{"id":31029,"date":"2025-04-21T07:07:27","date_gmt":"2025-04-20T23:07:27","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/31029.html"},"modified":"2025-04-21T07:07:27","modified_gmt":"2025-04-20T23:07:27","slug":"%e3%80%90%e6%95%b0%e5%ad%a6%e5%bb%ba%e6%a8%a1%e3%80%91%e4%b8%80%e8%87%b4%e7%9f%a9%e9%98%b5%e7%9a%84%e5%ba%94%e7%94%a8%e5%8f%8a%e5%85%b6%e5%9c%a8%e5%b1%82%e6%ac%a1%e5%88%86%e6%9e%90%e6%b3%95ahp","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/31029.html","title":{"rendered":"\u3010\u6570\u5b66\u5efa\u6a21\u3011\u4e00\u81f4\u77e9\u9635\u7684\u5e94\u7528\u53ca\u5176\u5728\u5c42\u6b21\u5206\u6790\u6cd5(AHP)\u4e2d\u7684\u6027\u8d28"},"content":{"rendered":"

\u4e00\u81f4\u77e9\u9635\u5728\u5c42\u6b21\u5206\u6790\u6cd5(AHP)\u4e2d\u7684\u5e94\u7528\u4e0e\u6027\u8d28<\/h2>\n

\u5728\u5c42\u6b21\u5206\u6790\u6cd5(AHP)\u4e2d，\u4e00\u81f4\u77e9\u9635\u662f\u5224\u65ad\u77e9\u9635\u7684\u4e00\u79cd\u7406\u60f3\u72b6\u6001，\u5b83\u53cd\u6620\u4e86\u51b3\u7b56\u8005\u5224\u65ad\u7684\u5b8c\u5168\u5408\u7406\u6027\u548c\u4e00\u81f4\u6027，\u4e5f\u5c31\u662f\u4e3a\u4e86\u907f\u514d\u51b3\u7b56\u8005\u8ba4\u4e3a\u201cA\u6bd4B\u91cd\u8981，B\u6bd4C\u91cd\u8981，\u4f46\u662fC\u53c8\u6bd4A\u91cd\u8981\u201d\u7684\u77db\u76fe\u3002<\/p>\n

\u672c\u6587\u5c06\u8be6\u7ec6\u4ecb\u7ecd\u4e00\u81f4\u77e9\u9635\u7684\u5b9a\u4e49\u3001\u6027\u8d28\u53ca\u5176\u5728AHP\u4e2d\u7684\u91cd\u8981\u610f\u4e49\u3002<\/p>\n

\u5173\u4e8e\u5c42\u6b21\u5206\u6790\u6cd5(AHP)\u7684\u4ecb\u7ecd，\u53ef\u4ee5\u53c2\u8003：\u3010\u6570\u5b66\u5efa\u6a21\u3011\u5c42\u6b21\u5206\u6790\u6cd5(AHP)\u8be6\u89e3\u53ca\u5176\u5e94\u7528 \u3002<\/p>\n

\u4e00\u3001\u4e00\u81f4\u77e9\u9635\u7684\u5b9a\u4e49<\/h3>\n

\u5b9a\u4e49：\u8bbe <\/p>\n

A <\/p>\n

= <\/p>\n

[ <\/p>\n

a <\/p>\n

i <\/p>\n

j <\/p>\n

] <\/p>\n

n <\/p>\n

\u00d7 <\/p>\n

n <\/p>\n

A = [a_{ij}]_{n \\\\times n} <\/p>\n

<\/span><\/span>A<\/span><\/span>=<\/span><\/span><\/span><\/span>[<\/span>a<\/span><\/span>ij<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>]<\/span><\/span>n<\/span>\u00d7<\/span>n<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u662f\u5224\u65ad\u77e9\u9635，\u5982\u679c\u5bf9\u4e8e\u4efb\u610f\u7684 <\/p>\n

i <\/p>\n

, <\/p>\n

j <\/p>\n

, <\/p>\n

k <\/p>\n

\u2208 <\/p>\n

{ <\/p>\n

1 <\/p>\n

, <\/p>\n

2 <\/p>\n

, <\/p>\n

\u2026 <\/p>\n

, <\/p>\n

n <\/p>\n

} <\/p>\n

i, j, k \\\\in \\\\{1, 2, \\\\ldots, n\\\\} <\/p>\n

<\/span><\/span>i<\/span>,<\/span><\/span>j<\/span>,<\/span><\/span>k<\/span><\/span>\u2208<\/span><\/span><\/span><\/span>{<\/span>1<\/span>,<\/span><\/span>2<\/span>,<\/span><\/span>\u2026<\/span><\/span>,<\/span><\/span>n<\/span>}<\/span><\/span><\/span><\/span><\/span>，\u90fd\u6709：<\/p>\n

<\/p>\n

a <\/p>\n

i <\/p>\n

j <\/p>\n

\u22c5 <\/p>\n

a <\/p>\n

j <\/p>\n

k <\/p>\n

= <\/p>\n

a <\/p>\n

i <\/p>\n

k <\/p>\n

a_{ij} \\\\cdot a_{jk} = a_{ik} <\/p>\n

<\/span><\/span>a<\/span><\/span>ij<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>a<\/span><\/span>jk<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>a<\/span><\/span>ik<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5219\u79f0\u77e9\u9635 <\/p>\n

A <\/p>\n

A <\/p>\n

<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span>\u4e3a\u4e00\u81f4\u77e9\u9635\u3002<\/p>\n

