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熵?信息熵??熵值法???是时候一次性解释清楚了!

发布于 2021-03-11

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&quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;box-sizing: border-box !important;overflow-wrap: break-word !important;"><span style="max-width: 100%;letter-spacing: 0.544px;color: rgb(178, 178, 178);font-family: -apple-system-font, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;box-sizing: border-box !important;overflow-wrap: break-word !important;"><strong style="max-width: 100%;color: rgb(53, 53, 53);font-size: 12px;letter-spacing: 0.544px;font-family: &quot;Helvetica Neue&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei&quot;, 黑体, Arial, sans-serif;box-sizing: border-box !important;overflow-wrap: break-word !important;"><strong style="max-width: 100%;font-family: -apple-system-font, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;box-sizing: border-box !important;overflow-wrap: break-word !important;"><span style="max-width: 100%;font-size: 20px;color: rgb(178, 178, 178);text-transform: uppercase;letter-spacing: 1px;font-family: didot;box-sizing: border-box !important;overflow-wrap: break-word !important;">&nbsp;&nbsp; /&nbsp;</span></strong></strong></span></em></span></strong><strong style="max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;"><span style="max-width: 100%;color: rgb(255, 255, 255);box-sizing: border-box !important;overflow-wrap: break-word !important;"><em style="max-width: 100%;color: rgb(51, 51, 51);font-size: 20px;letter-spacing: 0.544px;background-color: rgb(255, 255, 255);font-family: -apple-system-font, system-ui, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;box-sizing: border-box !important;overflow-wrap: break-word !important;"><span style="max-width: 100%;letter-spacing: 0.544px;color: rgb(178, 178, 178);font-family: -apple-system-font, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;box-sizing: border-box !important;overflow-wrap: break-word !important;"><strong style="max-width: 100%;color: rgb(53, 53, 53);font-size: 12px;letter-spacing: 0.544px;font-family: &quot;Helvetica Neue&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei&quot;, 黑体, Arial, sans-serif;box-sizing: border-box !important;overflow-wrap: break-word !important;"><strong style="max-width: 100%;font-family: -apple-system-font, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;box-sizing: border-box !important;overflow-wrap: break-word !important;"><span style="max-width: 100%;font-size: 20px;color: rgb(178, 178, 178);text-transform: uppercase;letter-spacing: 1px;font-family: didot;box-sizing: border-box !important;overflow-wrap: break-word !important;">εντροπία</span></strong></strong></span></em></span></strong><strong style="max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;"><span style="max-width: 100%;background-color: rgb(0, 0, 0);color: rgb(255, 255, 255);box-sizing: border-box !important;overflow-wrap: break-word !important;"><em style="max-width: 100%;color: rgb(51, 51, 51);font-size: 20px;letter-spacing: 0.544px;background-color: rgb(255, 255, 255);font-family: -apple-system-font, system-ui, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;box-sizing: border-box !important;overflow-wrap: break-word !important;"><span style="max-width: 100%;letter-spacing: 0.544px;color: rgb(178, 178, 178);font-family: -apple-system-font, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;box-sizing: border-box !important;overflow-wrap: break-word !important;"><strong style="max-width: 100%;color: rgb(53, 53, 53);font-size: 12px;letter-spacing: 0.544px;font-family: &quot;Helvetica Neue&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei&quot;, 黑体, Arial, sans-serif;box-sizing: border-box !important;overflow-wrap: break-word !important;"><strong style="max-width: 100%;font-family: -apple-system-font, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;box-sizing: border-box !important;overflow-wrap: break-word !important;"><span style="max-width: 100%;font-size: 20px;color: rgb(178, 178, 178);text-transform: uppercase;letter-spacing: 1px;font-family: didot;box-sizing: border-box !important;overflow-wrap: break-word !important;">/</span></strong></strong></span></em></span></strong></section></section><section style="text-align: center;margin: 5px 8px;max-width: 100%;box-sizing: border-box;background-color: rgb(255, 255, 255);letter-spacing: 2px;font-family: -apple-system, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;line-height: 1.75em;overflow-wrap: break-word !important;"><strong style="max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;"><span style="max-width: 100%;font-size: 20px;letter-spacing: 0.544px;color: rgb(178, 178, 178);font-family: -apple-system-font, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;box-sizing: border-box !important;overflow-wrap: break-word !important;"><strong style="max-width: 100%;color: rgb(53, 53, 53);font-size: 12px;letter-spacing: 0.544px;font-family: &quot;Helvetica Neue&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei&quot;, 黑体, Arial, sans-serif;box-sizing: border-box !important;overflow-wrap: break-word !important;"><strong style="max-width: 100%;font-family: -apple-system-font, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;box-sizing: border-box !important;overflow-wrap: break-word !important;"><span style="max-width: 100%;font-size: 20px;color: rgb(178, 178, 178);text-transform: uppercase;letter-spacing: 1px;font-family: didot;box-sizing: border-box !important;overflow-wrap: break-word !important;"><em style="max-width: 100%;color: rgb(51, 51, 51);font-size: 17px;letter-spacing: 0.544px;caret-color: rgb(51, 51, 51);font-family: -apple-system-font, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;box-sizing: border-box !important;overflow-wrap: break-word !important;"><strong style="max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;"><span style="text-transform: uppercase;max-width: 100%;color: rgb(62, 62, 62);letter-spacing: 2px;font-size: 12px;font-family: didot;box-sizing: border-box !important;overflow-wrap: break-word !important;">熵</span></strong></em></span></strong></strong></span></strong></section><section style="text-align: center;margin: 5px 8px;max-width: 100%;box-sizing: border-box;background-color: rgb(255, 255, 255);letter-spacing: 2px;font-family: -apple-system, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;line-height: 1.75em;text-indent: 0em;overflow-wrap: break-word !important;"><br /></section><section style="text-align: justify;margin: 5px 8px;max-width: 100%;box-sizing: border-box;background-color: rgb(255, 255, 255);text-indent: 0em;letter-spacing: 2px;font-family: -apple-system, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;line-height: 1.75em;overflow-wrap: break-word !important;"><strong><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;">“熵值法”</span></strong><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;">对于禾略人,就像呼吸一般的存在。