如何在 R 中使用 PROMETHEE 多准则方法
How to use PROMETHEE multicriteria method in R
我使用 TOPSIS 多标准方法从 34 个选项中 select 获得了最佳聚类数。作为 weights 我为每个标准使用了 0.5。 coverage 标准是最小化，production 标准是最大化。在这些相同的条件下，我想使用 PROMETHEE multicriteria 方法。据我所知，R (https://cran.r-project.org/web/packages/PROMETHEE/index.html) 中有一个 PROMETHEE 包，但不幸的是我不能为我的情况做。
你能帮帮我吗？
我留下 TOPSIS 代码是为了让您了解我想要什么，即对最佳备选方案进行排名。在这种情况下，最好的选择是簇数等于 2，因为它排名第 1。
library(topsis)
df1<-structure(list(nclusters = c(2, 3, 4, 5, 6, 7, 8, 9, 10, 11,
12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27,
28, 29, 30, 31, 32, 33, 34, 35), Coverage = c(0.0363201192049018,
0.0315198954715543, 0.112661460735583, 0.112661460735583, 0.112661460735583,
0.0813721071219816, 0.0862146652218061, 0.0697995564757394, 0.0599194966471805,
0.0507632014547115, 0.052076958349629, 0.052076958349629, 0.052076958349629,
0.052076958349629, 0.052076958349629, 0.052076958349629, 0.0410332568832433,
0.0389940601722214, 0.0441742111970355, 0.0441742111970355, 0.0441742111970355,
0.0438099091238968, 0.0409906284310306, 0.0409906284310306, 0.035480410134286,
0.035480410134286, 0.035480410134286, 0.035480410134286, 0.035480410134286,
0.035480410134286, 0.035480410134286, 0.0345381204372174, 0.0287729883480053,
0.0287729883480053), Production = c(1635156.04305, 474707.64025,
170773.40775, 64708.312, 64708.312, 64708.312, 949.72635, 949.72635,
949.72635, 949.72635, 949.72635, 949.72635, 949.72635, 949.72635,
949.72635, 949.72635, 949.72635, 949.72635, 949.72635, 949.72635,
949.72635, 949.72635, 949.72635, 949.72635, 949.72635, 949.72635,
949.72635, 949.72635, 949.72635, 949.72635, 949.72635, 949.72635,
949.72635, 949.72635)), class = "data.frame", row.names = c(NA,-34L))
row.names(df1) <- df1$nclusters
df2 <- df1[c(2:3)]
df2<-data.matrix(df2)
w <- c(0.5,0.5)
i <- c("-", "+")
result<-topsis(df2, w, i)
result<-data.frame(nclusters = df1[,1],result[,2:3])
> result
nclusters score rank
1 2 0.97709831 1.0
2 3 0.35391229 2.0
3 4 0.09999171 30.0
4 5 0.03763326 33.5
5 6 0.03763326 33.5
6 7 0.09914059 31.0
7 8 0.07676999 32.0
8 9 0.11960647 29.0
9 10 0.14366970 28.0
10 11 0.16484786 21.0
11 12 0.16187453 24.5
12 13 0.16187453 24.5
13 14 0.16187453 24.5
14 15 0.16187453 24.5
15 16 0.16187453 24.5
16 17 0.16187453 24.5
17 18 0.18619947 16.0
18 19 0.19052672 13.0
19 20 0.17943485 19.0
20 21 0.17943485 19.0
21 22 0.17943485 19.0
22 23 0.18022565 17.0
23 24 0.18629045 14.5
24 25 0.18629045 14.5
25 26 0.19786466 9.0
26 27 0.19786466 9.0
27 28 0.19786466 9.0
28 29 0.19786466 9.0
29 30 0.19786466 9.0
30 31 0.19786466 9.0
31 32 0.19786466 9.0
32 33 0.19980731 5.0
33 34 0.21146288 3.5
34 35 0.21146288 3.5
这与 the vignette of the PROMETHEE package 密切相关，但希望有助于阐明如何针对问题中显示的示例进行调整。
设置
对于 PROMETHEE 函数的每个参数，需要提供一个（备选方案 x 标准）矩阵。这意味着例如最大化 production 需要为每个备选方案（行）指定，而不仅仅是一次。
# Preference function (options: Level, Linear, V-shape and Gaussian)
PreferenceF <- data.frame(
"Coverage" = rep("Linear", nrow(df2)), "Production" = rep("Linear", nrow(df2))
)