\u8fd9\u4e00\u5b9a\u4e49\u8868\u660e，\u5728\u4e00\u81f4\u77e9\u9635\u4e2d，\u5143\u7d20 <\/p>\n

i <\/p>\n

i <\/p>\n

<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u5bf9\u5143\u7d20 <\/p>\n

k <\/p>\n

k <\/p>\n

<\/span><\/span>k<\/span><\/span><\/span><\/span><\/span>\u7684\u91cd\u8981\u6027\u53ef\u4ee5\u901a\u8fc7\u5143\u7d20 <\/p>\n

i <\/p>\n

i <\/p>\n

<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u5bf9\u5143\u7d20 <\/p>\n

j <\/p>\n

j <\/p>\n

<\/span><\/span>j<\/span><\/span><\/span><\/span><\/span>\u7684\u91cd\u8981\u6027\u4e0e\u5143\u7d20 <\/p>\n

j <\/p>\n

j <\/p>\n

<\/span><\/span>j<\/span><\/span><\/span><\/span><\/span>\u5bf9\u5143\u7d20 <\/p>\n

k <\/p>\n

k <\/p>\n

<\/span><\/span>k<\/span><\/span><\/span><\/span><\/span>\u7684\u91cd\u8981\u6027\u7684\u4e58\u79ef\u6765\u786e\u5b9a\u3002<\/p>\n

\u4e8c\u3001\u4e00\u81f4\u77e9\u9635\u7684\u57fa\u672c\u6027\u8d28<\/h3>\n

1. \u5012\u6570\u6027<\/h4>\n

\u4e00\u81f4\u77e9\u9635\u6ee1\u8db3\u5012\u6570\u6027，\u5373：<\/p>\n

<\/p>\n

a <\/p>\n

j <\/p>\n

i <\/p>\n

= <\/p>\n

1 <\/p>\n

a <\/p>\n

i <\/p>\n

j <\/p>\n

a_{ji} = \\\\frac{1}{a_{ij}} <\/p>\n

<\/span><\/span>a<\/span><\/span>ji<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>a<\/span><\/span>ij<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u8fd9\u8868\u793a\u5143\u7d20 <\/p>\n

j <\/p>\n

j <\/p>\n

<\/span><\/span>j<\/span><\/span><\/span><\/span><\/span>\u76f8\u5bf9\u4e8e\u5143\u7d20 <\/p>\n

i <\/p>\n

i <\/p>\n

<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u7684\u91cd\u8981\u6027\u662f\u5143\u7d20 <\/p>\n

i <\/p>\n

i <\/p>\n

<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u76f8\u5bf9\u4e8e\u5143\u7d20 <\/p>\n

j <\/p>\n

j <\/p>\n

<\/span><\/span>j<\/span><\/span><\/span><\/span><\/span>\u7684\u91cd\u8981\u6027\u7684\u5012\u6570\u3002<\/p>\n

2. \u4f20\u9012\u6027<\/h4>\n

\u4e00\u81f4\u77e9\u9635\u6ee1\u8db3\u4f20\u9012\u6027，\u5373：<\/p>\n

<\/p>\n

a <\/p>\n

i <\/p>\n

j <\/p>\n

\u22c5 <\/p>\n

a <\/p>\n

j <\/p>\n

k <\/p>\n

= <\/p>\n

a <\/p>\n

i <\/p>\n

k <\/p>\n

a_{ij} \\\\cdot a_{jk} = a_{ik} <\/p>\n

<\/span><\/span>a<\/span><\/span>ij<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>a<\/span><\/span>jk<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>a<\/span><\/span>ik<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u8fd9\u8868\u793a\u5224\u65ad\u7684\u4f20\u9012\u6027，\u662f\u4e00\u81f4\u77e9\u9635\u7684\u5b9a\u4e49\u4e0e\u6838\u5fc3\u7279\u5f81\u3002<\/p>\n

3. \u79e9\u4e3a1<\/h4>\n

\u4e00\u81f4\u77e9\u9635 <\/p>\n

A <\/p>\n

A <\/p>\n

<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span>\u7684\u79e9 <\/p>\n

r <\/p>\n

a <\/p>\n

n <\/p>\n

k <\/p>\n

( <\/p>\n

A <\/p>\n

) <\/p>\n

= <\/p>\n

1 <\/p>\n

rank(A) = 1 <\/p>\n

<\/span><\/span>r<\/span>ank<\/span>(<\/span>A<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>，\u5373\u4e00\u81f4\u77e9\u9635\u662f\u4e00\u4e2a\u79e91\u77e9\u9635\u3002<\/p>\n

4. \u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf<\/h4>\n

\u4e00\u81f4\u77e9\u9635 <\/p>\n

A <\/p>\n

A <\/p>\n

<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span>\u6709\u4e14\u4ec5\u6709\u4e00\u4e2a\u975e\u96f6\u7279\u5f81\u503c <\/p>\n

\u03bb <\/p>\n

m <\/p>\n

a <\/p>\n

x <\/p>\n

= <\/p>\n

n <\/p>\n

\\\\lambda_{max} = n <\/p>\n

<\/span><\/span>\u03bb<\/span><\/span>ma<\/span>x<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>n<\/span><\/span><\/span><\/span><\/span>，\u5bf9\u5e94\u7684\u7279\u5f81\u5411\u91cf\u6b63\u662f\u6743\u91cd\u5411\u91cf <\/p>\n

W <\/p>\n

W <\/p>\n

<\/span><\/span>W<\/span><\/span><\/span><\/span><\/span>\u3002\u5176\u4f59 <\/p>\n

n <\/p>\n

\u2212 <\/p>\n

1 <\/p>\n

n-1 <\/p>\n

<\/span><\/span>n<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u4e2a\u7279\u5f81\u503c\u5747\u4e3a0\u3002<\/p>\n

<\/p>\n

A <\/p>\n

\u22c5 <\/p>\n

W <\/p>\n

= <\/p>\n

n <\/p>\n

\u22c5 <\/p>\n

W <\/p>\n

A \\\\cdot W = n \\\\cdot W <\/p>\n

<\/span><\/span>A<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>W<\/span><\/span>=<\/span><\/span><\/span><\/span>n<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>W<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

5. \u8868\u793a\u5f62\u5f0f<\/h4>\n

\u4efb\u610f\u4e00\u81f4\u77e9\u9635 <\/p>\n

A <\/p>\n

A <\/p>\n

<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span>\u90fd\u53ef\u4ee5\u8868\u793a\u4e3a：<\/p>\n