小编在刚进入公司的时候,也惊呼其之神奇,似乎万物皆可熵值法。但是时间长了,大家似乎都有点倦了,开始审美疲劳。于是,小编开始反思:<span style="color: rgb(255, 255, 255);background-color: rgb(102, 102, 102);">熵值法果真是灵丹妙药,还是“精神鸦片”?</span></span></section><section style="text-align: justify;margin: 5px 8px;max-width: 100%;box-sizing: border-box;background-color: rgb(255, 255, 255);text-indent: 0em;letter-spacing: 2px;font-family: -apple-system, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;line-height: 1.75em;overflow-wrap: break-word !important;"><br /></section><section style="text-align: justify;margin: 5px 8px;max-width: 100%;box-sizing: border-box;background-color: rgb(255, 255, 255);text-indent: 0em;letter-spacing: 2px;font-family: -apple-system, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;line-height: 1.75em;overflow-wrap: break-word !important;"><span style="color: rgb(102, 102, 102);font-size: 14px;text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-family: PingFangSC-Light;">现在,小编就带大家追根朔源,让我们<span style="background-color: rgb(102, 102, 102);color: rgb(255, 255, 255);">客观审视一下熵值法</span>。</span><br /></section><section style="text-align: justify;margin: 5px 8px;max-width: 100%;box-sizing: border-box;background-color: rgb(255, 255, 255);text-indent: 2em;letter-spacing: 2px;font-family: -apple-system, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;line-height: 1.75em;overflow-wrap: break-word !important;"><br /></section><section style="text-align: justify;margin: 5px 8px;max-width: 100%;box-sizing: border-box;background-color: rgb(255, 255, 255);text-indent: 0em;letter-spacing: 2px;font-family: -apple-system, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;line-height: 1.75em;overflow-wrap: break-word !important;"><span style="color: rgb(136, 136, 136);font-size: 12px;letter-spacing: 0.544px;text-align: center;text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-family: PingFangSC-Light;">The application of entropy method in risk investment evaluation of real estate.</span></section><section style="text-align: justify;text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><br /></section></section><section data-tools="135编辑器" data-id="93717" style="max-width: 100%;box-sizing: border-box;overflow-wrap: break-word !important;"><section style="max-width: 100%;box-sizing: border-box;background-image: url(&quot;https://mmbiz.qpic.cn/mmbiz_png/7QRTvkK2qC6tIGvc3ozCHcBonywI7fDV4Ksmoy5hWQHibq7TQpAQ5tricOQ7dnLg81iapxGeoUkic5Ob8vHOSI24xQ/640?wx_fmt=png&quot;);background-size: 100%;overflow-wrap: break-word !important;"><section style="padding: 1em;max-width: 100%;box-sizing: border-box;line-height: 1.75em;letter-spacing: 1px;overflow-wrap: break-word !important;"><section style="max-width: 100%;box-sizing: border-box;overflow-wrap: break-word !important;"><section style="margin-right: 8px;margin-left: 8px;max-width: 100%;box-sizing: border-box;color: rgb(0, 0, 0);font-size: 14px;text-align: left;overflow-wrap: break-word !important;"><section style="margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="max-width: 100%;font-family: PingFangTC-Light;box-sizing: border-box !important;overflow-wrap: break-word !important;"><strong style="max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;">▷&nbsp;</strong></span><span style="text-indent: 28px;font-weight: bold;caret-color: red;font-family: PingFangTC-Light;">本文主要回答以下</span><span style="text-indent: 28px;font-weight: bold;caret-color: red;font-family: &quot;Segoe UI Symbol&quot;, sans-serif;">4</span><span style="text-indent: 28px;font-weight: bold;caret-color: red;font-family: PingFangTC-Light;">个问题:</span></section></section><section style="margin-right: 8px;margin-left: 8px;max-width: 100%;text-align: left;box-sizing: border-box !important;overflow-wrap: break-word !important;"><section style="text-indent: 0em;letter-spacing: 2px;margin: 5px 8px;line-height: 1.75em;"><span style="color: rgb(123, 127, 131);font-size: 12px;caret-color: red;text-indent: 28px;font-family: PingFangTC-Light;">1.<span style="letter-spacing: 1px;">什么是“熵”;</span></span></section><section style="text-indent: 0em;letter-spacing: 2px;margin: 5px 8px;line-height: 1.75em;"><span style="color: rgb(123, 127, 131);font-size: 12px;caret-color: red;text-indent: 28px;font-family: PingFangTC-Light;">2.<span style="letter-spacing: 1px;">什么是“信息熵”,”</span><span style="letter-spacing: 1px;">信息熵”和“熵”的联系;</span></span></section><section style="text-indent: 0em;letter-spacing: 2px;margin: 5px 8px;line-height: 1.75em;"><span style="color: rgb(123, 127, 131);font-size: 12px;caret-color: red;text-indent: 28px;font-family: PingFangTC-Light;">3.<span style="letter-spacing: 1px;">什么是“熵值法”,和上述的两个“熵“有关联吗;</span></span></section><section style="text-indent: 0em;letter-spacing: 2px;margin: 5px 8px;line-height: 1.75em;"><span style="color: rgb(123, 127, 131);font-size: 12px;caret-color: red;text-indent: 28px;font-family: PingFangTC-Light;">4.<span style="letter-spacing: 1px;">熵值法对于我们的价值。</span></span></section></section></section></section></section></section><section style="text-align: center;line-height: 1.75em;margin-left: 8px;margin-right: 8px;"><br /></section><section style="text-align: center;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(136, 136, 136);font-size: 12px;letter-spacing: 0.544px;text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-family: PingFangSC-Light;">注:本文篇幅较长,如果您对此感兴趣,请耐心看完。