng)城34.94%33.33%28.57%35.71%32.43%34.94%解放(一汽35.45%35.24%16.51%20.75%32.65%35.45%吉林中國(guó)重汽35.71%32.77%20.16%20.00%13.95%35.71%東風(fēng)標(biāo)致36.92%33.33%31.07%25.93%33.33%36.92%南京依維34.62%33.33%29.93%60.00%50.00%34.62%柯東風(fēng)本田48.88%46.64%34.86%46.97%45.79%48.88%廣州豐田45.40%43.64%31

15、.15%45.00%45.10%45.40%一汽馬自43.75%40.63%26.76%47.62%45.16%43.75%達(dá)一汽轎車41.91%43.81%26.05%46.43%45.35%41.91%(紅旗昌河鈴木23.60%21.69%21.25%21.95%19.67%23.60%華晨中華39.29%35.71%26.07%36.84%36.36%39.29%北京(福0.00%2.17%1.52%0.00%0.00%0.00%田宇通45.45%33.33%42.86%28.57%25.00%45.45%鄭州日產(chǎn)45.83%47.62%38.30%56.00%42.86%45.83%南

16、駿63.64%66.67%5.56%100.00%100.00%63.64%南京菲亞44.44%44.44%34.55%33.33%50.00%44.44%特躍進(jìn)36.71%35.77%19.70%33.33%41.67%36.71%長(zhǎng)豐36.05%34.67%28.35%28.00%25.00%36.05%解放(一汽37.50%36.67%23.00%0.00%27.27%37.50%紅塔北汽43.27%40.22%20.99%47.06%64.29%43.27%品牌37.88%36.66%24.27%38.26%38.99%37.88%平均值30.44%30.48%44.34%28.91%

17、38.38%38.98%41.52%34.58%56.59%44.33%52.91%31.82%38.06%29.70%26.04%50.32%33.32%29.34%26.39%32.92%40.42%45.34%42.61%41.28%40.91%21.96%35.59%0.62%36.78%46.07%66.58%41.87%33.98%31.35%26.99%43.18%35.66%37.86%個(gè)人資料整理 僅限學(xué)習(xí)使用120.00%100.00%80.00%60.00%40.00%20.00%0.00%眾 安 代 杯 龍 瑞 放 木 亞利 城 致田 木通 特)值塔大 長(zhǎng) 現(xiàn) 金 鐵

18、奇 解 鈴 起吉 長(zhǎng) 標(biāo)豐 鈴宇 亞均紅海京雪安 達(dá)風(fēng)州 河菲平汽上北風(fēng)長(zhǎng) 悅東廣 昌京一東風(fēng)南(放東解東南42.86%23.53%44.44%47.37%42.86%40.21%東風(fēng)悅達(dá)51.72%44.61%56.02%53.79%51.72%51.57%起亞江鈴36.52%25.42%28.00%29.41%36.52%31.17%上海通用38.31%32.39%35.87%37.04%38.31%36.38%雪佛蘭吉利30.12%18.16%32.54%33.98%30.12%28.98%201011201011201012201101201102201103平均值個(gè)人資料整理 僅限學(xué)

19、習(xí)使用昌河26.83%19.19%23.26%28.57%26.83%24.94%海南馬自42.11%30.65%66.67%46.15%42.11%45.54%達(dá)長(zhǎng)城33.33%26.92%33.52%29.97%33.33%31.41%解放(一汽35.24%16.14%20.00%32.98%35.24%27.92%吉林中國(guó)重汽32.77%19.71%22.73%16.22%32.77%24.84%東風(fēng)標(biāo)致33.33%30.00%15.15%27.12%33.33%27.79%南京依維33.33%28.80%50.00%45.45%33.33%38.18%柯東風(fēng)本田46.64%34.90%

20、47.37%45.75%46.64%44.26%廣州豐田43.64%31.72%43.59%40.00%43.64%40.52%一汽馬自40.63%23.50%44.44%43.59%40.63%38.56%達(dá)一汽轎車43.81%23.33%48.84%45.45%43.81%41.05%(紅旗昌河鈴木21.69%19.49%21.05%19.30%21.69%20.64%華晨中華35.71%25.48%34.78%32.39%35.71%32.82%北京(福2.17%1.54%27.27%15.79%2.17%9.79%田宇通33.33%40.74%0.00%0.00%33.33%21.48

21、%鄭州日產(chǎn)47.62%37.35%65.00%46.67%47.62%48.85%南駿66.67%5.26%100.00%100.00%66.67%67.72%南京菲亞44.44%36.36%33.33%50.00%44.44%41.72%特躍進(jìn)35.77%19.37%33.33%39.02%35.77%32.65%長(zhǎng)豐34.67%25.31%26.09%25.00%34.67%29.15%解放(一汽36.67%23.39%0.00%27.27%36.67%24.80%紅塔北汽40.22%19.92%43.75%63.89%40.22%41.60%品牌36.66%22.46%37.21%37.