<\/p>\n

A <\/p>\n

= <\/p>\n

[ <\/p>\n

w <\/p>\n

1 <\/p>\n

w <\/p>\n

1 <\/p>\n

w <\/p>\n

1 <\/p>\n

w <\/p>\n

2 <\/p>\n

\u22ef <\/p>\n

w <\/p>\n

1 <\/p>\n

w <\/p>\n

n <\/p>\n

w <\/p>\n

2 <\/p>\n

w <\/p>\n

1 <\/p>\n

w <\/p>\n

2 <\/p>\n

w <\/p>\n

2 <\/p>\n

\u22ef <\/p>\n

w <\/p>\n

2 <\/p>\n

w <\/p>\n

n <\/p>\n

\u22ee <\/p>\n

\u22ee <\/p>\n

\u22f1 <\/p>\n

\u22ee <\/p>\n

w <\/p>\n

n <\/p>\n

w <\/p>\n

1 <\/p>\n

w <\/p>\n

n <\/p>\n

w <\/p>\n

2 <\/p>\n

\u22ef <\/p>\n

w <\/p>\n

n <\/p>\n

w <\/p>\n

n <\/p>\n

] <\/p>\n

A = \\\\begin{bmatrix} \\\\frac{w_1}{w_1} & \\\\frac{w_1}{w_2} & \\\\cdots & \\\\frac{w_1}{w_n} \\\\\\\\ \\\\frac{w_2}{w_1} & \\\\frac{w_2}{w_2} & \\\\cdots & \\\\frac{w_2}{w_n} \\\\\\\\ \\\\vdots & \\\\vdots & \\\\ddots & \\\\vdots \\\\\\\\ \\\\frac{w_n}{w_1} & \\\\frac{w_n}{w_2} & \\\\cdots & \\\\frac{w_n}{w_n} \\\\end{bmatrix} <\/p>\n

<\/span><\/span>A<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span> <\/p>\n

<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>w<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>w<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>w<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>w<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u22ee<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>w<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>w<\/span><\/span>n<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>w<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>w<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>w<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>w<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u22ee<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>w<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>w<\/span><\/span>n<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u22ef<\/span><\/span><\/span><\/span>\u22ef<\/span><\/span><\/span><\/span>\u22f1<\/span><\/span><\/span><\/span>\u22ef<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>w<\/span><\/span>n<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>w<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>w<\/span><\/span>n<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>w<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u22ee<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>w<\/span><\/span>n<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>w<\/span><\/span>n<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> <\/p>\n

<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5176\u4e2d <\/p>\n

W <\/p>\n

= <\/p>\n

( <\/p>\n

w <\/p>\n

1 <\/p>\n

, <\/p>\n

w <\/p>\n

2 <\/p>\n

, <\/p>\n

\u2026 <\/p>\n

, <\/p>\n

w <\/p>\n

n <\/p>\n

) <\/p>\n

T <\/p>\n

W = (w_1, w_2, \\\\ldots, w_n)^T <\/p>\n

<\/span><\/span>W<\/span><\/span>=<\/span><\/span><\/span><\/span>(<\/span>w<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>w<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>\u2026<\/span><\/span>,<\/span><\/span>w<\/span><\/span>n<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>T<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u662f\u6743\u91cd\u5411\u91cf\u3002<\/p>\n

\u4e09\u3001\u4e00\u81f4\u77e9\u9635\u7684\u5224\u5b9a<\/h3>\n

1. \u5b9a\u4e49\u6cd5\u5224\u5b9a<\/h4>\n

\u68c0\u9a8c\u77e9\u9635 <\/p>\n

A <\/p>\n

A <\/p>\n

<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span>\u4e2d\u7684\u6240\u6709\u5143\u7d20\u662f\u5426\u6ee1\u8db3 <\/p>\n

a <\/p>\n

i <\/p>\n

j <\/p>\n

\u22c5 <\/p>\n

a <\/p>\n

j <\/p>\n

k <\/p>\n

= <\/p>\n

a <\/p>\n

i <\/p>\n

k <\/p>\n

a_{ij} \\\\cdot a_{jk} = a_{ik} <\/p>\n

<\/span><\/span>a<\/span><\/span>ij<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>a<\/span><\/span>jk<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>a<\/span><\/span>ik<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

2. \u7279\u5f81\u503c\u6cd5\u5224\u5b9a<\/h4>\n

\u8ba1\u7b97\u5224\u65ad\u77e9\u9635 <\/p>\n

A <\/p>\n

A <\/p>\n

<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span>\u7684\u6700\u5927\u7279\u5f81\u503c <\/p>\n

\u03bb <\/p>\n

m <\/p>\n

a <\/p>\n

x <\/p>\n

\\\\lambda_{max} <\/p>\n

<\/span><\/span>\u03bb<\/span><\/span>ma<\/span>x<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u5982\u679c <\/p>\n

\u03bb <\/p>\n

m <\/p>\n

a <\/p>\n

x <\/p>\n

= <\/p>\n

n <\/p>\n

\\\\lambda_{max} = n <\/p>\n

<\/span><\/span>\u03bb<\/span><\/span>ma<\/span>x<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>n<\/span><\/span><\/span><\/span><\/span>，\u5219 <\/p>\n

A <\/p>\n

A <\/p>\n

<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span>\u4e3a\u4e00\u81f4\u77e9\u9635\u3002<\/p>\n

3. \u4e00\u81f4\u6027\u6307\u6807\u5224\u5b9a<\/h4>\n

\u8ba1\u7b97\u4e00\u81f4\u6027\u6307\u6807 <\/p>\n

C <\/p>\n

I <\/p>\n

CI <\/p>\n

<\/span><\/span>C<\/span>I<\/span><\/span><\/span><\/span><\/span>：<\/p>\n

<\/p>\n

C <\/p>\n

I <\/p>\n

= <\/p>\n

\u03bb <\/p>\n

m <\/p>\n

a <\/p>\n

x <\/p>\n

\u2212 <\/p>\n

n <\/p>\n

n <\/p>\n

\u2212 <\/p>\n

1 <\/p>\n

CI = \\\\frac{\\\\lambda_{max} – n}{n-1} <\/p>\n

<\/span><\/span>C<\/span>I<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>n<\/span><\/span>\u2212<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03bb<\/span><\/span>ma<\/span>x<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>n<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5982\u679c <\/p>\n