</span></section><section style="max-width: 100%;min-height: 1em;line-height: 1.75em;margin-left: 8px;margin-right: 8px;box-sizing: border-box !important;overflow-wrap: break-word !important;"><br /></section><section style="max-width: 100%;min-height: 1em;line-height: 1.75em;margin-left: 8px;margin-right: 8px;box-sizing: border-box !important;overflow-wrap: break-word !important;"><br /></section><section style="max-width: 100%;min-height: 1em;line-height: 1.75em;margin-left: 8px;margin-right: 8px;box-sizing: border-box !important;overflow-wrap: break-word !important;"><br /></section><section data-role="paragraph" data-width="18%" style="box-sizing: border-box;margin-right: auto;margin-left: auto;max-width: 100%;letter-spacing: 0.544px;background-color: rgb(255, 255, 255);width: 18%;flex: 0 0 18%;font-family: -apple-system, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;overflow-wrap: break-word !important;"><section style="max-width: 100%;min-height: 1em;line-height: 1.75em;margin-left: 8px;margin-right: 8px;box-sizing: border-box !important;overflow-wrap: break-word !important;"><br /></section></section><section style="text-align: center;line-height: 1.75em;margin-left: 8px;margin-right: 8px;"><img class="rich_pages" data-ratio="0.4546296296296296" data-s="300,640" data-src="https://mmbiz.qpic.cn/mmbiz_png/AJkYaTAujIyWURddlHITkZgKz53a4xug0kMHobuMXyUP4BaAg8jbok2gkiasHeVq9uvsJcxYiaWX0u5iamicBcs3rw/640?wx_fmt=png" data-type="png" data-w="1080" style="" /></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;">首先对于第一个问题,小编再熟悉不过了,热能专业若不知道“熵”,建议再去烧锅炉学习半年。</span></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><br /></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;">先背一段热力学第二定律:“热量不能自发地从低温物体转移到高温物体“。OK,没了,就是这么简单。</span></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><br /></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;">正所谓大道至简,热力学第二定律又被称为”熵增“定律,从它的描述中大家也能明白一二:在自然状态下,热量只会从热水杯传递给冷水杯,这个过程是不可逆的,而”熵“则是这个不可逆过程的度量。</span></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><br /></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;">换而言之,封闭系统的熵只会不变或增加,不会减少。关于“热力学熵”,最原始的宏观表达式是:</span></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><br /></section><section style="text-align: center;text-indent: 2em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><img data-ratio="0.6441441441441441" data-src="https://mmbiz.qpic.cn/mmbiz_png/AJkYaTAujIyWURddlHITkZgKz53a4xugD5bRazLJBzU3sSvKE7nxvFP4dia0NXXic9cw739NzqbbyFVGxGwicq2XQ/640?wx_fmt=png" data-type="png" data-w="222" height="57" style="box-sizing:border-box;width: 88px;height: 57px;" width="88" /></section><section style="text-align: center;text-indent: 2em;line-height: 1.75em;margin-left: 8px;margin-right: 8px;"><br /></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;">即熵的增量等于物体吸收的热量除以它的温度。但是热量传递的过程是连续变化的,所以后面又有微观形式的微分表达,进行一系列假设(这里不做赘述)后,进行积分,并将对象由变化量的“熵增”转向物体本身的状态量“熵”,由单个物体扩展到一个封闭系统,最后得到了如下表达式,这个“熵”也被称作“吉布斯熵”:</span></section><section style="text-align: center;text-indent: 2em;line-height: 1.75em;margin-left: 8px;margin-right: 8px;"><br /></section><section style="text-align: center;text-indent: 2em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><img data-ratio="0.26525198938992045" data-src="https://mmbiz.qpic.cn/mmbiz_png/AJkYaTAujIyWURddlHITkZgKz53a4xugyLYwN1aRroD13nt5ZjDvlcEo69CDlys0micP2sdAbPI0esWnE5RrRIg/640?wx_fmt=png" data-type="png" data-w="377" height="53" style="box-sizing:border-box;width: 199px;height: 53px;" width="199" /></section><section style="text-align: center;text-indent: 2em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><br /></section><section style="text-align: center;text-indent: 2em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><br /></section><section style="text-align: center;text-indent: 2em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><br /></section><section data-role="paragraph" data-width="18%" style="box-sizing: border-box;margin-right: auto;margin-left: auto;max-width: 100%;letter-spacing: 0.544px;background-color: rgb(255, 255, 255);width: 18%;flex: 0 0 18%;font-family: -apple-system, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;overflow-wrap: break-word !important;"><section style="max-width: 100%;min-height: 1em;line-height: 1.75em;margin-left: 8px;margin-right: 8px;box-sizing: border-box !important;overflow-wrap: break-word !important;"><br /></section></section><section style="text-align: center;line-height: 1.75em;margin-left: 8px;margin-right: 8px;"><img class="rich_pages" data-ratio="0.4546296296296296" data-s="300,640" data-src="https://mmbiz.qpic.cn/mmbiz_png/AJkYaTAujIyWURddlHITkZgKz53a4xugFSrliaIsbphLnjXTHicKbQnJg8iapNvPoOXrHs5TQBWyoDbynWw1FpG4g/640?wx_fmt=png" data-type="png" data-w="1080" style="" /></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;">那么什么又是“信息熵“呢?这里不得不提到一个人,那就是大名鼎鼎的信息论之父——克劳德 • 香农。在这之前,先举一个简单的例子:</span></section><section style="text-indent: 2em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><br /></section><section data-tools="135编辑器" data-id="93717" style="max-width: 100%;box-sizing: border-box;overflow-wrap: break-word !important;"><section style="max-width: 100%;box-sizing: border-box;background-image: url(&quot;https://mmbiz.qpic.cn/mmbiz_png/7QRTvkK2qC6tIGvc3ozCHcBonywI7fDV4Ksmoy5hWQHibq7TQpAQ5tricOQ7dnLg81iapxGeoUkic5Ob8vHOSI24xQ/640?wx_fmt=png&quot;);background-size: 100%;overflow-wrap: break-word !important;"><section style="padding: 1em;max-width: 100%;box-sizing: border-box;line-height: 1.75em;letter-spacing: 1px;overflow-wrap: break-word !important;"><section style="max-width: 100%;box-sizing: border-box;overflow-wrap: break-word !important;"><section style="margin-right: 8px;margin-left: 8px;max-width: 100%;box-sizing: border-box;color: rgb(0, 0, 0);font-size: 14px;text-align: left;overflow-wrap: break-word !important;"><section style="text-align: justify;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><strong><span style="color: rgb(123, 127, 131);font-size: 12px;text-indent: 28px;caret-color: red;font-family: PingFangTC-Light;">事件1:我们抛掷一枚硬币每种情况出现的概率为1/2,记为P1;</span><br /></strong></section></section><section style="margin-right: 8px;margin-left: 8px;max-width: 100%;text-align: left;box-sizing: border-box !important;overflow-wrap: break-word !important;"><section style="text-align: justify;text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><strong><span style="color: rgb(123, 127, 131);font-size: 12px;letter-spacing: 1px;text-align: left;text-indent: 28px;caret-color: rgb(255, 0, 0);font-family: PingFangTC-Light;">事件2:抛掷一个骰子每种情况出现的概率为1/6,记为P2;</span></strong></section><section style="text-align: justify;text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><strong><span style="color: rgb(123, 127, 131);font-size: 12px;letter-spacing: 1px;text-align: left;text-indent: 28px;caret-color: rgb(255, 0, 0);font-family: PingFangTC-Light;">事件3:同时抛掷硬币和骰子,每种情况出现的概率为1/12,记为P3。