{"id":567,"date":"2017-07-13T16:00:13","date_gmt":"2017-07-13T07:00:13","guid":{"rendered":"http:\/\/namekata.in.net\/wp\/prism\/?p=567"},"modified":"2019-03-24T21:40:00","modified_gmt":"2019-03-24T12:40:00","slug":"%e6%af%94%e4%be%8b%e9%85%8d%e5%88%86%e5%80%a4%e3%81%ae%e3%83%80%e3%83%9f%e3%83%bc%e3%83%97%e3%83%ac%e3%82%a4%e3%83%a4%e3%83%bc%e6%80%a7","status":"publish","type":"post","link":"https:\/\/namekata.in.net\/wp\/prism\/2017\/07\/13\/%e6%af%94%e4%be%8b%e9%85%8d%e5%88%86%e5%80%a4%e3%81%ae%e3%83%80%e3%83%9f%e3%83%bc%e3%83%97%e3%83%ac%e3%82%a4%e3%83%a4%e3%83%bc%e6%80%a7\/","title":{"rendered":"\u6bd4\u4f8b\u914d\u5206\u5024\u306e\u30c0\u30df\u30fc\u30d7\u30ec\u30a4\u30e4\u30fc\u6027"},"content":{"rendered":"

\u6bd4\u4f8b\u914d\u5206\u5024\u304c\u30c0\u30df\u30fc\u30d7\u30ec\u30a4\u30e4\u30fc\u6027\u3092\u6e80\u305f\u3059\u3053\u3068\u3092\u4ee5\u4e0b\u3067\u8a3c\u660e\u3059\u308b\u3002\u307e\u305a\u3001\u6bd4\u4f8b\u914d\u5206\u5024\u306e\u7c21\u5358\u306a\u8aac\u660e\u3068\u30c0\u30df\u30fc\u30d7\u30ec\u30a4\u30e4\u30fc\u6027\u306e\u8aac\u660e\u3092\u884c\u3046\u3002<\/p>\n

\u6bd4\u4f8b\u914d\u5206\u5024<\/h3>\n

\u63d0\u643a\u5f62\u30b2\u30fc\u30e0$(N,v)$\u306e\u6bd4\u4f8b\u914d\u5206\u5024<\/strong>${\\rm Prop}(N,v)$\u306f\u6b21\u306e\u3088\u3046\u306b\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb${\\rm Po}$\u3092\u5229\u7528\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u308b\u3002<\/p>\n

\\[
\n{\\rm Prop}_j(N,v) = \\frac{{\\rm Po}(N)}{{\\rm Po}\\left(N – \\{j\\}\\right)} \\left( j \\in N \\right)
\n\\]<\/p>\n

\u4e00\u65b9\u3001\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb<\/strong>${\\rm Po}$\u306f\u6b21\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u308b\u3002<\/p>\n

\\begin{eqnarray}
\n {\\rm Po}(\\emptyset) &=& 1 \\\\
\n {\\rm Po}(S) &=& \\frac{v(S)}{\\sum_{j \\in S}\\frac{1}{{\\rm Po}\\left( S – \\{j\\} \\right)}} \\left( S \\subset N \\right)
\n\\end{eqnarray}<\/p>\n

\u30c0\u30df\u30fc\u30d7\u30ec\u30a4\u30e4\u30fc\u6027<\/h3>\n

\u63d0\u643a\u5f62\u30b2\u30fc\u30e0$(N,v)$\u306e\u3042\u308b\u89e3$f(N,v)$\u304c\u30c0\u30df\u30fc\u30d7\u30ec\u30a4\u30e4\u30fc\u6027\u3092\u6e80\u305f\u3059\u3068\u306f\u3001\u30c0\u30df\u30fc\u30d7\u30ec\u30a4\u30e4\u30fc$j \\in N$\u306b\u5bfe\u3057\u3066\u3001$f_j(N,v)=v\\left( \\{ j \\} \\right)$\u3068\u306a\u308b\u3053\u3068\u3067\u3042\u308b\u3002\u3053\u3053\u3067\u3001\u30d7\u30ec\u30a4\u30e4\u30fc$j$\u304c\u30c0\u30df\u30fc\u30d7\u30ec\u30a4\u30e4\u30fc\u3067\u3042\u308b\u3068\u306f\u3001<\/p>\n