C <\/p>\n

I <\/p>\n

= <\/p>\n

0 <\/p>\n

CI = 0 <\/p>\n

<\/span><\/span>C<\/span>I<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>，\u5219 <\/p>\n

A <\/p>\n

A <\/p>\n

<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span>\u4e3a\u4e00\u81f4\u77e9\u9635\u3002<\/p>\n

\u56db\u3001\u4e00\u81f4\u77e9\u9635\u7684\u6784\u9020<\/h3>\n

1. \u76f4\u63a5\u6784\u9020\u6cd5<\/h4>\n

\u5982\u679c\u5df2\u77e5\u6743\u91cd\u5411\u91cf <\/p>\n

W <\/p>\n

= <\/p>\n

( <\/p>\n

w <\/p>\n

1 <\/p>\n

, <\/p>\n

w <\/p>\n

2 <\/p>\n

, <\/p>\n

\u2026 <\/p>\n

, <\/p>\n

w <\/p>\n

n <\/p>\n

) <\/p>\n

T <\/p>\n

W = (w_1, w_2, \\\\ldots, w_n)^T <\/p>\n

<\/span><\/span>W<\/span><\/span>=<\/span><\/span><\/span><\/span>(<\/span>w<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>w<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>\u2026<\/span><\/span>,<\/span><\/span>w<\/span><\/span>n<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>T<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u5219\u53ef\u4ee5\u76f4\u63a5\u6784\u9020\u4e00\u81f4\u77e9\u9635：<\/p>\n

<\/p>\n

a <\/p>\n

i <\/p>\n

j <\/p>\n

= <\/p>\n

w <\/p>\n

i <\/p>\n

w <\/p>\n

j <\/p>\n

a_{ij} = \\\\frac{w_i}{w_j} <\/p>\n

<\/span><\/span>a<\/span><\/span>ij<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>w<\/span><\/span>j<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>w<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

2. \u4ece\u975e\u4e00\u81f4\u77e9\u9635\u5bfc\u51fa<\/h4>\n

\u5bf9\u4e8e\u975e\u4e00\u81f4\u77e9\u9635，\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u6b65\u9aa4\u6784\u9020\u6700\u63a5\u8fd1\u7684\u4e00\u81f4\u77e9\u9635：<\/p>\n

  • \u8ba1\u7b97\u975e\u4e00\u81f4\u77e9\u9635\u7684\u6743\u91cd\u5411\u91cf\n

    W <\/p>\n

    W <\/p>\n

    <\/span><\/span>W<\/span><\/span><\/span><\/span><\/span><\/li>\n

  • \u5229\u7528\n

    W <\/p>\n

    W <\/p>\n

    <\/span><\/span>W<\/span><\/span><\/span><\/span><\/span>\u6784\u9020\u4e00\u81f4\u77e9\u9635 <\/p>\n

    A <\/p>\n

    \u2032 <\/p>\n

    A' <\/p>\n

    <\/span><\/span>A<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u5176\u4e2d <\/p>\n

    a <\/p>\n

    i <\/p>\n

    j <\/p>\n

    \u2032 <\/p>\n

    = <\/p>\n

    w <\/p>\n

    i <\/p>\n

    w <\/p>\n

    j <\/p>\n

    a'_{ij} = \\\\frac{w_i}{w_j} <\/p>\n

    <\/span><\/span>a<\/span><\/span>ij<\/span><\/span><\/span><\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>w<\/span><\/span>j<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>w<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n

    \u4e94\u3001\u4e00\u81f4\u77e9\u9635\u5728AHP\u4e2d\u7684\u610f\u4e49<\/h3>\n

    1. \u7406\u60f3\u5224\u65ad\u7684\u6807\u51c6<\/h4>\n

    \u4e00\u81f4\u77e9\u9635\u4ee3\u8868\u4e86\u51b3\u7b56\u8005\u5224\u65ad\u7684\u5b8c\u5168\u4e00\u81f4\u6027，\u662f\u5224\u65ad\u77e9\u9635\u7684\u7406\u60f3\u72b6\u6001\u3002\u5728\u5b9e\u9645\u51b3\u7b56\u8fc7\u7a0b\u4e2d，\u7531\u4e8e\u4eba\u7684\u8ba4\u77e5\u9650\u5236，\u5f88\u96be\u76f4\u63a5\u7ed9\u51fa\u4e00\u81f4\u77e9\u9635，\u4f46\u5b83\u662f\u6211\u4eec\u8ffd\u6c42\u7684\u76ee\u6807\u3002<\/p>\n

    2. \u4e00\u81f4\u6027\u68c0\u9a8c\u7684\u57fa\u7840<\/h4>\n

    \u5728AHP\u4e2d，\u901a\u8fc7\u6bd4\u8f83\u5b9e\u9645\u5224\u65ad\u77e9\u9635\u4e0e\u4e00\u81f4\u77e9\u9635\u7684\u5dee\u5f02，\u6765\u8bc4\u4f30\u5224\u65ad\u7684\u4e00\u81f4\u6027\u7a0b\u5ea6\u3002\u4e00\u81f4\u6027\u6bd4\u7387 <\/p>\n

    C <\/p>\n

    R <\/p>\n

    CR <\/p>\n

    <\/span><\/span>CR<\/span><\/span><\/span><\/span><\/span>\u8d8a\u5c0f，\u8868\u793a\u5224\u65ad\u77e9\u9635\u8d8a\u63a5\u8fd1\u4e00\u81f4\u77e9\u9635，\u5224\u65ad\u7684\u4e00\u81f4\u6027\u8d8a\u597d\u3002<\/p>\n

