{"id":1076,"date":"2025-07-11T17:14:08","date_gmt":"2025-07-11T09:14:08","guid":{"rendered":"http:\/\/heqiwei.cn\/?p=1076"},"modified":"2025-07-11T17:22:11","modified_gmt":"2025-07-11T09:22:11","slug":"%e6%95%b0%e5%ad%a6%e5%bb%ba%e6%a8%a1-%e6%a8%a1%e7%b3%8a%e7%bb%bc%e5%90%88%e8%af%84%e4%bb%b7","status":"publish","type":"post","link":"https:\/\/heqiwei.cn\/index.php\/2025\/07\/11\/%e6%95%b0%e5%ad%a6%e5%bb%ba%e6%a8%a1-%e6%a8%a1%e7%b3%8a%e7%bb%bc%e5%90%88%e8%af%84%e4%bb%b7\/","title":{"rendered":"\u6570\u5b66\u5efa\u6a21\u2014\u2014\u6a21\u7cca\u7efc\u5408\u8bc4\u4ef7"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">\u6a21\u7cca\u7684\u6982\u5ff5<\/h2>\n\n\n\n<p>\u73b0\u5b9e\u4e2d\u7684\u8bb8\u591a\u73b0\u8c61\u53ca\u5173\u7cfb\u6bd4\u8f83\u6a21\u7cca\u3002\u5982\u9ad8\u4e0e\u77ee\uff0c \u957f\u4e0e\u77ed\uff0c\u5927\u4e0e\u5c0f\uff0c\u591a\u4e0e\u5c11\uff0c\u7a77\u4e0e\u5bcc\uff0c\u597d\u4e0e\u5dee\uff0c\u5e74\u8f7b\u4e0e\u5e74\u8001\u7b49\u3002\u8fd9\u7c7b\u73b0\u8c61\u4e0d\u6ee1\u8db3 \u201c\u975e\u6b64\u5373\u5f7c\u201d \u7684\u6392\u4e2d\u5f8b\uff0c\u800c\u5177\u6709 \u201c\u4ea6\u6b64\u4ea6\u5f7c\u201d \u7684\u6a21\u7cca\u6027\u3002\u9700\u8981\u6307\u51fa\u7684\u662f\uff0c\u6a21\u7cca\u4e0d\u786e\u5b9a\u4e0d\u540c\u4e8e\u968f\u673a\u4e0d\u786e\u5b9a\u3002\u968f\u673a\u4e0d\u786e\u5b9a\u662f\u56e0\u679c\u5f8b\u7834\u635f\u9020\u6210\u7684\u4e0d\u786e\u5b9a\uff0c\u800c\u6a21\u7cca\u4e0d\u786e\u5b9a\u662f\u7531\u4e8e<mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">\u6392\u4e2d\u5f8b\u7834\u635f<\/mark>\u9020\u6210\u7684\u4e0d\u786e\u5b9a\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u6a21\u7cca\u96c6\u5408\u7684\u57fa\u672c\u6982\u5ff5<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\u4f20\u7edf\u96c6\u5408\u7684\u6982\u5ff5<\/h3>\n\n\n\n<p>\u4f20\u7edf\u96c6\u5408\u662f\u6307\u5177\u6709\u76f8\u540c\u5c5e\u6027\u7684\u4e8b\u7269\u7684\u96c6\u4f53\uff0c\u5982\u6b63\u6574\u6570\u96c6\u5408\uff0c\u5177\u6709\u5982\u4e0b\u6027\u8d28\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u4e92\u5f02\u6027<\/strong>\uff1a\u96c6\u5408\u4e2d\u4efb\u610f\u4e24\u4e2a\u5143\u7d20\u90fd\u662f\u4e0d\u540c\u7684\u5bf9\u8c61\uff0c\u5982[math]\\{1 1 2\\}[\/math]\u548c[math]\\{1 2\\}[\/math]\u8fd9\u4e24\u4e2a\u96c6\u5408\u662f\u7b49\u4ef7\u7684\uff1b<\/li>\n\n\n\n<li><strong>\u903b\u8f91\u6027<\/strong>\uff1a\u6bcf\u4e00\u4e2a\u5bf9\u8c61\u90fd\u80fd\u786e\u5b9a\u662f\u4e0d\u662f\u67d0\u4e00\u96c6\u5408\u7684\u5143\u7d20\uff0c\u8fd9\u4e2a\u6027\u8d28\u4e3b\u8981\u7528\u4e8e\u5224\u65ad\u4e00\u4e2a\u96c6\u5408\u662f\u5426\u80fd\u5f62\u6210\u96c6\u5408\uff1b<\/li>\n\n\n\n<li><strong>\u72ec\u7acb\u6027<\/strong>\uff1a\u96c6\u5408\u7684\u57fa\u6570\u3001\u96c6\u5408\u672c\u8eab\u7684\u4e2a\u6570\u5fc5\u987b\u4e3a\u81ea\u7136\u6570\uff1b<\/li>\n\n\n\n<li><strong>\u65e0\u5e8f\u6027<\/strong>\uff1a[math]\\{a b c\\}[\/math]\u548c[math]\\{c b a\\}[\/math]\u662f\u540c\u4e00\u4e2a\u96c6\u5408\uff1b<\/li>\n\n\n\n<li><strong>\u7eaf\u7cb9\u6027<\/strong>\uff1a\u6240\u8c13\u96c6\u5408\u7684\u7eaf\u7cb9\u6027\uff0c\u7528\u4e2a\u4f8b\u5b50\u6765\u8868\u793a\uff0c\u96c6\u5408[math]A = \\{x|x &lt; 2\\}[\/math]\uff0c\u96c6\u5408A\u4e2d\u6240\u6709\u7684\u5143\u7d20\u90fd\u8981\u7b26\u5408[math] x &lt; 2 [\/math]\uff1b<\/li>\n\n\n\n<li><strong>\u5b8c\u5907\u6027<\/strong>\uff1a\u4ecd\u7528\u4e0a\u9762\u7684\u4f8b\u5b50\uff0c\u6240\u6709\u7b26\u5408[math] x &lt; 2 [\/math]\u7684\u6570\u90fd\u5728\u96c6\u5408A\u4e2d\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u4f20\u7edf\u96c6\u5408\u7684\u7279\u5f81\u51fd\u6570<\/h3>\n\n\n\n<p>\u5b9a\u4e49[math]U[\/math]\u4e3a\u8bba\u57df\uff0c[math]f_A[\/math]\u662f[math]A[\/math]\u96c6\u5408\u7684\u7279\u5f81\u51fd\u6570\uff0c\u6709\uff1a[math] f_A:U \\to \\{0, 1\\}[\/math]<\/p>\n\n\n\n<p>\u6240\u8c13\u8bba\u57df\u53ef\u7b80\u5355\u7406\u89e3\u4e3a\u6211\u4eec\u8981\u7814\u7a76\u7684\u96c6\u5408\uff0c\u4e0a\u9762\u516c\u5f0f\u610f\u4e49\u662f\u5c06[math]U[\/math]\u8fd9\u4e2a\u8bba\u57df\u6620\u5c04\u5230[math]\\{0, 1\\}[\/math]\u8fd9\u4e2a\u96c6\u5408\u5185\uff0c\u8fd9\u91cc\u7684\u5192\u53f7\u53ef\u7406\u89e3\u6210\u201c\u4f5c\u7528\u4e8e\u201d\u7684\u610f\u601d\u3002<\/p>\n\n\n\n<p>\u4f8b\u5982\uff1a\u53ca\u683c\u96c6\u5408[math]A = \\{60, 61, 62, \\dots, 100\\}[\/math]\uff0c[math]f_A = \\begin{cases} 1, &amp; \\text{\u6210\u7ee9} \\geq 60 \\\\ 0, &amp; \\text{\u6210\u7ee9} \\lt 60 \\end{cases}[\/math]\uff0c<\/p>\n\n\n\n<p>\u5168\u73ed\u6210\u7ee9\u96c6\u5408[math]U = \\{78, 97, 43, \\dots, 59\\}[\/math]\u5219\u53ef\u4ee5\u8868\u793a\u4e3a\uff1a[math]f_A(x) = \\begin{cases} 1, &amp; x \\in A \\\\ 0, &amp; x \\notin A \\end{cases}, \\forall x \\in U[\/math]\uff0c\u5373\u5c06[math]U[\/math]\u8fd9\u4e2a\u96c6\u5408\u6309\u7167[math]f_A[\/math]\u7684\u7279\u5f81\uff0c\u6620\u5c04\u6210\u4e86\u4e00\u4e2a\u65b0\u7684[math]\\{0, 1\\}[\/math]\u96c6\u5408\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u6a21\u7cca\u96c6\u5408\u7684\u96b6\u5c5e\u51fd\u6570<\/h3>\n\n\n\n<p>\u5b9a\u4e49[math]U[\/math]\u4e3a\u8bba\u57df\uff0c[math]\\mu_A [\/math] \u662f [math] A [\/math] \u96c6\u5408\u7684\u7279\u5f81\u51fd\u6570\uff0c\u6709\uff1a[math]\\mu_A:U \\to [0, 1][\/math]\uff08\u6ce8\u610f\u8fd9\u91cc\u662f\u95ed\u533a\u95f4\uff09<\/p>\n\n\n\n<p>\u8fd9\u91cc\u7684 [math] A = \\text {\u201c\u5e74\u8f7b\u201d}[\/math]\uff0c[math] U = (0, 120)[\/math]<\/p>\n\n\n\n<p>\u5b9a\u4e49\u96b6\u5c5e\u51fd\u6570\uff1a<\/p>\n\n\n\n<p>[math]\\mu_A = \\begin{cases} <br>1, &amp; 0 &lt; x &lt; 20 \\\\ <br>\\dfrac{40 &#8211; x}{20}, &amp; 20 \\leq x \\leq 40 \\\\ <br>0, &amp; 40 &lt; x &lt; 120 <br>\\end{cases}[\/math]<\/p>\n\n\n\n<p>\u5bf9\u4e8e [math] U [\/math] \u4e2d\u7684\u6bcf\u4e00\u4e2a\u5143\u7d20\uff0c\u5747\u5bf9\u5e94\u4e8e [math] A [\/math] \u4e2d\u7684\u4e00\u4e2a\u96b6\u5c5e\u5ea6\uff0c\u96b6\u5c5e\u5ea6\u4ecb\u4e8e [math][0, 1][\/math]\uff0c\u8d8a\u5927\u8868\u793a\u8d8a\u5c5e\u4e8e\u8fd9\u4e2a\u96c6\u5408\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u6a21\u7cca\u96c6\u5408\u7684\u8868\u793a\u65b9\u6cd5<\/h3>\n\n\n\n<p>\u5bf9\u4e8e\u8bba\u57df [math] U = \\{x_1, x_2, \\ldots, x_n\\}[\/math]\uff0c\u6a21\u7cca\u96c6\u5408\u4e3a [math] A [\/math]\uff0c\u96b6\u5c5e\u5ea6\u4e3a[math] A (x_i) \\ (i = 1, 2, \\ldots, n)[\/math]<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u624e\u5fb7\u8868\u793a\u6cd5<\/strong>\uff1a[math] A = \\frac {A (x_1)}{x_1} + \\frac {A (x_2)}{x_2} + \\ldots + \\frac {A (x_n)}{x_n}[\/math]\uff08\u6ce8\uff1a\u8fd9\u91cc\u7684 [math]+[\/math] \u53f7\u5e76\u975e\u662f\u76f8\u52a0\u7684\u610f\u601d\uff0c\u800c\u4ec5\u4ec5\u8868\u793a\u8bb0\u6cd5\uff09\uff1b<\/li>\n\n\n\n<li><strong>\u5e8f\u5076\u8868\u793a\u6cd5<\/strong>\uff1a[math]\\{(x_1, A(x_1)), (x_2, A(x_2)), \\ldots, (x_n, A(x_n))\\}[\/math]\uff1b<\/li>\n\n\n\n<li><strong>\u5411\u91cf\u8868\u793a\u6cd5<\/strong>\uff1a[math] A = \\{A (x_1), A (x_2), \\ldots, A (x_n)\\}[\/math]\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u6a21\u7cca\u96c6\u5408\u4e0e\u7279\u5f81\u51fd\u6570\u7684\u5173\u7cfb<\/h3>\n\n\n\n<p>\u5f53\u8bba\u57df [math] U [\/math] \u4e3a\u65e0\u9650\u96c6\u65f6\uff0c[math] U [\/math] \u4e0a\u7684\u6a21\u7cca\u96c6 [math] A = \\int_{x \\in U} \\frac {\\mu_A (x)}{x} dx [\/math]<\/p>\n\n\n\n<p>\u4f8b\u5982\u5bf9\u4e8e\u96b6\u5c5e\u51fd\u6570[math]\\mu_A = \\begin{cases} 1, &amp; 0 &lt; x &lt; 20 \\\\ \\dfrac{40 &#8211; x}{20}, &amp; 20 \\leq x \\leq 40 \\\\ 0, &amp; 40 &lt; x &lt; 120 \\end{cases}[\/math]\uff0c\u6c42\u5176\u6a21\u7cca\u96c6 [math] A [\/math]\u5f97\uff1a<\/p>\n\n\n\n<p class=\"has-text-align-left\">[math]A = \\int_{x \\in [0, 20]} \\frac{1}{x} dx + \\int_{x \\in [20, 40]} \\frac{\\frac{40 &#8211; x}{20}}{x} dx + \\int_{x \\in [40, 120]} \\frac{0}{x} dx[\/math]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u6a21\u7cca\u96c6\u5408\u7684\u5206\u7c7b<\/h3>\n\n\n\n<figure class=\"wp-block-table\">\n<table class=\"has-fixed-layout\" style=\"vertical-align: middle;\">\n<thead>\n<tr>\n<th class=\"has-text-align-center\" style=\"vertical-align: middle;\" data-align=\"center\">\u6781\u5c0f\u578b\uff08\u5e74\u8f7b\u3001\u5c0f\u3001\u51b7\uff09<\/th>\n<th class=\"has-text-align-center\" style=\"vertical-align: middle;\" data-align=\"center\">\u4e2d\u95f4\u578b\uff08\u4e2d\u5e74\u3001\u4e2d\u3001\u6696\uff09<\/th>\n<th class=\"has-text-align-center\" style=\"vertical-align: middle;\" data-align=\"center\">\u6781\u5927\u578b\uff08\u8001\u5e74\u3001\u5927\u3001\u70ed\uff09<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td class=\"has-text-align-center\" style=\"vertical-align: middle;\" data-align=\"center\">[math]\\mu_A(x) = \\begin{cases} 1, &amp; x &lt; a \\\\ \\dfrac{b &#8211; x}{b &#8211; a}, &amp; a \\leq x \\leq b \\\\ 0, &amp; x &gt; b \\end{cases}[\/math]<\/td>\n<td class=\"has-text-align-center\" style=\"vertical-align: middle;\" data-align=\"center\">[math]\\mu_A(x) = \\begin{cases} 0, &amp; x &lt; a \\\\ \\dfrac{x &#8211; a}{b &#8211; a}, &amp; a \\leq x &lt; b \\\\ 1, &amp; b \\leq x &lt; c \\\\ \\dfrac{d &#8211; x}{d &#8211; c}, &amp; c \\leq x &lt; d \\\\ 0, &amp; x \\geq d \\end{cases}[\/math]<\/td>\n<td class=\"has-text-align-center\" style=\"vertical-align: middle;\" data-align=\"center\">[math]\\mu_A(x) = \\begin{cases} 0, &amp; x &lt; a \\\\ \\dfrac{x &#8211; a}{b &#8211; a}, &amp; a \\leq x \\leq b \\\\ 1, &amp; x &gt; b \\end{cases}[\/math]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">\u96b6\u5c5e\u51fd\u6570\u7684\u786e\u5b9a\u65b9\u6cd5<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">F\u5206\u5e03\u786e\u5b9a\u96b6\u5c5e\u51fd\u6570<\/h3>\n\n\n\n<!DOCTYPE html>\n<html lang=\"zh-CN\">\n\n<head>\n  <meta charset=\"UTF-8\">\n  <style>\n    \/* \u8868\u683c\u6574\u4f53\u6837\u5f0f\uff0c\u8bbe\u7f6e\u8fb9\u6846\u5408\u5e76\uff0c\u65b9\u4fbf\u540e\u7eed\u8c03\u6574 *\/\n    table {\n      border-collapse: collapse;\n      width: 100%;\n      \/* \u8ba9\u8868\u683c\u5c3d\u91cf\u5360\u6ee1\u5bb9\u5668\u5bbd\u5ea6\uff0c\u53ef\u6839\u636e\u9700\u6c42\u8c03\u6574 *\/\n    }\n\n    \/* \u8868\u5934\u5355\u5143\u683c\u6837\u5f0f *\/\n    th {\n      border: 1px solid #000;\n      \/* \u8868\u5934\u8fb9\u6846 *\/\n      padding: 8px;\n      \/* \u5185\u8fb9\u8ddd\uff0c\u63a7\u5236\u5185\u5bb9\u4e0e\u8fb9\u6846\u8ddd\u79bb *\/\n      text-align: center;\n      \/* \u6c34\u5e73\u5c45\u4e2d *\/\n      vertical-align: middle;\n      \/* \u7ad6\u76f4\u5c45\u4e2d *\/\n      font-size: 15px;\n      \/* \u5047\u8bbe\u539f\u672c\u9ed8\u8ba4\u5b57\u53f716\uff0c\u7f29\u5c0f1\u4e3a15\uff0c\u53ef\u6839\u636e\u5b9e\u9645\u9ed8\u8ba4\u503c\u8c03\u6574 *\/\n    }\n\n    \/* \u6570\u636e\u5355\u5143\u683c\u6837\u5f0f *\/\n    td {\n      border: 1px solid #000;\n      \/* \u5355\u5143\u683c\u8fb9\u6846 *\/\n      padding: 8px;\n      \/* \u5185\u8fb9\u8ddd *\/\n      vertical-align: middle;\n      \/* \u7ad6\u76f4\u5c45\u4e2d *\/\n      font-size: 14px;\n      \/* \u5047\u8bbe\u539f\u672c\u9ed8\u8ba4\u5b57\u53f715\uff0c\u7f29\u5c0f1\u4e3a14\uff0c\u53ef\u6839\u636e\u5b9e\u9645\u9ed8\u8ba4\u503c\u8c03\u6574 *\/\n    }\n\n    \/* \u6700\u5de6\u4fa7\u5217\uff08\u7c7b\u578b\u5217\uff09\u6c34\u5e73\u5c45\u4e2d *\/\n    td:first-child {\n      text-align: center;\n    }\n\n    \/* \u5176\u4f59\u975e\u8868\u5934\u5355\u5143\u683c\uff08\u9664\u7b2c\u4e00\u5217\uff09\u9760\u5de6\u5bf9\u9f50 *\/\n    td:not(:first-child) {\n      text-align: left;\n    }\n\n    \/* \u82e5\u8981\u8ba9\u6570\u5b66\u516c\u5f0f\u6e32\u67d3\u66f4\u9002\u914d\uff0c\u53ef\u8865\u5145\u9488\u5bf9 math \u6807\u7b7e\u7684\u6837\u5f0f\uff08\u82e5\u4f7f\u7528\u7279\u5b9a\u6e32\u67d3\u5e93\u53ef\u80fd\u9700\u914d\u5408\u8c03\u6574\uff09 *\/\n    math {\n      display: inline-block;\n      vertical-align: middle;\n    }\n  <\/style>\n<\/head>\n\n<body>\n  <table>\n    <thead>\n      <tr>\n        <th>\u7c7b\u578b<\/th>\n        <th>\u6781\u5c0f\u578b<\/th>\n        <th>\u4e2d\u95f4\u578b<\/th>\n        <th>\u6781\u5927\u578b<\/th>\n      <\/tr>\n    <\/thead>\n    <tbody>\n      <tr>\n        <td>\u77e9\u9635\u578b<\/td>\n        <td>[math]\\mu_A = \\begin{cases} 1, &#038; x \\leq a \\\\ 0, &#038; x > a \\end{cases}[\/math]<\/td>\n        <td>[math]\\mu_A = \\begin{cases} 1, &#038; a \\leq x \\leq b \\\\ 0, &#038; x < a \\text{\u6216} x > b \\end{cases}[\/math]<\/td>\n        <td>[math]\\mu_A = \\begin{cases} 1, &#038; x \\geq a \\\\ 0, &#038; x < a \\end{cases}[\/math]<\/td>\n      <\/tr>\n      <tr>\n        <td>\u68af\u5f62\u578b<\/td>\n        <td>[math]\\mu_A = \\begin{cases} 1, &#038; x \\leq a \\\\ \\dfrac{b &#8211; x}{b &#8211; a}, &#038; a \\leq x \\leq b \\\\ 0, &#038; x > b \\end{cases}[\/math]<\/td>\n        <td>[math]\\mu_A = \\begin{cases} \\dfrac{x &#8211; a}{b &#8211; a}, &#038; a \\leq x \\leq b \\\\ 1, &#038; b \\leq x \\leq c \\\\ \\dfrac{d &#8211; x}{d &#8211; c}, &#038; c \\leq x \\leq d \\\\ 0, &#038; x < a, x \\geq d \\end{cases}[\/math]<\/td>\n        <td>[math]\\mu_A = \\begin{cases} 0, &#038; x < a \\\\ \\dfrac{x - a}{b - a}, &#038; a \\leq x \\leq b \\\\ 1, &#038; x > b \\end{cases}[\/math]<\/td>\n      <\/tr>\n      <tr>\n        <td>k\u6b21\u629b\u7269\u578b<\/td>\n        <td>[math]\\mu_A = \\begin{cases} 1, &#038; x \\leq a \\\\ \\left( \\dfrac{b &#8211; x}{b &#8211; a} \\right)^k, &#038; a \\leq x \\leq b \\\\ 0, &#038; x > b \\end{cases}[\/math]<\/td>\n        <td>[math]\\mu_A = \\begin{cases} \\left( \\dfrac{x &#8211; a}{b &#8211; a} \\right)^k, &#038; a \\leq x \\leq b \\\\ 1, &#038; b \\leq x \\leq c \\\\ \\left( \\dfrac{d &#8211; x}{d &#8211; c} \\right)^k, &#038; c \\leq x \\leq d \\\\ 0, &#038; x < a, x \\geq d \\end{cases}[\/math]<\/td>\n        <td>[math]\\mu_A = \\begin{cases} 0, &#038; x < a \\\\ \\left( \\dfrac{x - a}{b - a} \\right)^k, &#038; a \\leq x \\leq b \\\\ 1, &#038; x > b \\end{cases}[\/math]<\/td>\n      <\/tr>\n      <tr>\n        <td>\u0393\u578b<\/td>\n        <td>[math]\\mu_A = \\begin{cases} 1, &#038; x \\leq a \\\\ e^{-k(x &#8211; a)}, &#038; x > a \\end{cases}[\/math]<\/td>\n        <td>[math]\\mu_A = \\begin{cases} e^{k(x &#8211; a)}, &#038; x < a \\\\ 1, &#038; a \\leq x \\leq b \\\\ e^{-k(x - a)}, &#038; x > b \\end{cases}[\/math]<\/td>\n        <td>[math]\\mu_A = \\begin{cases} 0, &#038; x < a \\\\ 1 - e^{-k(x - a)}, &#038; x \\geq a \\end{cases}[\/math]<\/td>\n      <\/tr>\n      <tr>\n        <td>\u6b63\u6001\u578b<\/td>\n        <td>[math]\\mu_A = \\begin{cases} 1, &#038; x \\leq a \\\\ \\exp\\left\\{ -\\left( \\dfrac{x &#8211; a}{\\sigma} \\right)^2 \\right\\}, &#038; x > a \\end{cases}[\/math]<\/td>\n        <td>[math]\\mu_A = \\exp\\left\\{ -\\left( \\dfrac{x &#8211; a}{\\sigma} \\right)^2 \\right\\}[\/math]<\/td>\n        <td>[math]\\mu_A = \\begin{cases} 0, &#038; x \\leq a \\\\ 1 &#8211; \\exp\\left\\{ -\\left( \\dfrac{x &#8211; a}{\\sigma} \\right)^2 \\right\\}, &#038; x > a \\end{cases}[\/math]<\/td>\n      <\/tr>\n      <tr>\n        <td>\u67ef\u897f\u578b<\/td>\n        <td>\n          [math]\\mu_A = \\begin{cases} 1, &#038; x \\leq a \\\\ \\dfrac{1}{1 + \\alpha(x &#8211; a)^\\beta}, &#038; x > a \\end{cases}[\/math] <br>\n          [math](\\alpha > 0, \\beta > 0)[\/math]\n        <\/td>\n        <td>\n          [math]\\mu_A = \\dfrac{1}{1 + \\alpha(x &#8211; a)^\\beta}[\/math] <br>\n          [math](\\alpha > 0, \\beta \\text{\u4e3a\u6b63\u5076\u6570})[\/math]\n        <\/td>\n        <td>\n          [math]\\mu_A = \\begin{cases} 0, &#038; x \\leq a \\\\ \\dfrac{1}{1 + \\alpha(x &#8211; a)^{-\\beta}}, &#038; x > a \\end{cases}[\/math] <br>\n          [math](\\alpha > 0, \\beta > 0)[\/math]\n        <\/td>\n      <\/tr>\n    <\/tbody>\n  <\/table>\n<\/body>\n\n<\/html>\n\n\n\n<h2 class=\"wp-block-heading\">\u6a21\u7cca\u7efc\u5408\u8bc4\u4ef7<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\u6a21\u7cca\u7efc\u5408\u8bc4\u4ef7\u7684\u5b9a\u4e49<\/h3>\n\n\n\n<p><strong>\u8bf4\u6cd5\u4e00<\/strong>\uff1a\u5c31\u662f\u4ee5\u6a21\u7cca\u6570\u5b66\u4e3a\u57fa\u7840\uff0c\u5c06\u4e00\u4e9b\u8fb9\u754c\u4e0d\u6e05\u3001\u4e0d\u6613\u5b9a\u91cf\u7684\u56e0\u7d20\u5b9a\u91cf\u5316.