22、84%36.66%34.16%平均值36.65%120.00%100.00%80.00%60.00%40.00%20.00%0.00%眾 安 代 杯 龍 瑞 放 木 亞利 城 致田 木 通特)值塔大 長(zhǎng) 現(xiàn) 金 鐵 奇 解 鈴 起吉 長(zhǎng) 標(biāo)豐 鈴 宇亞均紅海京雪安 達(dá)風(fēng)州 河菲平汽上北風(fēng)長(zhǎng) 悅東廣 昌京一東風(fēng)南(放東解四)按照承保車輛使用性質(zhì)統(tǒng)計(jì)1)2018 年 9 月-2018 年 3 月當(dāng)年到期車輛續(xù)保率及圖象201011201012201101201102201103平均值201809201810201811201812201801201802201803家庭自用25.81%26.53%

23、26.48%27.05%35.68%36.81%36.37%黨政機(jī)關(guān)客36.01%36.45%36.41%36.36%42.79%43.73%43.97%車平均值30.68%39.39%個(gè)人資料整理 僅限學(xué)習(xí)使用企業(yè)客車42.66%43.50%43.57%43.89%53.57%56.29%53.28%非營(yíng)業(yè)貨車12.74%14.34%14.56%15.03%34.11%36.00%34.59%出租租賃31.72%32.29%32.56%33.28%75.08%70.26%50.97%城市公交70.83%70.72%70.67%70.80%90.91%86.36%72.22%公路客運(yùn)25.98

24、%26.64%26.36%27.04%20.59%20.00%32.00%營(yíng)業(yè)貨車17.59%17.81%17.32%17.42%30.26%33.64%34.55%特種車37.46%37.36%37.03%36.53%42.72%40.00%48.40%使用性質(zhì)23.22%23.88%23.78%24.27%38.26%38.99%37.88%平均值48.11%23.05%46.59%76.07%25.52%24.08%39.93%30.04%38.35%100.00%20100980.00%20101060.00%20101140.00%20101220.00%2011010.00%201

25、102201103平均值2)2018 年 9 月-2018 年 3 月目標(biāo)客戶續(xù)保率及圖像201809201810201811201812201801201802201803家庭自用23.57%24.40%24.46%24.85%34.25%35.28%34.71%黨政機(jī)關(guān)客33.99%34.12%34.07%34.39%39.19%40.21%40.97%車企業(yè)客車43.09%43.71%44.08%44.13%53.48%56.75%53.45%非營(yíng)業(yè)貨車12.14%13.76%14.02%14.43%33.12%35.48%34.25%出租租賃32.28%32.86%33.28%34.2

26、0%74.42%70.00%52.63%城市公交68.75%68.51%68.11%68.11%91.84%86.67%71.08%公路客運(yùn)27.89%29.65%29.41%30.56%18.75%18.18%28.89%營(yíng)業(yè)貨車16.61%16.86%16.56%16.77%30.36%33.31%33.50%特種車36.49%36.31%35.98%35.53%43.01%39.35%47.99%使用性質(zhì)21.28%22.00%22.03%22.46%37.21%37.84%36.66%平均值平均值28.79%36.71%48.38%22.46%47.10%74.72%26.19%23.

27、42%39.24%28.50%37.55%個(gè)人資料整理 僅限學(xué)習(xí)使用100.00%90.00%80.00%20100970.00%20101060.00%50.00%20101140.00%20101230.00%20.00%20110110.00%2011020.00%201103平均值五)按照承保渠道統(tǒng)計(jì)1 )2018 年 9 月-2018 年 3 月當(dāng)年到期車輛續(xù)保率及圖象201809201810201811201812201801201802201803電話銷售39.41%40.00%40.00%40.00%交叉銷售19.94%19.02%19.14%19.83%16.67%26.47

28、%28.79%車商渠道32.25%40.38%41.95%44.30%53.70%53.05%50.00%合計(jì)23.22%23.88%23.78%24.27%38.26%38.99%37.88%平均值平均值39.85%21.41%45.09%30.04%34.10%60.00%50.00%40.00%電話銷售30.00%交叉銷售20.00%車商渠道10.00%合計(jì)0.00%201009 201010 201011 201012 201101 201102 2011032)2018 年 9 月-2018 年 3 月目標(biāo)客戶續(xù)保率及圖像2018092018102018112018122018012

29、01802201803電話銷售48.40%25.00%25.00%25.00%交叉銷售16.94%16.54%16.73%17.67%13.33%23.33%27.12%車商渠道30.70%39.61%40.12%42.52%53.91%54.98%51.67%合計(jì)21.28%22.00%22.03%22.46%37.21%37.84%36.66%平均值平均值30.85%17.42%43.64%27.14%29.76%個(gè)人資料整理 僅限學(xué)習(xí)使用60.00%50.00%電話銷售40.00%交叉銷售30.00%20.00%車商渠道10.00%0.00%合計(jì)平均值六)按照新車購(gòu)買價(jià)統(tǒng)計(jì)萬(wàn)14.26%

