{"id":1047,"date":"2025-07-06T16:01:14","date_gmt":"2025-07-06T08:01:14","guid":{"rendered":"http:\/\/heqiwei.cn\/?p=1047"},"modified":"2025-07-08T11:40:26","modified_gmt":"2025-07-08T03:40:26","slug":"%e6%95%b0%e5%ad%a6%e5%bb%ba%e6%a8%a1-topsis%e6%b3%95","status":"publish","type":"post","link":"https:\/\/heqiwei.cn\/index.php\/2025\/07\/06\/%e6%95%b0%e5%ad%a6%e5%bb%ba%e6%a8%a1-topsis%e6%b3%95\/","title":{"rendered":"\u6570\u5b66\u5efa\u6a21\u2014\u2014TOPSIS\u6cd5"},"content":{"rendered":"\n<p>\u8be5\u65b9\u6cd5\u5e38\u7528\u4e8e\uff1a\u5df2\u77e5[math]X[\/math]\u548c[math]\\omega[\/math]\uff0c\u6c42\u7efc\u5408\u8bc4\u4ef7\u6307\u6807[math]Y[\/math]<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">TOPSIS\u6cd5\u7684\u4e3b\u8981\u64cd\u4f5c<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>\u7528\u5411\u91cf\u89c4\u8303\u5316\u7684\u65b9\u6cd5\u6c42\u5f97\u89c4\u8303\u51b3\u7b56\u77e9\u9635<\/strong><\/h3>\n\n\n\n<p>\u8bbe\u539f\u95ee\u9898\u7684\u51b3\u7b56\u77e9\u9635&nbsp;[math]A = (x_{ij})_{m \\times n}[\/math]\uff0c\u89c4\u8303\u5316\u540e\u7684\u51b3\u7b56\u77e9\u9635\u4e3a&nbsp;[math]B = (b_{ij})_{m \\times n}[\/math]\uff0c\u5176\u4e2d\uff0c[math]b_{ij} = x_{ij} \/ \\sqrt{\\sum_{i=1}^{m} x_{ij}^2}[\/math]\uff0c[math]i = 1,2,\\dots,m[\/math]\uff1b[math]j = 1,2,\\dots,n[\/math]\uff0c[math]m[\/math]\u4e3a\u77e9\u9635\u6570\u636e\u7684\u884c\u6570\uff0c[math]n[\/math]\u4e3a\u77e9\u9635\u6570\u636e\u7684\u5217\u6570\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>\u6784\u9020\u52a0\u6743\u89c4\u8303\u77e9\u9635<\/strong><\/h3>\n\n\n\n<p>\u5b9a\u4e49\u52a0\u6743\u89c4\u8303\u77e9\u9635 [math] Z = (z_{ij}){m \\times n}[\/math]\uff0c\u8bbe\u5404\u5c5e\u6027\u7684\u6743\u91cd\u4e3a [math] w{ij}[\/math]\uff0c\u5219 [math] z_{ij} = w_{ij} \\times b_{ij}[\/math]\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>\u786e\u5b9a\u6b63\u7406\u60f3\u89e3\u548c\u8d1f\u7406\u60f3\u89e3<\/strong><\/h3>\n\n\n\n<p>\u6b63\u7406\u60f3\u89e3\uff1a<\/p>\n\n\n\n<p class=\"has-text-align-center\">[math] Z^+ = (\\max\\{z_{11},z_{21},\\dots,z_{i1}\\},\\max\\{z_{12},z_{22},\\dots,z_{i2}\\},\\dots,\\max\\{z_{1j},z_{2j},\\dots,z_{ij}\\}) [\/math]<\/p>\n\n\n\n<p class=\"has-text-align-center\">[math]= (Z_1^+, Z_2^+, \\dots, Z_j^+)[\/math]<br><\/p>\n\n\n\n<p>\u8d1f\u7406\u60f3\u89e3\uff1a<\/p>\n\n\n\n<p class=\"has-text-align-center\">[math]  Z^- = (\\min\\{z_{11},z_{21},\\dots,z_{i1}\\},\\min\\{z_{12},z_{22},\\dots,z_{i2}\\},\\dots,\\min\\{z_{1j},z_{2j},\\dots,z_{ij}\\}) [\/math]<\/p>\n\n\n\n<p class=\"has-text-align-center\">[math] = (Z_1^-, Z_2^-, \\dots, Z_j^-)[\/math]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>\u8ba1\u7b97\u5404\u65b9\u6848\u5230\u6b63\u7406\u60f3\u89e3\u4e0e\u8d1f\u7406\u60f3\u89e3\u7684\u8ddd\u79bb<\/strong><\/h3>\n\n\n\n<p>\u5907\u9009\u65b9\u6848\u5230\u6b63\u7406\u60f3\u89e3\u7684\u8ddd\u79bb\uff1a[math] D_i^+ = \\sqrt {\\sum_{j=1}^{n} (z_{ij} &#8211; Z_j^+)^2}[\/math]\uff1b<br>\u5907\u9009\u65b9\u6848\u5230\u8d1f\u7406\u60f3\u89e3\u7684\u8ddd\u79bb\uff1a[math] D_i^- = \\sqrt {\\sum_{j=1}^{n} (z_{ij} &#8211; Z_j^-)^2}[\/math]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>\u8ba1\u7b97\u5404\u65b9\u6848\u5230\u7406\u60f3\u65b9\u6848\u7684\u76f8\u5bf9\u8d34\u8fd1\u5ea6<\/strong><\/h3>\n\n\n\n<p>[math] C_i = D_i^- \/ (D_i^- + D_i^+)[\/math]\u3002[math] D_i^-[\/math] \u8d8a\u5927\uff0c[math] C_i [\/math] \u8d8a\u63a5\u8fd1\u4e8e 1 \u8d8a\u597d\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>\u5c06\u76f8\u5bf9\u8d34\u8fd1\u5ea6\u7531\u5927\u5230\u5c0f\u6392\u5e8f<\/strong><\/h3>\n\n\n\n<h2 class=\"wp-block-heading\">\u6ce8\u610f\u4e8b\u9879<\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u5f53<mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">\u5df2\u77e5\u5404\u4e2a\u6307\u6807\u7684\u6570\u636e\uff0c\u60f3\u6c42\u7efc\u5408\u8bc4\u4ef7\u503cy<\/mark>\u7684\u65f6\u5019\uff0cTOPSIS \u6cd5\u662f\u4e00\u4e2a\u4e0d\u9519\u7684\u9009\u62e9\uff0c\u663e\u5f97\u8981\u6bd4\u7b80\u5355\u7684\u7ebf\u6027\u52a0\u6743\u6c42\u548c\u66f4\u6709\u8bf4\u670d\u529b\u3002<\/li>\n\n\n\n<li>TOPSIS \u6cd5\u662f\u4e00\u4e2a\u57fa\u7840\u7684\u5e38\u7528\u8bc4\u4ef7\u6a21\u578b\uff0c\u5728\u7f8e\u8d5b E \u548c F \u9898\u7684 O \u5956\u8bba\u6587\u4e2d\u5341\u5206\u5e38\u89c1\uff0c\u901a\u5e38\u51fa\u73b0\u5728\u7b2c\u4e00\u95ee\uff0c\u56e0\u4e3a\u8bc4\u4ef7\u6a21\u578b\u662f\u6574\u4e2a\u95ee\u9898\u5206\u6790\u7684\u57fa\u7840\u3002<\/li>\n\n\n\n<li>\u6bd4\u8d5b\u4e2d\uff0c\u5e38\u7528 <a href=\"http:\/\/www.spsspro.com\">SPSSPRO <\/a>\u6765\u5b9e\u73b0 TOPSIS \u6cd5\uff0c\u5df2\u7ecf\u8db3\u591f\u7528\u4e86\uff0c\u4e0d\u9700\u8981\u7528 MATLAB \u6216\u8005 Python \u8fd0\u884c\u4ee3\u7801\uff0c\u6548\u7387\u592a\u4f4e\u3002<\/li>\n\n\n\n<li>\u5728\u8bba\u6587\u5199\u4f5c\u4e2d\uff0c\u53ef\u4ee5\u4f9d\u846b\u82a6\u753b\u74e2\uff0c\u6309\u7167 O \u5956\u8bba\u6587\u7684\u5199\u6cd5\uff0c\u6839\u636e\u76f8\u5e94\u7684\u9898\u76ee\uff0c\u4fee\u6539\u53d8\u91cf\u8bf4\u660e\u5373\u53ef\uff0c\u516c\u5f0f\u53ef\u4ee5\u76f4\u63a5\u7167\u642c\uff0c\u56e0\u4e3a\u6bd4\u8d5b\u53ea\u4f1a\u5bf9\u6587\u5b57\u67e5\u91cd\uff0c\u4e0d\u4f1a\u5bf9\u516c\u5f0f\u548c\u56fe\u7247\u67e5\u91cd\u3002<\/li>\n\n\n\n<li>TOPSIS \u6cd5\u7f3a\u70b9\uff1a<mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">\u6307\u6807\u6743\u91cd\u5b8c\u5168\u7531\u5176\u4ed6\u7684\u8bc4\u4ef7\u65b9\u6cd5\u6765\u786e\u5b9a<\/mark>\uff0c\u4f7f\u7528\u4e0d\u540c\u7684\u8bc4\u4ef7\u65b9\u6cd5\u80fd\u5f97\u5230\u4e0d\u540c\u7684\u6743\u91cd\u3002\u56e0\u6b64\uff0c\u5728 O \u5956\u8bba\u6587\u4e2d\uff0c\u4f1a\u53d1\u73b0\u8be5\u65b9\u6cd5\u8fd8\u9700\u8981\u8ddf\u5176\u4ed6\u8bc4\u4ef7\u65b9\u6cd5\uff08\u5982\u71b5\u6743\u6cd5\u3001\u5c42\u6b21\u5206\u6790\u6cd5\uff09\u8054\u5408\u4f7f\u7528\uff0c\u6765\u5f25\u8865\u81ea\u8eab\u7684\u4e0d\u8db3\u3002<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u8be5\u65b9\u6cd5\u5e38\u7528\u4e8e\uff1a\u5df2\u77e5[math]X[\/math]\u548c[math]\\omega[\/math]\uff0c\u6c42\u7efc\u5408\u8bc4\u4ef7\u6307\u6807[mat [&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-1047","post","type-post","status-publish","format-standard","hentry","category-19"],"_links":{"self":[{"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/posts\/1047","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=1047"}],"version-history":[{"count":21,"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/posts\/1047\/revisions"}],"predecessor-version":[{"id":1543,"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/posts\/1047\/revisions\/1543"}],"wp:attachment":[{"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/media?parent=1047"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/categories?post=1047"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/heqiwei.cn\/index.php\/wp-json\/wp\/v2\/tags?post=1047"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}