</span></strong><span style="color: rgb(123, 127, 131);font-size: 12px;letter-spacing: 1px;text-align: left;text-indent: 28px;caret-color: rgb(255, 0, 0);font-family: PingFangTC-Light;"></span></section></section></section></section></section></section><section style="text-align: center;line-height: 1.75em;margin-left: 8px;margin-right: 8px;"><br /></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;">如何建立事件和其发生概率之间的联系呢?聪明的你肯定发现了:</span></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;"><br /></span></section><section data-tools="135编辑器" data-id="93717" style="max-width: 100%;box-sizing: border-box;overflow-wrap: break-word !important;"><section style="max-width: 100%;box-sizing: border-box;background-image: url(&quot;https://mmbiz.qpic.cn/mmbiz_png/7QRTvkK2qC6tIGvc3ozCHcBonywI7fDV4Ksmoy5hWQHibq7TQpAQ5tricOQ7dnLg81iapxGeoUkic5Ob8vHOSI24xQ/640?wx_fmt=png&quot;);background-size: 100%;overflow-wrap: break-word !important;"><section style="padding: 1em;max-width: 100%;box-sizing: border-box;line-height: 1.75em;letter-spacing: 1px;overflow-wrap: break-word !important;"><section style="max-width: 100%;box-sizing: border-box;overflow-wrap: break-word !important;"><section style="margin-right: 8px;margin-left: 8px;max-width: 100%;box-sizing: border-box;color: rgb(0, 0, 0);font-size: 14px;text-align: center;overflow-wrap: break-word !important;"><section style="margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(123, 127, 131);font-size: 12px;text-indent: 28px;caret-color: red;font-family: PingFangTC-Light;"></span><strong><span style="color: rgb(123, 127, 131);font-size: 12px;letter-spacing: 1px;text-align: left;text-indent: 28px;caret-color: rgb(255, 0, 0);font-family: PingFangTC-Light;">P3=P2*P1</span></strong></section></section></section></section></section></section><section style="text-align: center;text-indent: 2em;line-height: 1.75em;margin-left: 8px;margin-right: 8px;"><br /></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;">同取对数并且两边同取负值得:</span></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;"><br /></span></section><section data-tools="135编辑器" data-id="93717" style="max-width: 100%;box-sizing: border-box;overflow-wrap: break-word !important;"><section style="max-width: 100%;box-sizing: border-box;background-image: url(&quot;https://mmbiz.qpic.cn/mmbiz_png/7QRTvkK2qC6tIGvc3ozCHcBonywI7fDV4Ksmoy5hWQHibq7TQpAQ5tricOQ7dnLg81iapxGeoUkic5Ob8vHOSI24xQ/640?wx_fmt=png&quot;);background-size: 100%;overflow-wrap: break-word !important;"><section style="padding: 1em;max-width: 100%;box-sizing: border-box;line-height: 1.75em;letter-spacing: 1px;overflow-wrap: break-word !important;"><section style="max-width: 100%;box-sizing: border-box;overflow-wrap: break-word !important;"><section style="margin-right: 8px;margin-left: 8px;max-width: 100%;box-sizing: border-box;color: rgb(0, 0, 0);font-size: 14px;text-align: center;overflow-wrap: break-word !important;"><section style="margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><strong><span style="color: rgb(123, 127, 131);font-size: 12px;text-indent: 28px;font-family: PingFangTC-Light;">log(1/P3)= log(1/P2)+ log(1/P1)</span></strong><br /></section></section></section></section></section></section><section style="text-align: center;line-height: 1.75em;margin-left: 8px;margin-right: 8px;"><br /></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;">这里解释两点:</span></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;"><br /></span></section><section data-tools="135编辑器" data-id="93717" style="max-width: 100%;box-sizing: border-box;overflow-wrap: break-word !important;"><section style="max-width: 100%;box-sizing: border-box;background-image: url(&quot;https://mmbiz.qpic.cn/mmbiz_png/7QRTvkK2qC6tIGvc3ozCHcBonywI7fDV4Ksmoy5hWQHibq7TQpAQ5tricOQ7dnLg81iapxGeoUkic5Ob8vHOSI24xQ/640?wx_fmt=png&quot;);background-size: 100%;overflow-wrap: break-word !important;"><section style="padding: 1em;max-width: 100%;box-sizing: border-box;line-height: 1.75em;letter-spacing: 1px;overflow-wrap: break-word !important;"><section style="max-width: 100%;box-sizing: border-box;overflow-wrap: break-word !important;"><section style="margin-right: 8px;margin-left: 8px;max-width: 100%;text-align: left;box-sizing: border-box !important;overflow-wrap: break-word !important;"><section style="text-align: justify;text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><strong><span style="color: rgb(123, 127, 131);font-size: 12px;letter-spacing: 1px;text-align: left;text-indent: 28px;caret-color: rgb(255, 0, 0);font-family: PingFangTC-Light;">1.为什么要取对数?因为相比于乘除,加减对于两个对象来说单位更加统一,作为事件的属性更为合适;</span></strong></section><section style="text-align: justify;text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><strong><span style="color: rgb(123, 127, 131);font-size: 12px;letter-spacing: 1px;text-align: left;text-indent: 28px;caret-color: rgb(255, 0, 0);font-family: PingFangTC-Light;">2.为什么要同取负值?因为概率Pi越小,代表事件i的不确定性越大,所含信息量越大,log(1/Pi)也越大,用log(1/Pi)来量化信息量非常合适。</span></strong><span style="color: rgb(123, 127, 131);font-size: 12px;letter-spacing: 1px;text-align: left;text-indent: 28px;caret-color: rgb(255, 0, 0);font-family: PingFangTC-Light;"></span></section></section></section></section></section></section><section style="text-align: center;line-height: 1.75em;margin-left: 8px;margin-right: 8px;"><br /></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;">这个想法得到了所有人的认同,那么就叫log(1/Pi)为事件i的“信息量”吧,并取单位为“比特“。