\\[
\nv \\left( S \\cup \\{ j \\} \\right) = v(S) + v \\left( \\{ j \\} \\right) \\left( S \\subset N – \\{ j \\} \\right)
\n\\]<\/p>\n

\u6bd4\u4f8b\u914d\u5206\u5024\u306f\u30c0\u30df\u30fc\u30d7\u30ec\u30a4\u30e4\u30fc\u6027\u3092\u6e80\u305f\u3059<\/h3>\n

\u4ee5\u4e0a\u306e\u3053\u3068\u3088\u308a\u3001\u6b21\u306e\u3053\u3068\u3092\u8a3c\u660e\u3059\u308c\u3070\u3088\u3044\u3002<\/p>\n

\n

\u3042\u308b\u30d7\u30ec\u30a4\u30e4\u30fc$j \\in N$\u306b\u5bfe\u3057\u3066<\/p>\n

\\[
\nv \\left( S \\cup \\{ j \\} \\right) = v(S) + v \\left( \\{ j \\} \\right) \\left( S \\subset N – \\{ j \\} \\right)
\n\\]<\/p>\n

\u304c\u6210\u308a\u7acb\u3066\u3070\u3001\u3059\u306a\u308f\u3061\u3001\u30d7\u30ec\u30a4\u30e4\u30fc$j$\u304c\u30c0\u30df\u30fc\u30d7\u30ec\u30a4\u30e4\u30fc\u306a\u3089\u3070\u3001<\/p>\n

\\[
\n \\frac{{\\rm Po}(N)}{{\\rm Po}\\left(N – \\{j\\}\\right)} = v \\left( \\{ j \\} \\right)
\n\\]\n<\/p><\/div>\n

\u8a3c\u660e<\/h4>\n

\\[
\n \\frac{{\\rm Po} \\left( S \\cup \\{ j \\} \\right)}{{\\rm Po}\\left( S \\right)} = v \\left( \\{ j \\} \\right) \\left( S \\subset N – \\{ j \\} \\right)
\n\\]<\/p>\n

\u3092\u96c6\u5408$S$\u306e\u8981\u7d20\u306e\u500b\u6570$|S|$\u306b\u3088\u308b\u5e30\u7d0d\u6cd5\u3067\u8a3c\u660e\u3059\u308b\u3002<\/p>\n

\\begin{eqnarray}
\n{\\rm Po} \\left( \\emptyset \\right) &=& 1 \\\\
\n{\\rm Po} \\left( \\{ i \\} \\right) &=& v \\left( \\{ i \\} \\right) \\left( \\forall i \\in N \\right)
\n\\end{eqnarray}<\/p>\n

\u3088\u308a\u3001$|S|=0$\u306e\u6642\u306f\u6210\u7acb\u3059\u308b\u3002\u6b21\u306b\u3001$|S|$\u4ee5\u4e0b\u306e\u6642\u6210\u7acb\u3059\u308b\u3068\u4eee\u5b9a\u3059\u308b\u3002<\/P>
\n\\begin{eqnarray}
\n{\\rm Po} \\left( S \\cup \\{ j \\} \\right) &=& \\frac{v(S) + v \\left( \\{ j \\} \\right)}{\\sum_{k \\in S \\cup \\{ j \\}}\\frac{1}{{\\rm Po}\\left( S \\cup \\{ j \\} – \\{ k \\} \\right)}} \\\\
\n &=& \\frac{v(S) + v \\left( \\{ j \\} \\right)}{ \\frac{1}{{\\rm Po}(S)} + \\sum_{k \\in S}\\frac{1}{{\\rm Po}\\left( S \\cup \\{ j \\} – \\{ k \\} \\right)}}
\n\\end{eqnarray}<\/p>\n

\u5e30\u7d0d\u6cd5\u306e\u4eee\u5b9a\u3088\u308a<\/p>\n

\\[
\n {\\rm Po}\\left( S \\cup \\{ j \\} – \\{ k \\} \\right) = {\\rm Po} \\left( S – \\{ k \\} \\right) v \\left( \\{ j \\} \\right)
\n\\]<\/p>\n