    3. \u6743\u91cd\u8ba1\u7b97\u7684\u7406\u8bba\u4f9d\u636e<\/h4>\n

    \u4e00\u81f4\u77e9\u9635\u7684\u7279\u6027\u4e3aAHP\u4e2d\u6743\u91cd\u8ba1\u7b97\u63d0\u4f9b\u4e86\u7406\u8bba\u4f9d\u636e\u3002\u5bf9\u4e8e\u4e00\u81f4\u77e9\u9635，\u5176\u6743\u91cd\u5411\u91cf\u5c31\u662f\u5bf9\u5e94\u4e8e\u6700\u5927\u7279\u5f81\u503c\u7684\u7279\u5f81\u5411\u91cf\u3002<\/p>\n

    \u516d\u3001\u4e00\u81f4\u77e9\u9635\u4e0e\u975e\u4e00\u81f4\u77e9\u9635\u7684\u5173\u7cfb<\/h3>\n

    \u5728\u5b9e\u9645\u5e94\u7528\u4e2d，\u7531\u4e8e\u51b3\u7b56\u8005\u8ba4\u77e5\u7684\u5c40\u9650\u6027，\u901a\u5e38\u5f97\u5230\u7684\u662f\u975e\u4e00\u81f4\u77e9\u9635\u3002\u975e\u4e00\u81f4\u77e9\u9635\u4e0e\u4e00\u81f4\u77e9\u9635\u7684\u5173\u7cfb\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u65b9\u5f0f\u8868\u793a：<\/p>\n

    <\/p>\n

    A <\/p>\n

    = <\/p>\n

    A <\/p>\n

    \u2032 <\/p>\n

    + <\/p>\n

    E <\/p>\n

    A = A' + E <\/p>\n

    <\/span><\/span>A<\/span><\/span>=<\/span><\/span><\/span><\/span>A<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>E<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

    \u5176\u4e2d <\/p>\n

    A <\/p>\n

    A <\/p>\n

    <\/span><\/span>A<\/span><\/span><\/span><\/span><\/span>\u662f\u5b9e\u9645\u7684\u5224\u65ad\u77e9\u9635， <\/p>\n

    A <\/p>\n

    \u2032 <\/p>\n

    A' <\/p>\n

    <\/span><\/span>A<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u662f\u5bf9\u5e94\u7684\u4e00\u81f4\u77e9\u9635， <\/p>\n

    E <\/p>\n

    E <\/p>\n

    <\/span><\/span>E<\/span><\/span><\/span><\/span><\/span>\u662f\u8bef\u5dee\u77e9\u9635\u3002<\/p>\n

    AHP\u7684\u4e00\u81f4\u6027\u68c0\u9a8c\u5c31\u662f\u8bc4\u4f30\u8bef\u5dee\u77e9\u9635 <\/p>\n

    E <\/p>\n

    E <\/p>\n

    <\/span><\/span>E<\/span><\/span><\/span><\/span><\/span>\u7684\u5927\u5c0f，\u5224\u65ad\u5b9e\u9645\u77e9\u9635 <\/p>\n

    A <\/p>\n

    A <\/p>\n

    <\/span><\/span>A<\/span><\/span><\/span><\/span><\/span>\u4e0e\u7406\u60f3\u4e00\u81f4\u77e9\u9635 <\/p>\n

    A <\/p>\n

    \u2032 <\/p>\n

    A' <\/p>\n

    <\/span><\/span>A<\/span><\/span>\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u7684\u63a5\u8fd1\u7a0b\u5ea6\u3002<\/p>\n

    \u4e03\u3001\u4e00\u81f4\u77e9\u9635\u7684\u6570\u5b66\u8bc1\u660e\u793a\u4f8b<\/h3>\n

    \u547d\u98981：\u4e00\u81f4\u77e9\u9635\u7684\u6700\u5927\u7279\u5f81\u503c\u7b49\u4e8e\u77e9\u9635\u7684\u9636\u6570<\/h4>\n

    \u8bc1\u660e： \u8bbe <\/p>\n

    A <\/p>\n

    A <\/p>\n

    <\/span><\/span>A<\/span><\/span><\/span><\/span><\/span>\u662f <\/p>\n

    n <\/p>\n

    n <\/p>\n

    <\/span><\/span>n<\/span><\/span><\/span><\/span><\/span>\u9636\u4e00\u81f4\u77e9\u9635，\u6743\u91cd\u5411\u91cf\u4e3a <\/p>\n

    W <\/p>\n

    = <\/p>\n

    ( <\/p>\n

    w <\/p>\n

    1 <\/p>\n

    , <\/p>\n

    w <\/p>\n

    2 <\/p>\n

    , <\/p>\n

    \u2026 <\/p>\n

    , <\/p>\n

    w <\/p>\n

    n <\/p>\n

    ) <\/p>\n

    T <\/p>\n

    W = (w_1, w_2, \\\\ldots, w_n)^T <\/p>\n

    <\/span><\/span>W<\/span><\/span>=<\/span><\/span><\/span><\/span>(<\/span>w<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>w<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>\u2026<\/span><\/span>,<\/span><\/span>w<\/span><\/span>n<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>T<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u5219：<\/p>\n

    <\/p>\n

    a <\/p>\n

    i <\/p>\n

    j <\/p>\n

    = <\/p>\n

    w <\/p>\n

    i <\/p>\n

    w <\/p>\n

    j <\/p>\n

    a_{ij} = \\\\frac{w_i}{w_j} <\/p>\n

    <\/span><\/span>a<\/span><\/span>ij<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>w<\/span><\/span>j<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>w<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