30、14.59%14.85%15.45%31.55%33.80%31.26%5,10萬(wàn)24.26%24.62%24.56%25.10%39.30%39.61%37.70%10,2031.97%33.27%32.81%32.89%42.67%43.08%42.49%萬(wàn)20,3029.52%30.84%30.67%30.64%40.59%40.04%41.44%萬(wàn)30,5032.51%33.28%32.21%32.56%37.53%40.06%44.06%萬(wàn)50,10029.53%30.21%29.31%30.23%38.10%37.99%38.75%萬(wàn)100,33.92%33.94%31.02%30

31、.74%31.25%32.38%28.57%+萬(wàn)新車購(gòu)置23.22%23.88%23.78%24.27%38.26%38.99%37.88%價(jià)平均值平均值22.25%30.74%37.03%34.82%36.03%33.45%31.69%30.04%32.01%50.00%45.00%40.00%20100935.00%20101030.00%25.00%20101120.00%20101215.00%20110110.00%5.00%2011020.00%201103平均值萬(wàn)13.69%14.02%14.35%14.98%31.17%33.57%31.28%5,10萬(wàn)22.79%23.18%

32、23.17%23.65%37.81%38.13%36.28%平均值21.87%29.29%個(gè)人資料整理 僅限學(xué)習(xí)使用10,2030.82%32.46%32.21%32.03%41.85%42.31%40.87%萬(wàn)36.08%20,3028.09%29.57%29.43%29.05%40.49%38.70%40.44%萬(wàn)33.68%30,5031.71%32.56%31.16%31.18%38.25%39.57%44.22%萬(wàn)35.52%50,10028.57%29.10%28.64%29.50%41.13%39.33%40.30%萬(wàn)33.80%100,35.71%34.59%31.10%30.

33、00%19.51%23.08%22.88%+萬(wàn)28.13%新車購(gòu)置21.28%22.00%22.03%22.46%37.21%37.84%36.66%價(jià)28.50%平均值30.86%50.00%45.00%20100940.00%35.00%20101030.00%20101125.00%20.00%20101215.00%10.00%2011015.00%2011020.00%201103平均值( 二根據(jù)圖表可得出如下數(shù)據(jù):當(dāng)年到期車輛續(xù)保率目標(biāo)客戶續(xù)保率承保車輛出現(xiàn)次數(shù)34.32%11.84%承保車輛年齡26.93%26.16%承保車輛品牌37.86%36.65%承保車輛的使用性質(zhì)38.3

34、5%37.55%承保車輛的銷售渠道34.10%39.76%新車購(gòu)買價(jià)格的不同32.01%30.86%三)影響續(xù)保率的六種因素中相互之間有聯(lián)系,這些影響因素的重要性,影響力,或者優(yōu)先程度可以根據(jù)層析分析模型來定性和定量的描述。4. 模型的建立及求解一)層次分析法的基本步驟將續(xù)保率問題分解為三個(gè)層次,最上面的為目標(biāo)層,即續(xù)保率;中間的為準(zhǔn)則層,有承保車輛出現(xiàn)次數(shù),承保車輛年齡,承保車輛品牌,承保車輛的使用性質(zhì),承保車輛的銷售渠道,以及新車購(gòu)買價(jià)格的不同;最下層為方案層,各層間的聯(lián)系用相連的直線表示。(2)通過相互比較確定的影響因素對(duì)于續(xù)保率的權(quán)重,及方案對(duì)于每一準(zhǔn)則的權(quán)重,從而得到權(quán)重的定量方法。個(gè)人資料整理 僅限學(xué)習(xí)使用(3)將方案層對(duì)準(zhǔn)則層的權(quán)重及準(zhǔn)則層對(duì)目標(biāo)層的權(quán)重進(jìn)行綜合,最終確定方案層對(duì)目標(biāo)層的權(quán)重。續(xù)保率當(dāng)年到期車輛續(xù)保率目標(biāo)客戶續(xù)保率照承承承承新承保保保保車保車車車車輛輛輛渠購(gòu)輛年品使出齡牌用道買現(xiàn)性價(jià)次質(zhì)數(shù)二) 構(gòu)造成對(duì)比較矩陣設(shè)要比較的六個(gè)因素X x1, x2 , xn對(duì)續(xù)保率 Z 的影響,確定它們?cè)?Z中所占的比重。比較第i 個(gè)元素與第j 個(gè)元素相對(duì)上一層某個(gè)因素的重要性時(shí),使用數(shù)量化的相對(duì)權(quán)重 aij 來描述。共有6 個(gè)元素參與比較,則n=6 )稱為成對(duì)比較矩陣。成對(duì)比較矩陣中 aij 的取值可參考Satty 的提議,按下述標(biāo)度進(jìn)行賦值。aij 在

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