# Preference threshold - to match the topsis results, we set this
# so high that that it will not effect the results
PreferenceT <- data.frame(
"Coverage" = rep(0.2, nrow(df2)), "Production" = rep(2e6, nrow(df2))
)
# indifference threshold - not used to reproduce topsis results
IndifferenceT <- data.frame(
"Coverage" = rep(0, nrow(df2)), "Production" = rep(0, nrow(df2))
)
# gauss preference threshold: only relevant to preference function "Gaussian"
S_Gauss <- data.frame(
"Coverage" = rep(0, nrow(df2)), "Production" = rep(0, nrow(df2))
)
# weights - use 0.5 as in the question
Weights <- data.frame(
"Coverage" = rep(0.5, nrow(df2)), "Production" = rep(0.5, nrow(df2))
)
# specify which parameters need to be minimized or maximized
Min_Max <- data.frame(
"Coverage" = rep("min", nrow(df2)), "Production" = rep("max", nrow(df2))
)
优化
为了排名，我选择了 PROMETHEE2 分数（净偏好流），但其他分数可从 PF 对象中获得。
library(PROMETHEE)
library(dplyr)
PF <- PROMETHEE(df2, PreferenceF, PreferenceT, IndifferenceT, Weights, Min_Max, S_Gauss)
result2 <- data.frame(nclusters = df1$nclusters, score = PF$PROMETHEE2) %>%
dplyr::arrange(desc(score)) %>%
rownames_to_column(var = "rank")
result2 %>% head()
rank nclusters score
1 1 2 0.22044145
2 2 3 0.07717187
3 3 34 0.01969528
4 4 35 0.01969528
5 5 33 0.01227048
6 6 26 0.01105693
将最高结果与问题中显示的 TOPSIS 排名进行比较显示出良好的一致性（尽管决胜局的处理方式似乎有所不同）。
result %>% arrange(rank) %>% head()
nclusters score rank
1 2 0.9770983 1.0
2 3 0.3539123 2.0
3 34 0.2114629 3.5
4 35 0.2114629 3.5
5 33 0.1998073 5.0
6 26 0.1978647 9.0
我使用 TOPSIS 多标准方法从 34 个选项中 select 获得了最佳聚类数。作为 weights 我为每个标准使用了 0.5。 coverage 标准是最小化，production 标准是最大化。在这些相同的条件下，我想使用 PROMETHEE multicriteria 方法。据我所知，R (https://cran.r-project.org/web/packages/PROMETHEE/index.html) 中有一个 PROMETHEE 包，但不幸的是我不能为我的情况做。
你能帮帮我吗？
我留下 TOPSIS 代码是为了让您了解我想要什么，即对最佳备选方案进行排名。在这种情况下，最好的选择是簇数等于 2，因为它排名第 1。
library(topsis)
df1<-structure(list(nclusters = c(2, 3, 4, 5, 6, 7, 8, 9, 10, 11,
12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27,
28, 29, 30, 31, 32, 33, 34, 35), Coverage = c(0.0363201192049018,
0.0315198954715543, 0.112661460735583, 0.112661460735583, 0.112661460735583,
0.0813721071219816, 0.0862146652218061, 0.0697995564757394, 0.0599194966471805,
0.0507632014547115, 0.052076958349629, 0.052076958349629, 0.052076958349629,
0.052076958349629, 0.052076958349629, 0.052076958349629, 0.0410332568832433,
0.0389940601722214, 0.0441742111970355, 0.0441742111970355, 0.0441742111970355,
0.0438099091238968, 0.0409906284310306, 0.0409906284310306, 0.035480410134286,
0.035480410134286, 0.035480410134286, 0.035480410134286, 0.035480410134286,
0.035480410134286, 0.035480410134286, 0.0345381204372174, 0.0287729883480053,
0.0287729883480053), Production = c(1635156.04305, 474707.64025,
170773.40775, 64708.312, 64708.312, 64708.312, 949.72635, 949.72635,
949.72635, 949.72635, 949.72635, 949.72635, 949.72635, 949.72635,
949.72635, 949.72635, 949.72635, 949.72635, 949.72635, 949.72635,