    \u8003\u8651 <\/p>\n

    A <\/p>\n

    \u22c5 <\/p>\n

    W <\/p>\n

    A \\\\cdot W <\/p>\n

    <\/span><\/span>A<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>W<\/span><\/span><\/span><\/span><\/span>\u7684\u7b2c <\/p>\n

    i <\/p>\n

    i <\/p>\n

    <\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u884c\u5143\u7d20：<\/p>\n

    <\/p>\n

    \u2211 <\/p>\n

    j <\/p>\n

    = <\/p>\n

    1 <\/p>\n

    n <\/p>\n

    a <\/p>\n

    i <\/p>\n

    j <\/p>\n

    \u22c5 <\/p>\n

    w <\/p>\n

    j <\/p>\n

    = <\/p>\n

    \u2211 <\/p>\n

    j <\/p>\n

    = <\/p>\n

    1 <\/p>\n

    n <\/p>\n

    w <\/p>\n

    i <\/p>\n

    w <\/p>\n

    j <\/p>\n

    \u22c5 <\/p>\n

    w <\/p>\n

    j <\/p>\n

    = <\/p>\n

    w <\/p>\n

    i <\/p>\n

    \u2211 <\/p>\n

    j <\/p>\n

    = <\/p>\n

    1 <\/p>\n

    n <\/p>\n

    1 <\/p>\n

    = <\/p>\n

    n <\/p>\n

    \u22c5 <\/p>\n

    w <\/p>\n

    i <\/p>\n

    \\\\sum_{j=1}^{n} a_{ij} \\\\cdot w_j = \\\\sum_{j=1}^{n} \\\\frac{w_i}{w_j} \\\\cdot w_j = w_i \\\\sum_{j=1}^{n} 1 = n \\\\cdot w_i <\/p>\n

    <\/span><\/span><\/span>j<\/span>=<\/span>1<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>n<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>a<\/span><\/span>ij<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>w<\/span><\/span>j<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>j<\/span>=<\/span>1<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>n<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>w<\/span><\/span>j<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>w<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>w<\/span><\/span>j<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>w<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>j<\/span>=<\/span>1<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>n<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span>=<\/span><\/span><\/span><\/span>n<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>w<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

    \u56e0\u6b64， <\/p>\n

    A <\/p>\n

    \u22c5 <\/p>\n

    W <\/p>\n

    = <\/p>\n

    n <\/p>\n

    \u22c5 <\/p>\n

    W <\/p>\n

    A \\\\cdot W = n \\\\cdot W <\/p>\n

    <\/span><\/span>A<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>W<\/span><\/span>=<\/span><\/span><\/span><\/span>n<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>W<\/span><\/span><\/span><\/span><\/span>，\u5373 <\/p>\n

    n <\/p>\n

    n <\/p>\n

    <\/span><\/span>n<\/span><\/span><\/span><\/span><\/span>\u662f <\/p>\n

    A <\/p>\n

    A <\/p>\n

    <\/span><\/span>A<\/span><\/span><\/span><\/span><\/span>\u7684\u7279\u5f81\u503c，\u5bf9\u5e94\u7684\u7279\u5f81\u5411\u91cf\u662f <\/p>\n

    W <\/p>\n

    W <\/p>\n

    <\/span><\/span>W<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

    \u53c8\u56e0\u4e3a <\/p>\n

    r <\/p>\n

    a <\/p>\n

    n <\/p>\n

    k <\/p>\n

    ( <\/p>\n

    A <\/p>\n

    ) <\/p>\n

    = <\/p>\n

    1 <\/p>\n

    rank(A) = 1 <\/p>\n

    <\/span><\/span>r<\/span>ank<\/span>(<\/span>A<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>，\u6240\u4ee5 <\/p>\n

    A <\/p>\n

    A <\/p>\n

    <\/span><\/span>A<\/span><\/span><\/span><\/span><\/span>\u6709\u4e14\u4ec5\u6709\u4e00\u4e2a\u975e\u96f6\u7279\u5f81\u503c，\u5373 <\/p>\n

    \u03bb <\/p>\n

    m <\/p>\n

    a <\/p>\n

    x <\/p>\n

    = <\/p>\n

    n <\/p>\n

    \\\\lambda_{max} = n <\/p>\n

    <\/span><\/span>\u03bb<\/span><\/span>ma<\/span>x<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>n<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

    \u547d\u98982：\u4e00\u81f4\u77e9\u9635\u7684\u4e00\u81f4\u6027\u6307\u6807CI\u4e3a0<\/h4>\n

    \u8bc1\u660e： \u7531\u547d\u98981\u53ef\u77e5，\u4e00\u81f4\u77e9\u9635\u7684\u6700\u5927\u7279\u5f81\u503c <\/p>\n

    \u03bb <\/p>\n

    m <\/p>\n

    a <\/p>\n

    x <\/p>\n

    = <\/p>\n

    n <\/p>\n

    \\\\lambda_{max} = n <\/p>\n

    <\/span><\/span>\u03bb<\/span><\/span>ma<\/span>x<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>n<\/span><\/span><\/span><\/span><\/span>，\u56e0\u6b64：<\/p>\n

    <\/p>\n

    C <\/p>\n

    I <\/p>\n

    = <\/p>\n

    \u03bb <\/p>\n

    m <\/p>\n

    a <\/p>\n

    x <\/p>\n

    \u2212 <\/p>\n

    n <\/p>\n

    n <\/p>\n

    \u2212 <\/p>\n

    1 <\/p>\n

    = <\/p>\n

    n <\/p>\n

    \u2212 <\/p>\n

    n <\/p>\n

    n <\/p>\n

    \u2212 <\/p>\n

    1 <\/p>\n

    = <\/p>\n

    0 <\/p>\n

    CI = \\\\frac{\\\\lambda_{max} – n}{n-1} = \\\\frac{n – n}{n-1} = 0 <\/p>\n

    <\/span><\/span>C<\/span>I<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>n<\/span><\/span>\u2212<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03bb<\/span><\/span>ma<\/span>x<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>n<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>n<\/span><\/span>\u2212<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/span>n<\/span><\/span>\u2212<\/span><\/span>n<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

    \u516b\u3001\u4e00\u81f4\u77e9\u9635\u7684\u5b9e\u4f8b<\/h3>\n

    \u4f8b1：2\u9636\u4e00\u81f4\u77e9\u9635<\/h4>\n

    <\/p>\n

    A <\/p>\n

    = <\/p>\n

    [ <\/p>\n

    1 <\/p>\n

    2 <\/p>\n

    1 <\/p>\n

    2 <\/p>\n

    1 <\/p>\n

    ] <\/p>\n

    A = \\\\begin{bmatrix} 1 & 2 \\\\\\\\ \\\\frac{1}{2} & 1 \\\\end{bmatrix} <\/p>\n

    <\/span><\/span>A<\/span><\/span>=<\/span><\/span><\/span><\/span>[<\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