<\/p>\n\n\n\n<p><strong>\u8bf4\u6cd5\u4e8c<\/strong>\uff1a\u8981\u628a\u8bba\u57df\u4e2d\u7684\u5bf9\u8c61\u5bf9\u5e94\u8bc4\u8bed\u96c6\u4e2d\u4e00\u4e2a\u6307\u5b9a\u7684\u8bc4\u8bed.<\/p>\n\n\n\n<p><strong>\u8bf4\u6cd5\u4e09<\/strong>\uff1a\u5c06\u65b9\u6848\u4f5c\u4e3a\u8bc4\u8bed\u96c6\u5e76\u9009\u62e9\u4e00\u4e2a\u6700\u4f18\u7684\u65b9\u6848.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u8bc4\u4ef7\u6307\u6807\u96c6 (\u56e0\u7d20\u96c6)<\/strong>\uff1a[math]U = \\{u_1, u_2, \\ldots, u_n\\}[\/math]<\/li>\n\n\n\n<li><strong>\u8bc4\u4ef7\u7b49\u7ea7 (\u8bc4\u8bed\u96c6)<\/strong>\uff1a[math]V = \\{v_1, v_2, \\ldots, v_m\\}[\/math]<\/li>\n\n\n\n<li><strong>\u6307\u6807\u7684\u6743\u91cd (\u6743\u91cd\u96c6)<\/strong>\uff1a[math]A = \\{a_1, a_2, \\ldots, a_n\\}[\/math]<\/li>\n<\/ul>\n\n\n\n<p>\u4f8b\u5982\uff0c\u8bc4\u4ef7\u4e00\u4ef6\u8863\u670d\u7684\u53d7\u5e02\u573a\u6b22\u8fce\u7a0b\u5ea6\uff0c\u53ef\u4ee5\u4ece [math] U = \\{\\text {\u82b1\u8272\u3001\u6837\u5f0f\u3001\u4ef7\u683c\u3001\u8010\u7528\u5ea6\u3001\u8212\u9002\u5ea6}\\}[\/math] \u65b9\u9762\u8003\u8651\uff0c\u4ee5\u6b64\u6765\u5224\u65ad\u8fd9\u4ef6\u8863\u670d\u662f [math] V = \\{\\text {\u5f88\u6b22\u8fce\u3001\u6b22\u8fce\u3001\u4e00\u822c\u3001\u4e0d\u6b22\u8fce}\\}[\/math]\uff0c\u5176\u4e2d\u6211\u4eec\u7ed9 [math] U [\/math] \u4e2d\u7684\u56e0\u7d20\u8d4b\u4e88\u6743\u91cd [math] A = \\{0.1, 0.2, 0.1, 0.4, 0.2\\}[\/math]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u4e00\u7ea7\u6a21\u7cca\u7efc\u5408\u8bc4\u4ef7<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">\u8bc4\u8bed\u96c6\u5e26\u6709\u8bc4\u4ef7\u8272\u5f69\u578b<\/h4>\n\n\n\n<p>\u4f8b 1. \u5728\u5bf9\u4f01\u4e1a\u5458\u5de5\u8fdb\u884c\u8003\u6838\u65f6\uff0c\u7531\u4e8e\u8003\u6838\u7684\u76ee\u7684\u3001\u8003\u6838\u5bf9\u8c61\u3001\u8003\u6838\u8303\u56f4\u7b49\u7684\u4e0d\u540c\uff0c\u8003\u6838\u7684\u5177\u4f53\u5185\u5bb9\u4e5f\u4f1a\u6709\u6240\u5dee\u522b\u3002\u6709\u7684\u8003\u6838\u6d89\u53ca\u7684\u6307\u6807\u8f83\u5c11\uff0c\u6709\u4e9b\u8003\u6838\u53c8\u5305\u542b\u4e86\u975e\u5e38\u5168\u9762\u4e14\u4e30\u5bcc\u7684\u5185\u5bb9\uff0c\u9700\u8981\u6d89\u53ca\u5f88\u591a\u6307\u6807\u3002\u9274\u4e8e\u8fd9\u79cd\u60c5\u51b5\uff0c\u4f01\u4e1a\u53ef\u4ee5\u6839\u636e\u9700\u8981\uff0c\u5728\u6307\u6807\u4e2a\u6570\u8f83\u5c11\u7684\u8003\u6838\u4e2d\uff0c\u8fd0\u7528\u4e00\u7ea7\u6a21\u7cca\u7efc\u5408\u8bc4\u5224\uff0c\u800c\u5728\u95ee\u9898\u8f83\u4e3a\u590d\u6742\u3001\u6307\u6807\u8f83\u591a\u65f6\uff0c\u8fd0\u7528\u591a\u5c42\u6b21\u6a21\u7cca\u7efc\u5408\u8bc4\u5224\uff0c\u4ee5\u63d0\u9ad8\u7cbe\u5ea6\u3002<\/p>\n\n\n\n<p><strong>Step 1. \u786e\u5b9a\u56e0\u7d20\u96c6<\/strong><br>\u53ef\u4ece\u5de5\u4f5c\u4e1a\u7ee9\u3001\u5de5\u4f5c\u6001\u5ea6\u3001\u6c9f\u901a\u80fd\u529b\u3001\u653f\u6cbb\u8868\u73b0\u65b9\u9762\u6784\u6210\u8bc4\u4ef7\u6307\u6807\u4f53\u7cfb\u96c6\u5408\uff0c\u5373\u56e0\u7d20\u96c6[math]U = \\{u_1, u_2, \\ldots, u_n\\}[\/math]<\/p>\n\n\n\n<p><strong>Step 2. \u786e\u5b9a\u8bc4\u8bed\u96c6<\/strong><br>\u5c06\u8bc4\u8bed\u5206\u4e3a\u597d\u3001\u8f83\u597d\u3001\u4e2d\u7b49\u3001\u5dee\u3001\u5f88\u5dee\uff0c\u5373\u6784\u6210\u8bc4\u8bed\u96c6[math]V = \\{v_1, v_2, \\ldots, v_m\\}[\/math]<\/p>\n\n\n\n<p><strong>Step 3. \u786e\u5b9a\u5404\u56e0\u7d20\u7684\u6743\u91cd<br><\/strong>\u4e5f\u5c31\u662f\u786e\u5b9a\u56e0\u7d20\u96c6\u7684\u91cd\u8981\u7a0b\u5ea6\uff0c\u5373\u6743\u91cd\u96c6 [math] A = {a_1, a_2, \\ldots, a_n}[\/math]\uff0c\u5176\u4e2d\uff0c[math] a_i [\/math] \u4e3a\u7b2c [math] i [\/math] \u4e2a\u56e0\u7d20\u7684\u6743\u91cd\uff0c\u4e14\u6ee1\u8db3 [math]\\sum_{i = 1}^{n} a_i = 1 [\/math]\u3002\u5bf9\u4e8e\u6743\u91cd\u7684\u786e\u5b9a\u65b9\u6cd5\uff0c\u5982\u679c\u9898\u76ee\u6ca1\u6709\u7ed9\u51fa\u6570\u636e\u5219\u7528\u5c42\u6b21\u5206\u6790\u6cd5\uff0c\u5982\u679c\u7ed9\u51fa\u4e86\u6570\u636e\u5219\u7528\u71b5\u6743\u6cd5\u7684TOPSiS\uff0c\u4e5f\u53ef\u4ee5\u4e0d\u786e\u5b9a\u6743\u91cd\u3002<\/p>\n\n\n\n<p><strong>Step 4. \u786e\u5b9a\u7efc\u5408\u6a21\u7cca\u5224\u65ad\u77e9\u9635<br><\/strong>\u5bf9\u6307\u6807 [math] u_i [\/math] \u6765\u8bf4\uff0c\u5bf9\u5404\u4e2a\u8bc4\u8bed\u7684\u96b6\u5c5e\u5ea6\u4e3a\u8bc4\u8bed\u96c6 [math] V [\/math] \u4e0a\u7684\u6a21\u7cca\u5b50\u96c6\u3002\u5bf9\u6307\u6807 [math] u_i [\/math] \u7684\u8bc4\u5224\u8bb0\u4f5c\uff1a[math] R_i = [r_{i1}, r_{i2}, \\ldots, r_{im}][\/math] \uff0c\u5176\u4e2d [math] r_{im}[\/math] \u8868\u793a\u6307\u6807 [math] u_i [\/math] \u5bf9\u8bc4\u8bed [math] v_m [\/math] \u7684\u96b6\u5c5e\u5ea6\u3002<\/p>\n\n\n\n<p>\u5404\u6307\u6807\u7684\u7efc\u5408\u6a21\u7cca\u5224\u65ad\u77e9\u9635\u4e3a\uff1a[math]R = \\begin{bmatrix} r_{11} &amp; r_{12} &amp; \\cdots &amp; r_{1m} \\\\ r_{21} &amp; r_{22} &amp; \\cdots &amp; r_{2m} \\\\ \\vdots &amp; \\vdots &amp; \\ddots &amp; \\vdots \\\\ r_{n1} &amp; r_{n2} &amp; \\cdots &amp; r_{nm} \\end{bmatrix} = \\begin{bmatrix} R_1 \\\\ R_2 \\\\ \\cdots \\\\ R_n \\end{bmatrix}[\/math]\uff0c\u5176\u610f\u4e49\u6309\u884c\u548c\u5217\u5206\u522b\u6709\u4e0d\u540c\u7684\u89e3\u91ca\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u56e0\u7d20\u96c6<\/strong> \u53ef\u4ece\u5de5\u4f5c\u4e1a\u7ee9\u3001\u5de5\u4f5c\u6001\u5ea6\u3001\u6c9f\u901a\u80fd\u529b\u3001\u653f\u6cbb\u8868\u73b0\u65b9\u9762\u6784\u6210\u8bc4\u4ef7\u6307\u6807\u4f53\u7cfb\u96c6\u5408\uff0c\u5373\u56e0\u7d20\u96c6\uff1b<\/li>\n\n\n\n<li><strong>\u8bc4\u8bed\u96c6<\/strong> \u5c06\u8bc4\u8bed\u5206\u4e3a\u597d\u3001\u8f83\u597d\u3001\u4e2d\u7b49\u3001\u5dee\u3001\u5f88\u5dee\uff0c\u5373\u6784\u6210\u8bc4\u8bed\u96c6\u3002<\/li>\n<\/ul>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">\u89e3\u9898\u6b65\u9aa4<\/mark><\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u53d6\u56e0\u7d20\u96c6 [math] U = \\{\\text {\u653f\u6cbb\u8868\u73b0} u_1, \\text {\u5de5\u4f5c\u80fd\u529b} u_2, \\text {\u5de5\u4f5c\u6001\u5ea6} u_3, \\text {\u5de5\u4f5c\u6210\u7ee9} u_4\\}[\/math]\u3002<\/li>\n\n\n\n<li>\u53d6\u8bc4\u8bed\u96c6 [math] V = \\{\\text {\u4f18\u79c0} v_1, \\text {\u826f\u597d} v_2, \\text {\u4e00\u822c} v_3, \\text {\u8f83\u5dee} v_4, \\text {\u5dee} v_5\\}[\/math]\u3002<\/li>\n\n\n\n<li>\u786e\u5b9a\u5404\u56e0\u7d20\u6743\u91cd [math] A = [0.25, 0.2, 0.25, 0.3][\/math]\uff08\u5c42\u6b21 or \u71b5\u6743\u6cd5\uff09<\/li>\n\n\n\n<li>\u5bf9\u6bcf\u4e2a\u56e0\u7d20 [math] u_i [\/math] \u505a\u51fa\u8bc4\u4ef7\uff08\u6ce8\uff1a\u96b6\u5c5e\u5ea6\u4e4b\u548c\u4e0d\u4e00\u5b9a\u4e3a1\uff0c\u548c\u96b6\u5c5e\u51fd\u6570\u7684\u9009\u53d6\u6709\u5173\uff09\n<ul class=\"wp-block-list\">\n<li>[math] u_1 [\/math] \u7531\u7fa4\u4f17\u8bc4\u8bae\u6253\u5206\u786e\u5b9a\uff1a[math] R_1 = [0.1, 0.5, 0.4, 0, 0][\/math]\uff0c\u8fd9\u4e2a\u5f0f\u5b50\u8868\u793a\uff0c\u6709 10% \u7684\u4eba\u8ba4\u4e3a\u653f\u6cbb\u8868\u73b0\u4f18\u79c0\uff0c50% \u7684\u4eba\u8ba4\u4e3a\u653f\u6cbb\u8868\u73b0\u826f\u597d\uff0c40% \u7684\u4eba\u8ba4\u4e3a\u653f\u6cbb\u8868\u73b0\u4e00\u822c\uff0c\u8ba4\u4e3a\u653f\u6cbb\u8868\u73b0\u8f83\u5dee\u6216\u5dee\u7684\u4eba\u6570\u4e3a <\/li>\n\n\n\n<li>[math] u_2 [\/math] \u548c [math] u_3 [\/math] \u7531\u90e8\u95e8\u9886\u5bfc\u6253\u5206\u786e\u5b9a\uff1a[math] R_2 = [0.2, 0.5, 0.2, 0.1, 0][\/math]\uff0c[math] R_3 = [0.2, 0.5, 0.3, 0, 0][\/math]\u3002<\/li>\n\n\n\n<li>[math] u_4 [\/math] \u7531\u5355\u4f4d\u8003\u6838\u7ec4\u6210\u5458\u6253\u5206\u786e\u5b9a\uff1a[math] R_4 = [0.2, 0.6, 0.2, 0, 0][\/math]<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u5c06\u4e0a\u8ff0\u5411\u91cf\u7ec4\u5408\uff0c\u5373\u53ef\u6784\u6210\u6a21\u7cca\u7efc\u5408\u5224\u65ad\u77e9\u9635\uff0c[math]R = \\begin{bmatrix} 0.1 &amp; 0.5 &amp; 0.4 &amp; 0 &amp; 0 \\\\ 0.2 &amp; 0.5 &amp; 0.2 &amp; 0.1 &amp; 0 \\\\ 0.2 &amp; 0.5 &amp; 0.3 &amp; 0 &amp; 0 \\\\ 0.2 &amp; 0.6 &amp; 0.2 &amp; 0 &amp; 0 \\end{bmatrix}[\/math] <\/li>\n\n\n\n<li>\u8fdb\u884c\u6a21\u7cca\u7efc\u5408\u8bc4\u5224[math]B = A \\cdot R = [0.25, 0.2, 0.25, 0.3] \\cdot \\begin{bmatrix} 0.1 &amp; 0.5 &amp; 0.4 &amp; 0 &amp; 0 \\\\ 0.2 &amp; 0.5 &amp; 0.2 &amp; 0.1 &amp; 0 \\\\ 0.2 &amp; 0.5 &amp; 0.3 &amp; 0 &amp; 0 \\\\ 0.2 &amp; 0.6 &amp; 0.2 &amp; 0 &amp; 0 \\end{bmatrix} = [0.175, 0.53, 0.275, 0.02, 0][\/math]\u53d6\u6570\u503c\u6700\u5927\u7684\u8bc4\u8bed\u4f5c\u4e3a\u6700\u540e\u7efc\u5408\u8bc4\u5224\u7ed3\u679c\uff0c\u6240\u4ee5\u8bc4\u5224\u7ed3\u679c\u4e3a\u201c\u826f\u597d\u201d\uff0e<\/li>\n<\/ol>\n\n\n\n<h4 class=\"wp-block-heading\">\u8bc4\u8bed\u4e0d\u5e26\u6709\u8bc4\u4ef7\u8272\u5f69\u578b<\/h4>\n\n\n\n<p>\u4f8b 2. \u67d0\u9732\u5929\u7164\u77ff\u6709\u4e94\u4e2a\u8fb9\u5761\u8bbe\u8ba1\u65b9\u6848\uff0c\u5176\u5404\u9879\u53c2\u6570\u6839\u636e\u5206\u6790\u8ba1\u7b97\u7ed3\u679c\u5f97\u5230\u8fb9\u5761\u8bbe\u8ba1\u65b9\u6848\u7684\u53c2\u6570\u5982\u4e0b\uff1a<\/p>\n\n\n\n<table border=\"1\" cellpadding=\"4\" cellspacing=\"0\" style=\"text-align: center; vertical-align: middle;\">\n  <thead>\n    <tr>\n      <th style=\"text-align: center; vertical-align: middle;\">\u9879\u76ee<\/th>\n      <th style=\"text-align: center; vertical-align: middle;\">\u65b9\u68481<\/th>\n      <th style=\"text-align: center; vertical-align: middle;\">\u65b9\u68482<\/th>\n      <th style=\"text-align: center; vertical-align: middle;\">\u65b9\u68483<\/th>\n      <th style=\"text-align: center; vertical-align: middle;\">\u65b9\u68484<\/th>\n      <th style=\"text-align: center; vertical-align: middle;\">\u65b9\u68485<\/th>\n    <\/tr>\n  <\/thead>\n  <tbody>\n    <tr>\n      <td style=\"text-align: center; vertical-align: middle;\">\u53ef\u91c7\u77ff\u91cf\/\u4e07\u5428<\/td>\n      <td style=\"text-align: center; vertical-align: middle;\">4700<\/td>\n      <td style=\"text-align: center; vertical-align: middle;\">6700<\/td>\n      <td style=\"text-align: center; vertical-align: middle;\">5900<\/td>\n      <td style=\"text-align: center; vertical-align: middle;\">8800<\/td>\n      <td style=\"text-align: center; vertical-align: middle;\">7600<\/td>\n    <\/tr>\n    <tr>\n      <td style=\"text-align: center; vertical-align: middle;\">\u57fa\u5efa\u6295\u8d44\/\u4e07\u5143<\/td>\n      <td style=\"text-align: center; vertical-align: middle;\">5000<\/td>\n      <td style=\"text-align: center; vertical-align: middle;\">5500<\/td>\n      <td style=\"text-align: center; vertical-align: middle;\">5300<\/td>\n      <td style=\"text-align: center; vertical-align: middle;\">6800<\/td>\n      <td style=\"text-align: center; vertical-align: middle;\">6000<\/td>\n    <\/tr>\n    <tr>\n      <td style=\"text-align: center; vertical-align: middle;\">\u91c7\u77ff\u6210\u672c<\/td>\n      <td style=\"text-align: center; vertical-align: middle;\">4.0<\/td>\n      <td style=\"text-align: center; vertical-align: middle;\">6.1<\/td>\n      <td style=\"text-align: center; vertical-align: middle;\">5.5<\/td>\n      <td style=\"text-align: center; vertical-align: middle;\">7.0<\/td>\n      <td style=\"text-align: center; vertical-align: middle;\">6.8<\/td>\n    <\/tr>\n    <tr>\n      <td style=\"text-align: center; vertical-align: middle;\">\u4e0d\u7a33\u5b9a\u8d39\u7528<\/td>\n      <td style=\"text-align: center; vertical-align: middle;\">30<\/td>\n      <td style=\"text-align: center; vertical-align: middle;\">50<\/td>\n      <td style=\"text-align: center; vertical-align: middle;\">40<\/td>\n      <td style=\"text-align: center; vertical-align: middle;\">200<\/td>\n      <td style=\"text-align: center; vertical-align: middle;\">160<\/td>\n    <\/tr>\n  <\/tbody>\n<\/table>\n\n\n\n<p>\u636e\u52d8\u63a2\uff0c\u8be5\u77ff\u63a2\u660e\u50a8\u91cf 8800 \u5428\uff0c\u5f00\u91c7\u6295\u8d44\u4e0d\u8d85\u8fc7 8000 \u4e07\u5143\uff0c\u8bd5\u505a\u51fa\u5404\u65b9\u6848\u7684\u4f18\u52a3\u6392\u5e8f\uff0c\u9009\u51fa\u6700\u4f73\u65b9\u6848\u3002<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\"><strong>\u89e3\u9898\u6b65\u9aa4<\/strong><\/mark><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u56e0\u7d20\u96c6 [math] U = \\{\\text {\u53ef\u91c7\u77ff\u91cf} u_1, \\text {\u57fa\u5efa\u6295\u8d44} u_2, \\text {\u91c7\u77ff\u6210\u672c} u_3, \\text {\u4e0d\u7a33\u5b9a\u8d39\u7528} u_4\\}[\/math]\u3002<\/li>\n\n\n\n<li>\u8bc4\u8bed\u96c6 [math] V = \\{\\text {\u65b9\u6848\u4e00} v_1, \\text {\u65b9\u6848\u4e8c} v_2, \\text {\u65b9\u6848\u4e09} v_3, \\text {\u65b9\u6848\u56db} v_4, \\text {\u65b9\u6848\u4e94} v_5\\}[\/math]\u3002<\/li>\n\n\n\n<li>\u7528\u5c42\u6b21\u5206\u6790\u6cd5\u6216\u71b5\u6743\u6cd5\u786e\u5b9a\u6743\u91cd\uff08\u4e0d\u552f\u4e00\uff09 [math] A = (0.25, 0.2, 0.2, 0.1, 0.25)[\/math]\u3002<\/li>\n\n\n\n<li>\u786e\u5b9a\u6a21\u7cca\u7efc\u5408\u5224\u65ad\u77e9\u9635\n<ul class=\"wp-block-list\">\n<li>\u786e\u5b9a\u96b6\u5c5e\u51fd\u6570\uff0c\u56e0\u4e3a\u8bc4\u8bed\u96c6\u4e0d\u5e26\u6709\u8bc4\u4ef7\u8272\u5f69\uff08\u65e0\u6cd5\u533a\u5206\u6781\u5927\u6781\u5c0f\u578b\uff09\uff0c\u6240\u4ee5\u8fd9\u91cc\u6211\u4eec\u9700\u8981\u81ea\u884c\u6784\u9020\u96b6\u5c5e\u51fd\u6570\u3002<\/li>\n\n\n\n<li>\u6839\u636e\u5e38\u8bc6\u53ef\u4ee5\u77e5\u9053\uff0c\u53ef\u91c7\u77ff\u91cf\u4e3a\u6781\u5927\u578b\uff0c\u57fa\u5efa\u6295\u8d44\u4e3a\u6781\u5c0f\u578b\uff0c\u91c7\u77ff\u6210\u672c\u4e3a\u6781\u5c0f\u578b\uff0c\u4e0d\u7a33\u5b9a\u8d39\u7528\u4e3a\u6781\u5c0f\u578b\u3002\n<ul class=\"wp-block-list\">\n<li>\u56e0\u4e3a\u8868\u4e2d\u52d8\u63a2\u7684\u5730\u8d28\u50a8\u91cf\u6700\u5927\u4e3a 8800 \u5428\uff0c\u6545\u53ef\u91c7\u77ff\u91cf\u7684\u96b6\u5c5e\u51fd\u6570 [math] u_A (x) = \\frac {x}{8800}[\/math]<\/li>\n\n\n\n<li>\u6295\u8d44\u7ea6\u675f\u662f 8000 \u4e07\u5143\uff0c\u6240\u4ee5 [math] u_B (x) = 1 &#8211; \\frac {x}{8000}[\/math]<\/li>\n\n\n\n<li>\u6839\u636e\u4e13\u5bb6\u610f\u89c1\uff0c\u91c7\u77ff\u6210\u672c [math] a_1 \\leq 5.5[\/math]\u5143\/\u5428\u4e3a\u4f4e\u6210\u672c\uff0c[math] a_2 = 8.0 [\/math]\u5143\/\u5428\u4e3a\u9ad8\u6210\u672c\uff0c\u6545<br>[math]u_c(x) = \\begin{cases} 1, &amp; 0 \\leq x \\leq 5.5 \\\\ \\dfrac{8.0 &#8211; x}{8.0 &#8211; 5.5}, &amp; 5.5 \\leq x \\leq 8.0 \\\\ 0, &amp; 8.0 &lt; x \\end{cases}[\/math]<\/li>\n\n\n\n<li>\u4e0d\u7a33\u5b9a\u8d39\u7528\u7684\u96b6\u5c5e\u51fd\u6570 [math] u_D (x) = 1 &#8211; \\frac {x}{200}[\/math]<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u4ee3\u5165\u6570\u636e\uff0c\u5f97\u5230\u6a21\u7cca\u7efc\u5408\u5224\u65ad\u77e9\u9635[math]R[\/math]\uff1a<\/li>\n\n\n\n<table border=\"1\" cellpadding=\"4\" cellspacing=\"0\" style=\"text-align: center; vertical-align: middle; width: 80%; margin: 0 auto;\">\n  <thead>\n    <tr style=\"background-color: transparent;\">\n      <th style=\"text-align: center; vertical-align: middle;\">\u9879\u76ee<\/th>\n      <th style=\"text-align: center; vertical-align: middle;\">\u65b9\u68481<\/th>\n      <th style=\"text-align: center; vertical-align: middle;\">\u65b9\u68482<\/th>\n      <th style=\"text-align: center; vertical-align: middle;\">\u65b9\u68483<\/th>\n      <th style=\"text-align: center; vertical-align: middle;\">\u65b9\u68484<\/th>\n      <th style=\"text-align: center; vertical-align: middle;\">\u65b9\u68485<\/th>\n    <\/tr>\n  <\/thead>\n  <tbody>\n    <tr>\n      <td style=\"text-align: center; vertical-align: middle;\">\u53ef\u91c7\u77ff\u91cf<\/td>\n      <td style=\"text-align: center; vertical-align: middle;\">0.5341<\/td>\n      <td style=\"text-align: center; vertical-align: middle;\">0.7614<\/td>\n      <td style=\"text-align: center; vertical-align: middle;\">0.6405<\/td>\n      <td style=\"text-align: center; vertical-align: middle;\">1<\/td>\n      <td style=\"text-align: center; vertical-align: middle;\">0.8636<\/td>\n    <\/tr>\n    <tr>\n      <td style=\"text-align: center; vertical-align: middle;\">\u57fa\u5efa\u6295\u8d44<\/td>\n      <td style=\"text-align: center; vertical-align: middle;\">0.3750<\/td>\n      <td style=\"text-align: center; vertical-align: middle;\">0.3125<\/td>\n      <td style=\"text-align: center; vertical-align: middle;\">0.3375<\/td>\n      <td style=\"text-align: center; vertical-align: middle;\">0.15<\/td>\n      <td style=\"text-align: center; vertical-align: middle;\">0.25<\/td>\n    <\/tr>\n    <tr>\n      <td style=\"text-align: center; vertical-align: middle;\">\u91c7\u77ff\u6210\u672c<\/td>\n      <td style=\"text-align: center; vertical-align: middle;\">1<\/td>\n      <td style=\"text-align: center; vertical-align: middle;\">0.76<\/td>\n      <td style=\"text-align: center; vertical-align: middle;\">1<\/td>\n      <td style=\"text-align: center; vertical-align: middle;\">0.4<\/td>\n      <td style=\"text-align: center; vertical-align: middle;\">0.48<\/td>\n    <\/tr>\n    <tr>\n      <td style=\"text-align: center; vertical-align: middle;\">\u4e0d\u7a33\u5b9a\u8d39\u7528<\/td>\n      <td style=\"text-align: center; vertical-align: middle;\">1<\/td>\n      <td style=\"text-align: center; vertical-align: middle;\">0.4480<\/td>\n      <td style=\"text-align: center; vertical-align: middle;\">0.6552<\/td>\n      <td style=\"text-align: center; vertical-align: middle;\">0<\/td>\n      <td style=\"text-align: center; vertical-align: middle;\">0.0345<\/td>\n    <\/tr>\n  <\/tbody>\n<\/table>\n\n\n\n<li>\u8fdb\u884c\u6a21\u7cca\u7efc\u5408\u8bc4\u5224\uff1a[math]B = A \\cdot R = (0.7435, 0.5919, 0.6789, 0.3600, 0.3905)[\/math]\u3002\u7531\u6b64\u53ef\u77e5\uff0c\u65b9\u6848\u4e00\u6700\u597d\u3002<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">\u591a\u7ea7\u6a21\u7cca\u7efc\u5408\u8bc4\u4ef7<\/h3>\n\n\n\n<p>\u5f53\u56e0\u7d20\u96c6\u4e2d\u6307\u6807\u8fc7\u591a\u65f6\uff0c\u4f1a\u5177\u6709\u8f83\u9ad8\u7684\u76f8\u5173\u6027\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u8fd9\u4e9b\u6307\u6807\u5206\u7c7b\u8ba8\u8bba\uff0c\u4f8b\u5982\uff1a<\/p>\n\n\n<div class=\"wp-block-image wp-duotone-unset-1\">\n<figure class=\"aligncenter size-full is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='http:\/\/heqiwei.cn\/wp-content\/uploads\/2025\/07\/image-13.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"926\" height=\"597\" data-original=\"http:\/\/heqiwei.cn\/wp-content\/uploads\/2025\/07\/image-13.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-1213\" style=\"width:627px;height:auto\"  sizes=\"auto, (max-width: 926px) 100vw, 926px\" \/><\/div><\/figure>\n<\/div>\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">\u89e3\u9898\u6b65\u9aa4<\/mark><\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u7b2c\u4e00\u6b65\uff1a\u5212\u5206\u56e0\u7d20\u96c6<\/strong><br>\u5212\u5206\u56e0\u7d20\u96c6 [math] U = \\{u_1, u_2, \\ldots, u_n\\}[\/math] \u4e3a\u82e5\u5e72\u7ec4 <br>[math] U_1 = \\{u_1, u_2, \\ldots, u_k\\}[\/math]\uff0c\u4e14\u4e0d\u540c\u5b50\u96c6\u4e92\u4e0d\u76f8\u540c\uff0c\u76f8\u4ea4\u4e3a\u7a7a\u3002<br>\u5373\uff0c[math] U = \\bigcup_{i=1}^{k} U_i \\ \\text {\u4e14} \\ U_i \\bigcap U_j = \\Phi \\ (i \\neq j)[\/math]<\/li>\n\n\n\n<li><strong>\u7b2c\u4e8c\u6b65\uff1a\u786e\u5b9a\u8bc4\u8bed\u96c6\u4e0e\u4e8c\u7ea7\u8bc4\u5224<\/strong><br>\u786e\u5b9a\u8bc4\u8bed\u96c6 [math] V = \\{v_1, v_2, \\ldots, v_m\\}[\/math]\uff0c\u5e76\u5bf9\u7b2c\u4e8c\u7ea7\u56e0\u7d20\u96c6 [math] U_i = \\{ u_1^{(i)}, u_2^{(i)}, \\ldots, u_{n_i}^{(i)} \\}[\/math] \u8fdb\u884c\u8bc4\u5224\uff0c\u5f97\u5230\u7efc\u5408\u5224\u65ad\u77e9\u9635[math]R_i = \\begin{bmatrix} <br>r_{11}^{(i)} &amp; r_{12}^{(i)} &amp; \\cdots &amp; r_{1m}^{(i)} \\\\ <br>r_{21}^{(i)} &amp; r_{22}^{(i)} &amp; \\cdots &amp; r_{2m}^{(i)} \\\\ <br>\\vdots &amp; \\vdots &amp; \\vdots &amp; \\vdots \\\\ <br>r_{n_i 1}^{(i)} &amp; r_{n_i 2}^{(i)} &amp; \\cdots &amp; r_{n_i m}^{(i)} <br>\\end{bmatrix}, \\ (i = 1, 2, \\ldots, k)[\/math]<br>\u82e5 [math] U_i = \\{ u_1^{(i)}, u_2^{(i)}, \\ldots, u_{n_i}^{(i)} \\}[\/math] \u7684\u6743\u91cd\u4e3a [math] A_i = \\{ a_1^{(i)}, a_2^{(i)}, \\ldots, a_{n_i}^{(i)} \\}[\/math]\uff0c\u5219\u4e8c\u7ea7\u7efc\u5408\u8bc4\u5224[math]B_i = A_i \\cdot R_i[\/math]\uff08\u5373 [math] U_i [\/math] \u5bf9\u4e8e\u8bc4\u8bed\u96c6 [math] V [\/math] \u7684\u96b6\u5c5e\u5ea6 \uff09<\/li>\n\n\n\n<li><strong>\u7b2c\u4e09\u6b65\uff1a\u4e00\u7ea7\u56e0\u7d20\u7efc\u5408\u8bc4\u5224<\/strong><br>\u5bf9\u7b2c\u4e00\u7ea7\u56e0\u7d20 [math] U = \\{U_1, U_2, \\ldots, U_k\\}[\/math] \u8fdb\u884c\u7efc\u5408\u8bc4\u5224\uff0c\u82e5\u7b2c\u4e00\u7ea7\u6743\u91cd\u4e3a [math] A = \\{a_1, a_2, \\ldots, a_k\\}[\/math]\uff0c\u6784\u9020\u7efc\u5408\u5224\u65ad\u77e9\u9635 [math] R = [B_1, B_2, \\ldots, B_k]^{\\text {T}}[\/math]\uff0c\u5219\u4e00\u7ea7\u7efc\u5408\u8bc4\u5224\uff1a[math]B = A \\cdot R[\/math]\u3002<\/li>\n\n\n\n<li><strong>\u7b2c\u56db\u6b65\uff1a\u6309\u6700\u5927\u96b6\u5c5e\u5ea6\u786e\u5b9a\u76f8\u5173\u8bc4\u8bed<\/strong><\/li>\n<\/ul>\n\n\n\n<p>\u5b9e\u9645\u4e0a\uff0c\u4e0a\u8ff0\u8fc7\u7a0b\u5c31\u662f\u5bf9\u6bcf\u7ec4\u4e8c\u7ea7\u4e2d\u7684\u56e0\u7d20\u96c6\u505a\u4e00\u6b21\u4e00\u7ea7\u6a21\u7cca\u7efc\u5408\u8bc4\u4ef7\uff0c\u5c06\u5176\u7ed3\u679c\u6309\u884c\u62fc\u63a5\u6210\u7b2c\u4e00\u7ea7\u7684\u5224\u65ad\u77e9\u9635\uff0c\u518d\u4e0e\u7b2c\u4e00\u7ea7\u7684\u6743\u91cd\u505a\u4e00\u6b21\u77e9\u9635\u4e58\u6cd5\uff0c\u5c31\u662f\u4e8c\u7ea7\u6a21\u7cca\u8bc4\u4ef7\u7684\u7ed3\u679c\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u603b\u7ed3<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\u7528\u6a21\u7cca\u7efc\u5408\u8bc4\u4ef7\u7684\u5957\u8def<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Step1\uff1a\u8be5\u65b9\u6cd5\u7528\u4e8e\u89e3\u51b3\u8bc4\u4ef7\u7c7b\u95ee\u9898\uff1b<\/li>\n\n\n\n<li>Step2\uff1a\u786e\u5b9a\u56e0\u7d20\u96c6\uff08\u5982\u679c\u56e0\u7d20\u8fc7\u591a\u53ef\u8003\u8651\u7528\u591a\u7ea7\uff0c\u53ef\u4ee5\u7528\u4e3b\u6210\u5206\u5206\u6790\u6cd5\uff09\u786e\u5b9a\u5404\u56e0\u7d20\u6743\u91cd\uff0c\u6ce8\u610f\u6bcf\u4e00\u7ea7\u6743\u91cd\u4e4b\u548c\u4e3a 1\uff1b<\/li>\n\n\n\n<li>Step3\uff1a\u786e\u5b9a\u8bc4\u8bed\u96c6\uff08\u6709\u65e0\u8bc4\u4ef7\u8272\u5f69\uff09\uff1b<\/li>\n\n\n\n<li>Step4\uff1a\u4ece\u6700\u540e\u4e00\u5c42\u5f00\u59cb\u9010\u7ea7\u786e\u5b9a\u6bcf\u7ea7\u56e0\u7d20\u5bf9\u8bc4\u8bed\u96c6\u7684\u96b6\u5c5e\u5ea6\uff08\u9010\u7ea7\u6253\u5206\uff09\uff1b<\/li>\n\n\n\n<li>Step5\uff1a\u6839\u636e\u96b6\u5c5e\u5ea6\u786e\u5b9a\u76f8\u5173\u8bc4\u8bed\uff08\u6700\u597d\u753b\u6210\u76f4\u65b9\u56fe\uff09<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u4e00\u4e9b\u5c0f\u5999\u62db<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u786e\u5b9a\u5404\u56e0\u7d20\u6743\u91cd\u662f\u4e00\u4e2a\u5934\u75bc\u7684\u95ee\u9898\uff0c\u8fd9\u91cc\u7ed9\u51fa\u4e00\u4e9b\u5efa\u8bae\uff1a<br>\u5bf9\u4e8e\u7ed9\u5b9a\u9898\u76ee\u6216\u8bfe\u9898\u4e2d\u6709\u6570\u636e\u7684\uff0c\u76f4\u63a5\u7528\u71b5\u6743\u6cd5\u7684<a href=\"http:\/\/heqiwei.cn\/index.php\/2025\/07\/06\/%e6%95%b0%e5%ad%a6%e5%bb%ba%e6%a8%a1-topsis%e6%b3%95\/\">TOPSIS<\/a>\uff1b\u5bf9\u4e8e\u6ca1\u6709\u6570\u636e\u7684\uff0c\u53ef\u4ee5\u7528<a href=\"http:\/\/heqiwei.cn\/index.php\/2025\/07\/05\/%e6%95%b0%e5%ad%a6%e5%bb%ba%e6%a8%a1-%e5%b1%82%e6%ac%a1%e5%88%86%e6%9e%90%e6%b3%95\/\">\u5c42\u6b21\u5206\u6790\u6cd5<\/a>\uff08\u8fc7\u7a0b\u7b80\u5199\uff0c\u4e3b\u6b21\u5206\u660e\uff09\uff0c\u7136\u540e\u5728\u8bba\u6587\u91cc\u5199\u4e0a\u4e00\u53e5 \u201c\u6839\u636e\u4e13\u5bb6\u610f\u89c1\u201d \u5373\u53ef\u3002<\/li>\n\n\n\n<li>\u6a21\u7cca\u7efc\u5408\u8bc4\u4ef7\u539f\u7406\u5e76\u4e0d\u96be\uff0c\u53ea\u662f\u5404\u79cd\u6a21\u7cca\u6570\u5b66\u3001\u77e9\u9635\u5411\u91cf\u8fd9\u4e9b\u5f62\u5f0f\u6bd4\u8f83\u552c\u4eba\uff0c\u5176\u5b9e\u771f\u6b63\u62c9\u5f00\u5dee\u8ddd\u7684\u70b9\u5728\u4e8e<mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">\u6a21\u578b\u9009\u53d6\u7684\u5408\u7406\u4e0e\u5426<\/mark>\uff08\u4f8b\u5982\u56e0\u7d20\u96c6\u7684\u9009\u53d6\uff09\uff0c\u53e6\u5916\uff0c\u5bf9\u4e8e\u8fd9\u79cd \u201c\u6ca1\u5565\u6280\u672f\u542b\u91cf\u201d \u7684\u6a21\u578b\uff0c\u53ef\u4ee5\u7528\u56fe\u6587\u5e76\u8302\u7684\u65b9\u6cd5\u5145\u5b9e\u6587\u7ae0\u3002<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u6a21\u7cca\u7684\u6982\u5ff5 \u73b0\u5b9e\u4e2d\u7684\u8bb8\u591a\u73b0\u8c61\u53ca\u5173\u7cfb\u6bd4\u8f83\u6a21\u7cca\u3002\u5982\u9ad8\u4e0e\u77ee\uff0c \u957f\u4e0e\u77ed\uff0c\u5927\u4e0e\u5c0f\uff0c\u591a\u4e0e\u5c11\uff0c\u7a77\u4e0e\u5bcc\uff0c\u597d\u4e0e\u5dee\uff0c\u5e74\u8f7b\u4e0e\u5e74\u8001\u7b49\u3002 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[19],"tags":[],"class_list":["post-1076","post","type-post","status-publish","format-standard","hentry","category-19"],"_links":{"self":[{"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/posts\/1076","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/comments?post=1076"}],"version-history":[{"count":156,"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/posts\/1076\/revisions"}],"predecessor-version":[{"id":1539,"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/posts\/1076\/revisions\/1539"}],"wp:attachment":[{"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/media?parent=1076"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/categories?post=1076"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/tags?post=1076"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}