\u3092\u4ee3\u5165\u3059\u308b\u3068\u3001<\/p>\n

\\[
\n{\\rm Po} \\left( S \\cup \\{ j \\} \\right) = \\frac{v(S) + v \\left( \\{ j \\} \\right)}{ \\frac{1}{{\\rm Po}(S)} + \\frac{1}{v \\left( \\{ j \\} \\right)}\\sum_{k \\in S}\\frac{1}{{\\rm Po}\\left( S – \\{ k \\} \\right)}}
\n\\]<\/p>\n

\u3053\u3053\u3067\u5206\u6bcd\u306e\u7b2c2\u9805\u306f<\/p>\n

\\[
\n \\sum_{k \\in S}\\frac{1}{{\\rm Po}\\left( S – \\{ k \\} \\right)} = \\frac{v(S)}{{\\rm Po}(S)}
\n\\]<\/p>\n

\u306a\u306e\u3067\u4ee3\u5165\u3059\u308b\u3068<\/p>\n

\\begin{eqnarray}
\n{\\rm Po} \\left( S \\cup \\{ j \\} \\right) &=& \\frac{v(S) + v \\left( \\{ j \\} \\right)}{ \\frac{1}{{\\rm Po}(S)} + \\frac{1}{v \\left( \\{ j \\} \\right)} \\frac{v(S)}{{\\rm Po}(S)}} \\\\
\n &=& {\\rm Po}(S) v \\left( \\{ j \\} \\right)
\n\\end{eqnarray}<\/p>\n

\u5f93\u3063\u3066\u3001$|S|+1$\u306e\u6642\u3082\u6210\u7acb\u3059\u308b\u3053\u3068\u304c\u793a\u3055\u308c\u305f\u3002\uff08\u8a3c\u660e\u7d42\u308f\u308a\uff09<\/p>\n","protected":false},"excerpt":{"rendered":"

\u6bd4\u4f8b\u914d\u5206\u5024\u304c\u30c0\u30df\u30fc\u30d7\u30ec\u30a4\u30e4\u30fc\u6027\u3092\u6e80\u305f\u3059\u3053\u3068\u3092\u4ee5\u4e0b\u3067\u8a3c\u660e\u3059\u308b\u3002\u307e\u305a\u3001\u6bd4\u4f8b\u914d\u5206\u5024\u306e\u7c21\u5358\u306a\u8aac\u660e\u3068\u30c0\u30df\u30fc\u30d7\u30ec\u30a4\u30e4\u30fc\u6027\u306e\u8aac\u660e\u3092\u884c\u3046\u3002 \u6bd4\u4f8b\u914d\u5206\u5024 \u63d0\u643a\u5f62\u30b2\u30fc\u30e0$(N,v)$\u306e\u6bd4\u4f8b\u914d\u5206\u5024${\\rm Prop}(N,v)$\u306f\u6b21\u306e\u3088\u3046\u306b […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[2,23],"tags":[24],"class_list":["post-567","post","type-post","status-publish","format-standard","hentry","category-2","category-23","tag-24","wpautop"],"_links":{"self":[{"href":"https:\/\/namekata.in.net\/wp\/prism\/wp-json\/wp\/v2\/posts\/567","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/namekata.in.net\/wp\/prism\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/namekata.in.net\/wp\/prism\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/namekata.in.net\/wp\/prism\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/namekata.in.net\/wp\/prism\/wp-json\/wp\/v2\/comments?post=567"}],"version-history":[{"count":44,"href":"https:\/\/namekata.in.net\/wp\/prism\/wp-json\/wp\/v2\/posts\/567\/revisions"}],"predecessor-version":[{"id":611,"href":"https:\/\/namekata.in.net\/wp\/prism\/wp-json\/wp\/v2\/posts\/567\/revisions\/611"}],"wp:attachment":[{"href":"https:\/\/namekata.in.net\/wp\/prism\/wp-json\/wp\/v2\/media?parent=567"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/namekata.in.net\/wp\/prism\/wp-json\/wp\/v2\/categories?post=567"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/namekata.in.net\/wp\/prism\/wp-json\/wp\/v2\/tags?post=567"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}