    \u9a8c\u8bc1：<\/p>\n

      \n
    • \n

      a <\/p>\n

      12 <\/p>\n

      \u22c5 <\/p>\n

      a <\/p>\n

      21 <\/p>\n

      = <\/p>\n

      2 <\/p>\n

      \u22c5 <\/p>\n

      1 <\/p>\n

      2 <\/p>\n

      = <\/p>\n

      1 <\/p>\n

      = <\/p>\n

      a <\/p>\n

      11 <\/p>\n

      a_{12} \\\\cdot a_{21} = 2 \\\\cdot \\\\frac{1}{2} = 1 = a_{11} <\/p>\n

      <\/span><\/span>a<\/span><\/span>12<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>a<\/span><\/span>21<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>2<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span>=<\/span><\/span><\/span><\/span>a<\/span><\/span>11<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n

    • \n

      a <\/p>\n

      21 <\/p>\n

      \u22c5 <\/p>\n

      a <\/p>\n

      12 <\/p>\n

      = <\/p>\n

      1 <\/p>\n

      2 <\/p>\n

      \u22c5 <\/p>\n

      2 <\/p>\n

      = <\/p>\n

      1 <\/p>\n

      = <\/p>\n

      a <\/p>\n

      22 <\/p>\n

      a_{21} \\\\cdot a_{12} = \\\\frac{1}{2} \\\\cdot 2 = 1 = a_{22} <\/p>\n

      <\/span><\/span>a<\/span><\/span>21<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>a<\/span><\/span>12<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>2<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span>=<\/span><\/span><\/span><\/span>a<\/span><\/span>22<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n

      \u6743\u91cd\u5411\u91cf： <\/p>\n

      W <\/p>\n

      = <\/p>\n

      ( <\/p>\n

      2 <\/p>\n

      \/ <\/p>\n

      3 <\/p>\n

      , <\/p>\n

      1 <\/p>\n

      \/ <\/p>\n

      3 <\/p>\n

      ) <\/p>\n

      T <\/p>\n

      W = (2\/3, 1\/3)^T <\/p>\n

      <\/span><\/span>W<\/span><\/span>=<\/span><\/span><\/span><\/span>(<\/span>2\/3<\/span>,<\/span><\/span>1\/3<\/span>)<\/span><\/span>T<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u4f8b2：3\u9636\u4e00\u81f4\u77e9\u9635<\/h4>\n

      <\/p>\n

      A <\/p>\n

      = <\/p>\n

      [ <\/p>\n

      1 <\/p>\n

      2 <\/p>\n

      6 <\/p>\n

      1 <\/p>\n

      2 <\/p>\n

      1 <\/p>\n

      3 <\/p>\n

      1 <\/p>\n

      6 <\/p>\n

      1 <\/p>\n

      3 <\/p>\n

      1 <\/p>\n

      ] <\/p>\n

      A = \\\\begin{bmatrix} 1 & 2 & 6 \\\\\\\\ \\\\frac{1}{2} & 1 & 3 \\\\\\\\ \\\\frac{1}{6} & \\\\frac{1}{3} & 1 \\\\end{bmatrix} <\/p>\n

      <\/span><\/span>A<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span> <\/p>\n

      <\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>6<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span><\/span>3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>6<\/span><\/span><\/span><\/span>3<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> <\/p>\n

      <\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u9a8c\u8bc1：<\/p>\n

        \n
      • \n

        a <\/p>\n

        12 <\/p>\n

        \u22c5 <\/p>\n

        a <\/p>\n

        23 <\/p>\n

        = <\/p>\n

        2 <\/p>\n

        \u22c5 <\/p>\n

        3 <\/p>\n

        = <\/p>\n

        6 <\/p>\n

        = <\/p>\n

        a <\/p>\n

        13 <\/p>\n

        a_{12} \\\\cdot a_{23} = 2 \\\\cdot 3 = 6 = a_{13} <\/p>\n

        <\/span><\/span>a<\/span><\/span>12<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>a<\/span><\/span>23<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>2<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>3<\/span><\/span>=<\/span><\/span><\/span><\/span>6<\/span><\/span>=<\/span><\/span><\/span><\/span>a<\/span><\/span>13<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n

      • \n

        a <\/p>\n

        21 <\/p>\n

        \u22c5 <\/p>\n

        a <\/p>\n

        13 <\/p>\n

        = <\/p>\n

        1 <\/p>\n

        2 <\/p>\n

        \u22c5 <\/p>\n

        6 <\/p>\n

        = <\/p>\n

        3 <\/p>\n

        = <\/p>\n

        a <\/p>\n

        23 <\/p>\n

        a_{21} \\\\cdot a_{13} = \\\\frac{1}{2} \\\\cdot 6 = 3 = a_{23} <\/p>\n

        <\/span><\/span>a<\/span><\/span>21<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>a<\/span><\/span>13<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>6<\/span><\/span>=<\/span><\/span><\/span><\/span>3<\/span><\/span>=<\/span><\/span><\/span><\/span>a<\/span><\/span>23<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n

      • \n

        a <\/p>\n

        31 <\/p>\n

        \u22c5 <\/p>\n

        a <\/p>\n

        12 <\/p>\n

        = <\/p>\n

        1 <\/p>\n

        6 <\/p>\n

        \u22c5 <\/p>\n

        2 <\/p>\n

        = <\/p>\n

        1 <\/p>\n

        3 <\/p>\n

        = <\/p>\n

        a <\/p>\n

        32 <\/p>\n

        a_{31} \\\\cdot a_{12} = \\\\frac{1}{6} \\\\cdot 2 = \\\\frac{1}{3} = a_{32} <\/p>\n

        <\/span><\/span>a<\/span><\/span>31<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>a<\/span><\/span>12<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>6<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>2<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>a<\/span><\/span>32<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n