</span></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><br /></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;">OK,对于普通人,事情已经结束了,但是天才就是天才,克劳德 • 香农脑路清奇,对于某一个事件本身,比如事件1,如果这枚硬币并不规则,正反面的概率有可能是1/3和2/3,那该如何量化其信息量呢?</span><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;">直觉上来说各为1/2时,不确定性更高,包含的信息量更大。</span></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;"><br /></span></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;">如果不能理解,试想如果硬币的正面的材质和掉落桌面的材质都具有磁性,那么这枚硬币反面朝上的概率说是95/100毫不为过,那正面朝上即为5/100。</span><span style="color: rgb(102, 102, 102);font-family: PingFangSC-Light;font-size: 14px;text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);">如果是这样,那么事件的不确定性极小,包含的信息量很小</span><span style="color: rgb(102, 102, 102);font-family: PingFangSC-Light;font-size: 14px;text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);">。</span></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);font-family: PingFangSC-Light;font-size: 14px;text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);"><br /></span></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);font-family: PingFangSC-Light;font-size: 14px;text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);">这样你能理解为什么说(1/2,1/2)的时候信息量大于(1/3,2/3),而且是最大了吧?</span></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><br /></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;">好了,目前为止,你得到了3个有用的信息,我来帮你理清楚:</span></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;"><br /></span></section><section data-tools="135编辑器" data-id="93717" style="max-width: 100%;box-sizing: border-box;overflow-wrap: break-word !important;"><section style="max-width: 100%;box-sizing: border-box;background-image: url(&quot;https://mmbiz.qpic.cn/mmbiz_png/7QRTvkK2qC6tIGvc3ozCHcBonywI7fDV4Ksmoy5hWQHibq7TQpAQ5tricOQ7dnLg81iapxGeoUkic5Ob8vHOSI24xQ/640?wx_fmt=png&quot;);background-size: 100%;overflow-wrap: break-word !important;"><section style="padding: 1em;max-width: 100%;box-sizing: border-box;line-height: 1.75em;letter-spacing: 1px;overflow-wrap: break-word !important;"><section style="max-width: 100%;box-sizing: border-box;overflow-wrap: break-word !important;"><section style="margin-right: 8px;margin-left: 8px;max-width: 100%;text-align: left;box-sizing: border-box !important;overflow-wrap: break-word !important;"><section style="text-align: justify;text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><strong><span style="color: rgb(123, 127, 131);font-size: 12px;letter-spacing: 1px;text-align: left;text-indent: 28px;caret-color: rgb(255, 0, 0);font-family: PingFangTC-Light;">1. &nbsp;&nbsp;&nbsp; (1/2,1/2)时候的信息量是log[1/(1/2)],而且最大;</span></strong></section><section style="text-align: justify;text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><strong><span style="color: rgb(123, 127, 131);font-size: 12px;letter-spacing: 1px;text-align: left;text-indent: 28px;caret-color: rgb(255, 0, 0);font-family: PingFangTC-Light;">2. &nbsp;&nbsp;&nbsp; 对于(P,1-P),1/2-P的绝对值越大,其信息量越小;</span></strong></section><section style="text-align: justify;text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><strong><span style="color: rgb(123, 127, 131);font-size: 12px;letter-spacing: 1px;text-align: left;text-indent: 28px;caret-color: rgb(255, 0, 0);font-family: PingFangTC-Light;">3. &nbsp;&nbsp;&nbsp; 当P或1-P趋向于0的时候,信息量极小,趋向于0。</span></strong><span style="color: rgb(123, 127, 131);font-size: 12px;letter-spacing: 1px;text-align: left;text-indent: 28px;caret-color: rgb(255, 0, 0);font-family: PingFangTC-Light;"></span></section></section></section></section></section></section><section style="text-align: center;line-height: 1.75em;margin-left: 8px;margin-right: 8px;"><br /></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;">我猜香农当时肯定一直在想如何用数学语言来量化的这一发现,是否可以用一个公式来诠释,而且向着更泛化的空间去扩展。作为平常人,我们并没有经过严格的数学训练可能很难去想象。但是只要你善于观察,不难发现,我们设(P,1-P)的信息量符合函数H(P,1-P):</span></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;"><br /></span></section><section data-tools="135编辑器" data-id="93717" style="max-width: 100%;box-sizing: border-box;overflow-wrap: break-word !important;"><section style="max-width: 100%;box-sizing: border-box;background-image: url(&quot;https://mmbiz.qpic.cn/mmbiz_png/7QRTvkK2qC6tIGvc3ozCHcBonywI7fDV4Ksmoy5hWQHibq7TQpAQ5tricOQ7dnLg81iapxGeoUkic5Ob8vHOSI24xQ/640?wx_fmt=png&quot;);background-size: 100%;overflow-wrap: break-word !important;"><section style="padding: 1em;max-width: 100%;box-sizing: border-box;line-height: 1.75em;letter-spacing: 1px;overflow-wrap: break-word !important;"><section style="max-width: 100%;box-sizing: border-box;overflow-wrap: break-word !important;"><section style="margin-right: 8px;margin-left: 8px;max-width: 100%;text-align: left;box-sizing: border-box !important;overflow-wrap: break-word !important;"><section style="text-align: justify;text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><strong><span style="color: rgb(123, 127, 131);font-size: 12px;letter-spacing: 1px;text-align: left;text-indent: 28px;caret-color: rgb(255, 0, 0);font-family: PingFangTC-Light;">P=1/2时:H(1/2,1/2)= log[1/(1/2)]=1/2* log[1/(1/2)]+ 1/2* log[1/(1/2)]</span></strong></section><section style="text-align: justify;text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><strong><span style="color: rgb(123, 127, 131);font-size: 12px;letter-spacing: 1px;text-align: left;text-indent: 28px;caret-color: rgb(255, 0, 0);font-family: PingFangTC-Light;">P→0时:H(P,1-P)→0=P*log(1/P)+(1-P)* log[1/(1-P)]</span></strong></section></section></section></section></section></section><section style="text-align: center;line-height: 1.75em;margin-left: 8px;margin-right: 8px;"><br /></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;">发现规律了吗?对的,就是第二个式子中H(P,1-P)= P*log(1/P)+(1-P)* log[1/(1-P)],很容易证明这个式子满足1、2、3条件,这就是香农想要的完美的解释他这一发现的数学公式!