前言：熵權(quán)法，也稱為熵決法，客觀求權(quán)重比，在評價類模型中相對比較簡單。根據(jù)已知評價對象 指標(biāo)的數(shù)值來確定每個指標(biāo)所占的權(quán)重，在相對數(shù)據(jù)集合中，以算法的形式剔除主觀因素，以客觀的方式獲取到相關(guān)權(quán)重。

適用場景：（純個人經(jīng)驗(yàn)）

1，每個對象會有幾個指標(biāo)。這幾個指標(biāo)哪個指標(biāo)所占的權(quán)重最大呢？

（指標(biāo)數(shù)相當(dāng)或相差不大。最好是同類指標(biāo)在不同源數(shù)據(jù)下形成的數(shù)據(jù)集合。）

2，指標(biāo)數(shù)大于2.

一、算法結(jié)果展示：?

指標(biāo)1	指標(biāo)1	指標(biāo)1	加權(quán)平均法	熵決法
65.00?	64.71?	100.00?	76.57?	9.360619
65.00?	52.94?		39.31?	9.781944
100.00?		65.00?	55.00?	9.781944
65.00?		100.00?	55.00?	9.781944
30.00?	100.00?	64.00?	64.67?	4.154868
64.00?	100.00?		54.67?	9.781944
65.00?	85.00?		50.00?	9.781944
79.79?		66.00?	48.60?	9.781944
40.00?		99.00?	46.33?	9.781944
	70.59?	64.00?	44.86?	9.781944
65.00?	60.00?	70.00?	65.00?	4.11448
100.00?	95.00?	105.00?	100.00?	4.11448

二、算法理論

原文鏈接：https://blog.csdn.net/qq_41686130/article/details/81867400

2.1，數(shù)據(jù)標(biāo)準(zhǔn)化

假設(shè)給定了k個指標(biāo)，其中。假設(shè)對各指標(biāo)數(shù)據(jù)標(biāo)準(zhǔn)化后的值為，

那么

? ? ? ? ? ? ? ? ? ? ? ? ? ?

2.2，求各指標(biāo)的信息熵

根據(jù)信息論中信息熵的定義，一組數(shù)據(jù)的信息熵

其中，如果，則定義? ??。

2.3，確定各指標(biāo)權(quán)重

根據(jù)信息熵的計算公式，計算出各個指標(biāo)的信息熵為?。通過信息熵計算各指標(biāo)的權(quán)重：

? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?

2.4，指標(biāo)缺失（為0）或?yàn)樨?fù)問題

可以使用數(shù)據(jù)平移法，即所有指標(biāo)都加上一個平移值x，再參與計算，平移值x不管大小，計算結(jié)果一樣。

三、java代碼

3.1，pom引入

<!-- 集成hutool工具類簡便操作 --><dependency><groupId>cn.hutool</groupId><artifactId>hutool-all</artifactId><version>5.3.10</version></dependency><dependency><groupId>org.apache.commons</groupId><artifactId>commons-math3</artifactId><version>3.6.1</version></dependency>