        \u6743\u91cd\u5411\u91cf： <\/p>\n

        W <\/p>\n

        = <\/p>\n

        ( <\/p>\n

        6 <\/p>\n

        \/ <\/p>\n

        10 <\/p>\n

        , <\/p>\n

        3 <\/p>\n

        \/ <\/p>\n

        10 <\/p>\n

        , <\/p>\n

        1 <\/p>\n

        \/ <\/p>\n

        10 <\/p>\n

        ) <\/p>\n

        T <\/p>\n

        W = (6\/10, 3\/10, 1\/10)^T <\/p>\n

        <\/span><\/span>W<\/span><\/span>=<\/span><\/span><\/span><\/span>(<\/span>6\/10<\/span>,<\/span><\/span>3\/10<\/span>,<\/span><\/span>1\/10<\/span>)<\/span><\/span>T<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

        \u4e5d\u3001\u4e00\u81f4\u77e9\u9635\u5728\u5b9e\u9645\u51b3\u7b56\u4e2d\u7684\u5e94\u7528<\/h3>\n

        \u5728\u5b9e\u9645\u51b3\u7b56\u8fc7\u7a0b\u4e2d，\u4e00\u81f4\u77e9\u9635\u4e3b\u8981\u6709\u4ee5\u4e0b\u5e94\u7528：<\/p>\n

      • \n

        \u4f5c\u4e3a\u5224\u65ad\u77e9\u9635\u4e00\u81f4\u6027\u7684\u53c2\u8003\u6807\u51c6：\u901a\u8fc7\u8ba1\u7b97\u4e00\u81f4\u6027\u6bd4\u7387CR，\u8bc4\u4f30\u5b9e\u9645\u5224\u65ad\u77e9\u9635\u4e0e\u7406\u60f3\u4e00\u81f4\u77e9\u9635\u7684\u63a5\u8fd1\u7a0b\u5ea6\u3002<\/p>\n<\/li>\n

      • \n

        \u4fee\u6b63\u4e0d\u4e00\u81f4\u5224\u65ad：\u5f53\u5224\u65ad\u77e9\u9635\u7684\u4e00\u81f4\u6027\u4e0d\u6ee1\u8db3\u8981\u6c42\u65f6，\u53ef\u4ee5\u5229\u7528\u4e00\u81f4\u77e9\u9635\u7684\u6027\u8d28\u5bf9\u539f\u5224\u65ad\u77e9\u9635\u8fdb\u884c\u4fee\u6b63\u3002<\/p>\n<\/li>\n

      • \n

        \u7b80\u5316\u5224\u65ad\u8fc7\u7a0b：\u5229\u7528\u4e00\u81f4\u77e9\u9635\u7684\u4f20\u9012\u6027，\u53ef\u4ee5\u51cf\u5c11\u5224\u65ad\u7684\u6b21\u6570\u3002\u7406\u8bba\u4e0a，\u5bf9\u4e8e <\/p>\n

        n <\/p>\n

        n <\/p>\n

        <\/span><\/span>n<\/span><\/span><\/span><\/span><\/span>\u4e2a\u5143\u7d20，\u53ea\u9700\u8981 <\/p>\n

        n <\/p>\n

        \u2212 <\/p>\n

        1 <\/p>\n

        n-1 <\/p>\n

        <\/span><\/span>n<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u6b21\u5224\u65ad\u5c31\u53ef\u4ee5\u6784\u9020\u5b8c\u6574\u7684\u4e00\u81f4\u77e9\u9635\u3002<\/p>\n<\/li>\n

        \u5341\u3001\u7ed3\u8bed<\/h3>\n

        \u4e00\u81f4\u77e9\u9635\u4f5c\u4e3a\u5c42\u6b21\u5206\u6790\u6cd5\u4e2d\u7684\u7406\u60f3\u5224\u65ad\u72b6\u6001，\u4e3a\u6211\u4eec\u63d0\u4f9b\u4e86\u8bc4\u4f30\u5224\u65ad\u4e00\u81f4\u6027\u7684\u6807\u51c6\u3002\u867d\u7136\u5728\u5b9e\u9645\u51b3\u7b56\u4e2d\u5f88\u96be\u76f4\u63a5\u5f97\u5230\u5b8c\u5168\u4e00\u81f4\u7684\u5224\u65ad\u77e9\u9635，\u4f46\u901a\u8fc7\u4e00\u81f4\u6027\u68c0\u9a8c\u548c\u5fc5\u8981\u7684\u4fee\u6b63，\u6211\u4eec\u53ef\u4ee5\u4f7f\u5224\u65ad\u77e9\u9635\u5c3d\u53ef\u80fd\u63a5\u8fd1\u4e00\u81f4\u77e9\u9635，\u4ece\u800c\u63d0\u9ad8\u51b3\u7b56\u7684\u79d1\u5b66\u6027\u548c\u5408\u7406\u6027\u3002<\/p>\n

        \u7406\u89e3\u4e00\u81f4\u77e9\u9635\u7684\u6027\u8d28\u548c\u610f\u4e49，\u5bf9\u4e8e\u6b63\u786e\u5e94\u7528\u5c42\u6b21\u5206\u6790\u6cd5\u3001\u63d0\u9ad8\u591a\u51c6\u5219\u51b3\u7b56\u7684\u8d28\u91cf\u5177\u6709\u91cd\u8981\u4ef7\u503c\u3002<\/p>\n

        \n

        \u53c2\u8003\u6587\u732e<\/h3>\n
      • Saaty, T. L. (1980). The Analytic Hierarchy Process. New York: McGraw-Hill.<\/li>\n
      • \u5f90\u6cfd\u6c34. (2002). \u5c42\u6b21\u5206\u6790\u6cd5\u539f\u7406. \u5929\u6d25: \u5929\u6d25\u5927\u5b66\u51fa\u7248\u793e.<\/li>\n
      • \u8bb8\u6811\u67cf. (1995). \u5c42\u6b21\u5206\u6790\u6cd5. \u5317\u4eac: \u4e2d\u56fd\u4eba\u6c11\u5927\u5b66\u51fa\u7248\u793e.<\/li>\n
      • Saaty, T. L. (1977). A scaling method for priorities in hierarchical structures. Journal of Mathematical Psychology, 15(3), 234-281.<\/li>\n","protected":false},"excerpt":{"rendered":"

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