如果这个事件有不止两种情况,那还可以扩展为:</span></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;"><br /></span></section><section data-tools="135编辑器" data-id="93717" style="max-width: 100%;box-sizing: border-box;overflow-wrap: break-word !important;"><section style="max-width: 100%;box-sizing: border-box;background-image: url(&quot;https://mmbiz.qpic.cn/mmbiz_png/7QRTvkK2qC6tIGvc3ozCHcBonywI7fDV4Ksmoy5hWQHibq7TQpAQ5tricOQ7dnLg81iapxGeoUkic5Ob8vHOSI24xQ/640?wx_fmt=png&quot;);background-size: 100%;overflow-wrap: break-word !important;"><section style="padding: 1em;max-width: 100%;box-sizing: border-box;line-height: 1.75em;letter-spacing: 1px;overflow-wrap: break-word !important;"><section style="max-width: 100%;box-sizing: border-box;overflow-wrap: break-word !important;"><section style="margin-right: 8px;margin-left: 8px;max-width: 100%;box-sizing: border-box;color: rgb(0, 0, 0);font-size: 14px;text-align: center;overflow-wrap: break-word !important;"><section style="text-align: center;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><strong><span style="color: rgb(123, 127, 131);font-size: 12px;text-indent: 28px;font-family: PingFangTC-Light;">H(P1,P2……,Pn)=∑Pi*log(1/Pi)= -∑Pi*logPi&nbsp; (∑Pi=1)</span></strong><br /></section></section></section></section></section></section><section style="text-align: center;line-height: 1.75em;margin-left: 8px;margin-right: 8px;"><br /></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;">这就是信息量的公式,如果你感兴趣,可以用归纳法证明它完全满足上述3个条件的扩展。</span></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><br /></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;">回到一开始,事件总是从不确定走向确定,这就像热量总会从高温传向低温一样是一个不可逆过程。</span></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><br /></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;">在这个过程中,事件包含的信息量不断减少,换句话说,信息的减少量不断增加,稳定性增加;同样的,在热量传递的过程中,系统熵增加,系统也越来越趋于混沌且稳定。</span></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><br /></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;">信息量在某些方面和“热力学熵“不谋而合,更重要是,信息量的数学描述和“热力学熵“的微观数学描述竟然如此相仿!于是冯诺依曼告诉香农说:“你就叫它信息熵吧,这有两个好理由:<span style="background-color: rgb(102, 102, 102);color: rgb(255, 255, 255);">一是你的不确定性函数已在热力学中用到过,在那里它就叫熵;二是没人真正理解熵为何物,这就让你在任何时候都可能进能退,立于不败之地”。</span></span></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;"><span style="background-color: rgb(102, 102, 102);color: rgb(255, 255, 255);"><br /></span></span></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;">所以在介绍完“熵”和”信息熵”后,对于第二个问题,我的观点是:<span style="background-color: rgb(102, 102, 102);color: rgb(255, 255, 255);">“熵”和”信息熵”只是数学描述相仿,没有本质的联系,要说他们之间有什么关联,你就只能佩服冯诺依曼天马行空的想象力。</span></span></section><section style="text-indent: 2em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><br /></section><h2 style="text-align: center;margin: 5px 8px;letter-spacing: 2px;text-indent: 0em;font-weight: bold;line-height: 1.75em;"><br /></h2><section style="line-height: 1.75em;margin-left: 8px;margin-right: 8px;"><br /></section><section style="line-height: 1.75em;margin-left: 8px;margin-right: 8px;"><br /></section><section data-role="paragraph" data-width="18%" style="box-sizing: border-box;margin-right: auto;margin-left: auto;max-width: 100%;letter-spacing: 0.544px;background-color: rgb(255, 255, 255);width: 18%;flex: 0 0 18%;font-family: -apple-system, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;overflow-wrap: break-word !important;"><section style="max-width: 100%;min-height: 1em;line-height: 1.75em;margin-left: 8px;margin-right: 8px;box-sizing: border-box !important;overflow-wrap: break-word !important;"><br /></section></section><section style="text-align: center;line-height: 1.75em;margin-left: 8px;margin-right: 8px;"><img class="rich_pages" data-ratio="0.4546296296296296" data-s="300,640" data-src="https://mmbiz.qpic.cn/mmbiz_png/AJkYaTAujIyWURddlHITkZgKz53a4xug9Mm6QmjlzibBPSUIMMrz2jiapnbJwgYF4X0dYvyMRKjZeghOaOZGcL3g/640?wx_fmt=png" data-type="png" data-w="1080" style="" /></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;">那么,什么是“熵值法“?</span></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><br /></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;">我们一直在用,至少包括小编在内的不少人一开始真的很难理解。介绍“熵值法“之前,我们还是先讲一个故事:张老师作为大学辅导员,学期末被学生评优工作搞的焦头烂额,学生的具体成绩单如下:</span></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><br /></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><img data-ratio="0.32411820781696854" data-src="https://mmbiz.qpic.cn/mmbiz_png/AJkYaTAujIyWURddlHITkZgKz53a4xugplfB5M74btMiaCH0tnZBOzrfcTRmBibh2ib3vePOQaYWwe7ERKuvfyMfQ/640?wx_fmt=png" data-type="png" data-w="1049" style="box-sizing: border-box;width: 100%;height: auto;" data-backw="562" data-backh="182" /></section><section style="text-indent: 2em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><br /></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;">他本来的想法是,将学生的分数直接累计,最后转换为百分制,这下学科平均分低的老师不乐意了,学科并没有高低之分啊,这不公平啊?张老师觉得也有道理,为了平息众怒,绝对公平,他将分数全部转化为占比,这下每个学科之间平衡了,大家加起来都是1,权重相等,老师们的怒火得到平息:</span></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><br /></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><img data-ratio="0.3237531699070161" data-src="https://mmbiz.qpic.cn/mmbiz_png/AJkYaTAujIyWURddlHITkZgKz53a4xugl1NzAhnOevZb6pxFQRdnR5tEk56Z8icaBjiactCW0RK2bE6sI1ByQ1qg/640?wx_fmt=png" data-type="png" data-w="1183" style="box-sizing: border-box;width: 100%;height: auto;" data-backw="562" data-backh="182" /></section><section style="text-indent: 2em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><br /></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;">可是这下,小黄不乐意了,看实际分数,大学语文我比小红高了30分,可是总评就多了2分。小明虽然得了第一,但他也不服气,成绩分化较大的大学语文和高等数学,他都遥遥领先,但是总评也只比第二名多了3分。</span></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><br /></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;">这种众生平等的权重分配显然也不合理,仔细观察,他们都是被初中地理、小学英语、语文和初中数学给拖累了,这四门学科除了个别NT外,大家都是满分,简而言之,这种大家都会的,根本就不要来比较了,体现不了差异化的指标,权重应该接近0。</span></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><br /></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;">那到底该如何比较呢?这时小明提议,分数分化较大的学科,说明大家在这方面的能力差异较大,该学科的权重应该增加;反之分数分化较小的学科,权重应该减少。换句话说:在将分数转化为占比的基础上,应该将占比的离散程度作为该学科的权重。