949.72635, 949.72635, 949.72635, 949.72635, 949.72635, 949.72635,
949.72635, 949.72635, 949.72635, 949.72635, 949.72635, 949.72635,
949.72635, 949.72635)), class = "data.frame", row.names = c(NA,-34L))
row.names(df1) <- df1$nclusters
df2 <- df1[c(2:3)]
df2<-data.matrix(df2)
w <- c(0.5,0.5)
i <- c("-", "+")
result<-topsis(df2, w, i)
result<-data.frame(nclusters = df1[,1],result[,2:3])
> result
nclusters score rank
1 2 0.97709831 1.0
2 3 0.35391229 2.0
3 4 0.09999171 30.0
4 5 0.03763326 33.5
5 6 0.03763326 33.5
6 7 0.09914059 31.0
7 8 0.07676999 32.0
8 9 0.11960647 29.0
9 10 0.14366970 28.0
10 11 0.16484786 21.0
11 12 0.16187453 24.5
12 13 0.16187453 24.5
13 14 0.16187453 24.5
14 15 0.16187453 24.5
15 16 0.16187453 24.5
16 17 0.16187453 24.5
17 18 0.18619947 16.0
18 19 0.19052672 13.0
19 20 0.17943485 19.0
20 21 0.17943485 19.0
21 22 0.17943485 19.0
22 23 0.18022565 17.0
23 24 0.18629045 14.5
24 25 0.18629045 14.5
25 26 0.19786466 9.0
26 27 0.19786466 9.0
27 28 0.19786466 9.0
28 29 0.19786466 9.0
29 30 0.19786466 9.0
30 31 0.19786466 9.0
31 32 0.19786466 9.0
32 33 0.19980731 5.0
33 34 0.21146288 3.5
34 35 0.21146288 3.5
这与 the vignette of the PROMETHEE package 密切相关，但希望有助于阐明如何针对问题中显示的示例进行调整。
设置
对于 PROMETHEE 函数的每个参数，需要提供一个（备选方案 x 标准）矩阵。这意味着例如最大化 production 需要为每个备选方案（行）指定，而不仅仅是一次。
# Preference function (options: Level, Linear, V-shape and Gaussian)
PreferenceF <- data.frame(
"Coverage" = rep("Linear", nrow(df2)), "Production" = rep("Linear", nrow(df2))
)
# Preference threshold - to match the topsis results, we set this
# so high that that it will not effect the results
PreferenceT <- data.frame(
"Coverage" = rep(0.2, nrow(df2)), "Production" = rep(2e6, nrow(df2))
)
# indifference threshold - not used to reproduce topsis results
IndifferenceT <- data.frame(
"Coverage" = rep(0, nrow(df2)), "Production" = rep(0, nrow(df2))
)
# gauss preference threshold: only relevant to preference function "Gaussian"
S_Gauss <- data.frame(
"Coverage" = rep(0, nrow(df2)), "Production" = rep(0, nrow(df2))
)
# weights - use 0.5 as in the question
Weights <- data.frame(
"Coverage" = rep(0.5, nrow(df2)), "Production" = rep(0.5, nrow(df2))
)
# specify which parameters need to be minimized or maximized
Min_Max <- data.frame(
"Coverage" = rep("min", nrow(df2)), "Production" = rep("max", nrow(df2))
)
优化
为了排名，我选择了 PROMETHEE2 分数（净偏好流），但其他分数可从 PF 对象中获得。
library(PROMETHEE)
library(dplyr)
PF <- PROMETHEE(df2, PreferenceF, PreferenceT, IndifferenceT, Weights, Min_Max, S_Gauss)
result2 <- data.frame(nclusters = df1$nclusters, score = PF$PROMETHEE2) %>%
dplyr::arrange(desc(score)) %>%
rownames_to_column(var = "rank")
result2 %>% head()
rank nclusters score
1 1 2 0.22044145
2 2 3 0.07717187
3 3 34 0.01969528
4 4 35 0.01969528
5 5 33 0.01227048
6 6 26 0.01105693
将最高结果与问题中显示的 TOPSIS 排名进行比较显示出良好的一致性（尽管决胜局的处理方式似乎有所不同）。
result %>% arrange(rank) %>% head()
nclusters score rank
1 2 0.9770983 1.0
2 3 0.3539123 2.0
3 34 0.2114629 3.5
4 35 0.2114629 3.5
5 33 0.1998073 5.0
6 26 0.1978647 9.0