3.2，核心類：

import java.util.ArrayList; import java.util.List;import cn.hutool.core.collection.CollUtil; import cn.hutool.core.util.NumberUtil;public class ShangFactory {private List<List<Double>> readyList;private Integer maxNum = 0; // 最大位數(shù)private Double pvg = 100.0; // 平移數(shù)值public ShangFactory(List<List<Double>> dataList) {getMaxNum(dataList);readyList = new ArrayList<List<Double>>();tranData(dataList);}public List<Double> listWeight() {System.err.println("平移標(biāo)準(zhǔn)化:" + readyList);// 完成數(shù)據(jù)標(biāo)準(zhǔn)化List<List<Double>> aveList = orderData(readyList);System.err.println("數(shù)據(jù)標(biāo)準(zhǔn)化:" + aveList);List<Double> shangList = listShang(readyList, aveList);// 獲取信息熵System.err.println("信息熵:" + shangList);List<Double> weightList = makeWeight(shangList);return weightList;}// 獲取最大位數(shù)和平移均值private void getMaxNum(List<List<Double>> dataList) {for (List<Double> list : dataList) {if (list.size() > maxNum) {maxNum = list.size();}double ws = 0.0;for (Double w : list) {if (w<pvg) {pvg=w;}ws = ws + w;}pvg = pvg + (ws / list.size());}pvg = pvg / dataList.size();}/*** 用平移法，補(bǔ)全缺位數(shù)據(jù)* * @param dataList* @return*/private void tranData(List<List<Double>> dataList) {List<Double> dataNumList;for (List<Double> list : dataList) {dataNumList = new ArrayList<Double>();for (Double weight : list) {dataNumList.add(weight + pvg);}// 補(bǔ)全for (int i = 0; i < maxNum - list.size(); i++) {dataNumList.add(pvg);}readyList.add(dataNumList);}}/*** 2.1，數(shù)據(jù)標(biāo)準(zhǔn)化* @param dataList* @return*/private List<List<Double>> orderData(List<List<Double>> dataList) {List<List<Double>> aveList = new ArrayList<List<Double>>();// 數(shù)據(jù)歸一化處理 (i-min)/(max-min)List<Double> numList;List<Double> dataNumList;double min, diff, temp;for (int i = 0; i < dataList.size(); i++) {numList = dataList.get(i);min = (double) CollUtil.min(numList);diff = CollUtil.max(numList) - min;dataNumList = new ArrayList<Double>();for (int j = 0; j < numList.size(); j++) {temp = ((double) numList.get(j) - min) / diff;dataNumList.add(j, temp);}aveList.add(dataNumList);}return aveList;}/*** 2.2，求各指標(biāo)的信息熵* @param dataList* @param aveList* @return*/private List<Double> listShang(List<List<Double>> dataList, List<List<Double>> aveList) {List<Double> shangList = new ArrayList<Double>();for (int i = 0; i < aveList.size(); i++) {List<Double> aveNumList = aveList.get(i);double pSum = (double) aveNumList.stream().reduce((x, y) -> (double) x + (double) y).get();double sum = 0;for (int j = 0; j < aveList.get(i).size(); j++) {double p = (double) aveNumList.get(j) / pSum;if (p != 0) {sum = sum + p * Math.log(p);}}shangList.add((-1) / Math.log(dataList.get(i).size()) * sum);}return shangList;}/*** 2.3，確定各指標(biāo)權(quán)重* @param shangList* @return*/private static List<Double> makeWeight(List<Double> shangList) {List<Double> weightList = new ArrayList<Double>();Double shangSum = shangList.stream().reduce(Double::sum).get();double weight;for (int i = 0; i < shangList.size(); i++) {weight = (1 - shangList.get(i)) / (shangList.size() - shangSum);weight = weight * 100.0; // BigDecimal weightDec = NumberUtil.round(weight, 6);weightList.add(NumberUtil.round(weight, 6).doubleValue());}return weightList;} }

3.3，測試類

import java.util.ArrayList; import java.util.Arrays; import java.util.List;import cn.hutool.core.util.NumberUtil;public class ShangTest {public static void main(String[] args) {List<List<Double>> dataList = readyData();ShangFactory shangFactory=new ShangFactory(dataList);List<Double> weightList = shangFactory.listWeight();// 獲取權(quán)重System.err.println("權(quán)重:" + weightList);for (Double double1 : weightList) {System.out.println(double1);}}private static List<List<Double>> readyData() {String dataStr = "[100.0, 83.33, 75.0], [83.33, 72.86, 70.0], [85.0, 66.0, 64.53, 5.0], [99.0, 55.0, 40.0, 17.17], [75.0, 65.53, 52.18], [70.0, 64.53, 33.0, 23.19], [75.0, 70.53, 28.99], [85.0, 83.33], [75.0, 64.53, 28.13], [75.0, 66.53], [75.0, 57.97], [83.33, 25.0], [100.0], [64.53, 34.38], [66.67, 31.25], [66.67, 25.0], [85.71], [83.33], [83.33], [83.33], [75.0], [75.0], [75.0], [75.0], [71.43], [65.53], [65.53], [64.53], [34.38]";List<List<Double>> dataList = new ArrayList<List<Double>>();List<String> list = Arrays.asList(dataStr.split("],"));List<Double> dataNumList;for (String string : list) {string = string.replace("[", "");string = string.replace("]", "");dataNumList = new ArrayList<Double>();List<String> numList = Arrays.asList(string.split(","));for (String numStr : numList) {dataNumList.add(NumberUtil.parseNumber(numStr.trim()).doubleValue());}dataList.add(dataNumList);}return dataList;} }

測試類中數(shù)據(jù)集是根據(jù)生產(chǎn)環(huán)境打印出來，也可以使用excle中導(dǎo)入，方便測試。

最后總結(jié)：因場景選擇錯誤，此方法是一個失敗案例。但是此方法相當(dāng)不錯。

總結(jié)

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