</span></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><br /></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;">接下来,在研究这个问题之前,我们还是先从简单出发,假设只有两名学生参与总评,那么就可以设某一学科的权重为E(P,1-P),P和1-P代表两名学生该学科的分数占比,结合E(P,1-P)梳理上述信息有:</span></section><section style="text-indent: 2em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><br /></section><section data-tools="135编辑器" data-id="93717" style="max-width: 100%;box-sizing: border-box;overflow-wrap: break-word !important;"><section style="max-width: 100%;box-sizing: border-box;background-image: url(&quot;https://mmbiz.qpic.cn/mmbiz_png/7QRTvkK2qC6tIGvc3ozCHcBonywI7fDV4Ksmoy5hWQHibq7TQpAQ5tricOQ7dnLg81iapxGeoUkic5Ob8vHOSI24xQ/640?wx_fmt=png&quot;);background-size: 100%;overflow-wrap: break-word !important;"><section style="padding: 1em;max-width: 100%;box-sizing: border-box;line-height: 1.75em;letter-spacing: 1px;overflow-wrap: break-word !important;"><section style="max-width: 100%;box-sizing: border-box;overflow-wrap: break-word !important;"><section style="margin-right: 8px;margin-left: 8px;max-width: 100%;box-sizing: border-box;color: rgb(0, 0, 0);font-size: 14px;text-align: left;overflow-wrap: break-word !important;"><section style="margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><strong><span style="color: rgb(123, 127, 131);font-size: 12px;text-indent: 28px;font-family: PingFangTC-Light;">1.P=1/2时,两个人分数一样,该学科离散程度为0,权重应该为0,即E(1/2,1/2)=0;</span></strong></section></section><section style="margin-right: 8px;margin-left: 8px;max-width: 100%;text-align: left;box-sizing: border-box !important;overflow-wrap: break-word !important;"><section style="text-align: justify;text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><strong><span style="color: rgb(123, 127, 131);font-size: 12px;letter-spacing: 1px;text-align: left;text-indent: 28px;caret-color: rgb(255, 0, 0);font-family: PingFangTC-Light;">2.对于(P,1-P),1/2-P的绝对值越大,代表两个人的分数差距越大,离散程度越高,即E(P,1-P)越大;</span></strong></section><section style="text-align: justify;text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><strong><span style="color: rgb(123, 127, 131);font-size: 12px;letter-spacing: 1px;text-align: left;text-indent: 28px;caret-color: rgb(255, 0, 0);font-family: PingFangTC-Light;">3. 当P或1-P等于1的时候,两个人的分数差距最大,E(P,1-P)达到最大值。</span></strong><span style="color: rgb(123, 127, 131);font-size: 12px;letter-spacing: 1px;text-align: left;text-indent: 28px;caret-color: rgb(255, 0, 0);font-family: PingFangTC-Light;"></span></section></section></section></section></section></section><section style="text-align: center;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><br /></section><section style="text-align: justify;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);font-size: 14px;text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-family: PingFangSC-Light;">不知道大家发现了没有,这个E(P,1-P)函数和前面的信息熵函数H(P,1-P)的描述似乎很像,对的,你没有猜错,如果取E(P,1-P)</span><span style="color: rgb(102, 102, 102);font-size: 14px;text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-family: PingFangSC-Light;">= -H(P,1-P),满足上述2、3个条件,还需要优化的地方在于保证条件1中E(1/2,1/2)=0,那我们可以令:</span></section><section style="text-align: justify;line-height: 1.75em;margin-left: 8px;margin-right: 8px;"><br /></section><section data-tools="135编辑器" data-id="93717" style="max-width: 100%;box-sizing: border-box;overflow-wrap: break-word !important;"><section style="max-width: 100%;box-sizing: border-box;background-image: url(&quot;https://mmbiz.qpic.cn/mmbiz_png/7QRTvkK2qC6tIGvc3ozCHcBonywI7fDV4Ksmoy5hWQHibq7TQpAQ5tricOQ7dnLg81iapxGeoUkic5Ob8vHOSI24xQ/640?wx_fmt=png&quot;);background-size: 100%;overflow-wrap: break-word !important;"><section style="padding: 1em;max-width: 100%;box-sizing: border-box;line-height: 1.75em;letter-spacing: 1px;overflow-wrap: break-word !important;"><section style="max-width: 100%;box-sizing: border-box;overflow-wrap: break-word !important;"><section style="margin-right: 8px;margin-left: 8px;max-width: 100%;box-sizing: border-box;color: rgb(0, 0, 0);font-size: 14px;text-align: center;overflow-wrap: break-word !important;"><section style="margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(123, 127, 131);font-size: 12px;text-indent: 28px;font-family: PingFangTC-Light;"><strong>E(P,1-P)=-H(P,1-P)+a(a为常数),且E(1/2,1/2)=0</strong></span><br /></section></section></section></section></section></section><section style="text-align: center;line-height: 1.75em;margin-left: 8px;margin-right: 8px;"><br /></section><section style="text-align: justify;text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;">很容易算出a= log[1/(1/2)],那么就有:</span></section><section style="text-align: justify;text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;"><br /></span></section><section data-tools="135编辑器" data-id="93717" style="max-width: 100%;box-sizing: border-box;overflow-wrap: break-word !important;"><section style="max-width: 100%;box-sizing: border-box;background-image: url(&quot;https://mmbiz.qpic.cn/mmbiz_png/7QRTvkK2qC6tIGvc3ozCHcBonywI7fDV4Ksmoy5hWQHibq7TQpAQ5tricOQ7dnLg81iapxGeoUkic5Ob8vHOSI24xQ/640?wx_fmt=png&quot;);background-size: 100%;overflow-wrap: break-word !important;"><section style="padding: 1em;max-width: 100%;box-sizing: border-box;line-height: 1.75em;letter-spacing: 1px;overflow-wrap: break-word !important;"><section style="max-width: 100%;box-sizing: border-box;overflow-wrap: break-word !important;"><section style="margin-right: 8px;margin-left: 8px;max-width: 100%;box-sizing: border-box;color: rgb(0, 0, 0);font-size: 14px;text-align: center;overflow-wrap: break-word !important;"><section style="margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><strong><span style="color: rgb(123, 127, 131);font-size: 12px;text-indent: 28px;font-family: PingFangTC-Light;">E(P,1-P)=-H(P,1-P)+ log[1/(1/2)]</span></strong><br /></section></section></section></section></section></section><section style="text-align: center;text-indent: 2em;line-height: 1.75em;margin-left: 8px;margin-right: 8px;"><br /></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;">如果进行扩展,就有:</span></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;"><br /></span></section><section data-tools="135编辑器" data-id="93717" style="max-width: 100%;box-sizing: border-box;overflow-wrap: break-word !important;"><section style="max-width: 100%;box-sizing: border-box;background-image: url(&quot;https://mmbiz.qpic.cn/mmbiz_png/7QRTvkK2qC6tIGvc3ozCHcBonywI7fDV4Ksmoy5hWQHibq7TQpAQ5tricOQ7dnLg81iapxGeoUkic5Ob8vHOSI24xQ/640?wx_fmt=png&quot;);background-size: 100%;overflow-wrap: break-word !important;"><section style="padding: 1em;max-width: 100%;box-sizing: border-box;line-height: 1.75em;letter-spacing: 1px;overflow-wrap: break-word !important;"><section style="max-width: 100%;box-sizing: border-box;overflow-wrap: break-word !important;"><section style="margin-right: 8px;margin-left: 8px;max-width: 100%;box-sizing: border-box;color: rgb(0, 0, 0);font-size: 14px;text-align: left;overflow-wrap: break-word !important;"><section style="margin: 5px 8px;letter-spacing: 2px;text-align: center;line-height: 1.75em;"><span style="color: rgb(123, 127, 131);font-size: 12px;text-indent: 28px;font-family: PingFangTC-Light;"></span><strong><span style="color: rgb(123, 127, 131);font-size: 12px;text-indent: 28px;font-family: PingFangTC-Light;">E(P1,P2……Pn)= -H(P1,P2……Pn)+ log[1/(1/n)]</span></strong><br /></section></section></section></section></section></section><section style="text-align: center;text-indent: 2em;line-height: 1.75em;margin-left: 8px;margin-right: 8px;"><br /></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;">没错,这就是熵值法的权重表达式,其实除了使用信息量的数学描述函数外,我们还可以用方差∑(P-(1/n))2,标准差∑|P-(1/n)|,甚至取对数降维使用∑|logP-log(1/n)|来描述数据的离散程度,这些都是符合上述3个条件的函数。所以,熵值法仅仅是符合“由数据离散程度分配权重“的一种。</span></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><br /></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;">所以对于第三个问题,我的观点是:<span style="background-color: rgb(102, 102, 102);color: rgb(255, 255, 255);">熵值法只是借用了信息量的数学模型,和信息熵并无本质的联系,本质上是对数据离散程度的表达。&nbsp;</span></span></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><br /></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;">但是人们通常很善于联想归纳,既然“熵值法”,”信息熵“和”热力学熵“的数学描述这么接近,是不是冥冥之中有一种统一理论的关联?</span><span style="color: rgb(102, 102, 102);font-size: 14px;text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-family: PingFangSC-Light;">有的人甚至说这是同一种东西在不同角度的表现。算了,这个话题的能级已经超过了小编的认知范围,再聊下去就要被打上”民科‘的标签了,可以用冯诺依曼的话来圆场:<strong>没人真正理解熵为何物,这就让你在任何时候都可能进能退,立于不败之地。</strong></span></section><section style="text-indent: 2em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><br /></section><section style="text-indent: 2em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><br /></section><section data-role="paragraph" data-width="18%" style="box-sizing: border-box;margin-right: auto;margin-left: auto;max-width: 100%;letter-spacing: 0.544px;background-color: rgb(255, 255, 255);width: 18%;flex: 0 0 18%;font-family: -apple-system, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;overflow-wrap: break-word !important;"><section style="max-width: 100%;min-height: 1em;line-height: 1.75em;margin-left: 8px;margin-right: 8px;box-sizing: border-box !important;overflow-wrap: break-word !important;"><br /></section></section><section style="text-align: center;line-height: 1.75em;margin-left: 8px;margin-right: 8px;"><img class="rich_pages" data-ratio="0.4546296296296296" data-s="300,640" data-src="https://mmbiz.qpic.cn/mmbiz_png/AJkYaTAujIyWURddlHITkZgKz53a4xugUFcsvzibFq5rc903FtvJcsxUa0K4ueiaUUJlibtM1Nz7RvGwMm8YMqEQA/640?wx_fmt=png" data-type="png" data-w="1080" style="" /></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;">第4个问题:熵值法对于我们的价值。</span></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><br /></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;">这个问题最难回答,每个人的观点不一样,人们通常喜欢对同类型的事物进行总体评价、排名,因为这样简单直观,但是往往事物本身包含方方面面。</span></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><br /></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;">A善于表达但学习能力欠佳,B不善言辞但学习能力很强,C不善言辞且学习能力也欠佳,你只能说综合这两个方面:A比C优秀且B比C优秀,但你能说A比B优秀或者B比A优秀吗?显然不能。</span></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><br /></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;">所以暂时来看,不仅仅是熵值法,各种赋权综合打分的表达只能解决在它所涉及的指标集合内绝对优劣的评价,但是对于互有优劣的,无法去评价,或者出来的打分结果可能也很难说明什么。</span></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><br /></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><span style="color: rgb(102, 102, 102);text-indent: 28px;widows: 1;caret-color: rgb(102, 102, 102);font-size: 14px;font-family: PingFangSC-Light;">那么,对于熵值法的价值,小编故作高深的认为:<span style="background-color: rgb(102, 102, 102);color: rgb(255, 255, 255);">评价权重的标尺完全取决于人。是某些人定义了黄金和贝壳的兑换标准,并获得了大部分人的认同后,才有了市场价值基准;是某些人或者某一群人定义了道德人伦,且获得了大多数人的追随后,才有了普世观念;同样如果大家认同了离散程度作为衡量指标的权重,且认同了熵值法来衡量离散程度,那它就是合理的,并影响着后续的发生…….</span></span></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><br /></section><section style="text-indent: 0em;margin: 5px 8px;letter-spacing: 2px;line-height: 1.75em;"><br /></section><section style="text-align: center;line-height: 1.75em;margin-left: 8px;margin-right: 8px;"><img class="rich_pages" data-ratio="0.04814814814814815" data-s="300,640" data-src="https://mmbiz.qpic.cn/mmbiz_png/AJkYaTAujIyWURddlHITkZgKz53a4xuguNUzA4IaM1HlnwOjtN0e3MNSsl0fBffOKia4OPkO3aY8udWMPhhqwrQ/640?wx_fmt=png" data-type="png" data-w="1080" style="" /></section><section data-role="outer" label="Powered by 135editor.com" style="white-space: normal;max-width: 100%;box-sizing: border-box !important;overflow-wrap: break-word !important;"><section data-role="outer" label="Powered by 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!important;overflow-wrap: break-word !important;">&nbsp;「 好 / 阳光米x石板墨x大不列颠红x深姜橘&nbsp;」&nbsp;</span></section><section style="text-align: center;max-width: 100%;box-sizing: border-box;min-height: 1em;color: rgb(0, 0, 0);font-size: 14px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;overflow-wrap: break-word !important;"><span style="max-width: 100%;color: rgb(127, 127, 127);caret-color: red;font-family: PingFangTC-Light;font-size: 10px;box-sizing: border-box !important;overflow-wrap: break-word !important;">#BE TRUE&nbsp; #BE WELL&nbsp; #BE WILD</span></section><section style="text-align: center;max-width: 100%;box-sizing: border-box;min-height: 1em;color: rgb(0, 0, 0);font-size: 14px;line-height: 1.75em;margin-left: 8px;margin-right: 8px;overflow-wrap: break-word !important;"><br /></section></section></section></section></section><section style="max-width: 100%;color: rgb(163, 163, 163);letter-spacing: 1.5px;font-family: 微软雅黑, Arial, sans-serif;line-height: 1.75em;margin-left: 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