Kevin Kam Fung YUEN (2026). Anchored Regularized Direct Least Squares (ARDLS): Integrating Established Prioritization Operators for Priority Elicitation in the Analytic Hierarchy Process. arXiv preprint arXiv:2608.21187. https://arxiv.org/pdf/2608.21187
# Created by Kevin Kam Fung YUEN
library(ARDLS)A0 <- matrix(c(
1, 3, 1/5, 5, 1/3,
1/3, 1, 3, 1/4, 2,
5, 1/3, 1, 2, 1/4,
1/5, 4, 1/2, 1, 5,
3, 1/2, 4, 1/5, 1
), nrow = 5, ncol = 5, byrow = TRUE,
dimnames = list(paste0("c", 1:5), paste0("c", 1:5)))
# Alternatives under c1: Expected Financial Return (A1)
A1 <- matrix(c(
1, 1/3, 1/5, 4,
3, 1, 1/3, 8,
5, 3, 1, 7,
1/4, 1/8, 1/7, 1
), nrow = 4, ncol = 4, byrow = TRUE,
dimnames = list(paste0("t", 1:4), paste0("t", 1:4)))
# Alternatives under c2: Implementation Cost Economy (A2)
A2 <- matrix(c(
1, 1/4, 1/3, 1/7,
4, 1, 3, 1/2,
3, 1/3, 1, 1/5,
7, 2, 5, 1
), nrow = 4, ncol = 4, byrow = TRUE,
dimnames = list(paste0("t", 1:4), paste0("t", 1:4)))
# Alternatives under c3: Technical Feasibility (A3)
A3 <- matrix(c(
1, 1/4, 1/3, 1/8,
4, 1, 3, 1/2,
3, 1/3, 1, 1/6,
8, 2, 6, 1
), nrow = 4, ncol = 4, byrow = TRUE,
dimnames = list(paste0("t", 1:4), paste0("t", 1:4)))
# Alternatives under c4: Market Potential (A4)
A4 <- matrix(c(
1, 2, 5, 7,
1/2, 1, 3, 8,
1/5, 1/3, 1, 4,
1/7, 1/8, 1/4, 1
), nrow = 4, ncol = 4, byrow = TRUE,
dimnames = list(paste0("t", 1:4), paste0("t", 1:4)))
# Alternatives under c5: Risk & Regulatory Compliance (A5)
A5 <- matrix(c(
1, 3, 7, 1/5,
1/3, 1, 5, 2,
1/7, 1/5, 1, 1/8,
5, 1/2, 8, 1
), nrow = 4, ncol = 4, byrow = TRUE,
dimnames = list(paste0("t", 1:4), paste0("t", 1:4)))
# Store all matrices in a named list for workflow processing
PRM_list <- list(
A0 = A0,
A1 = A1,
A2 = A2,
A3 = A3,
A4 = A4,
A5 = A5
)
dls_solve <- function(PRM)
{
solve_DLS(PRM)$weights
}
# List of all your derivation functions to test the divergence
POs = list(
NRS = NRS,
NRCS = NRCS,
AMNC = AMNC,
NGMR = geoMean,
EV = SaatyEigen,
SVD = SVD,
CosMax = CosMax,
PIGM = PIGM,
DLS = dls_solve
)CRs = list()
for (a in names(PRM_list))
{
#cat(strrep("-", 30),a,strrep("-", 30),"\n")
CRs[[a]] = ConsistencyRatio(PRM_list[[a]])
}
CRs## $A0
## [1] 0.8523963
##
## $A1
## [1] 0.07417222
##
## $A2
## [1] 0.03021444
##
## $A3
## [1] 0.03085185
##
## $A4
## [1] 0.04671233
##
## $A5
## [1] 0.4323662final_AHP_PO_results <- function(AHP_PO_results, digits=3)
{
baseline_WR = data.frame()
for (nm in names(AHP_PO_results)) {
a = AHP_PO_results[[nm]]
tmp = paste0(round(a$Final_Result,digits),":(",a$Rank,")")
baseline_WR = rbind(baseline_WR, tmp)
}
rownames(baseline_WR)= names(AHP_PO_results)
colnames(baseline_WR) = names(a$Rank)
baseline_WR
}AHP_base_results = list()
for (a in names(POs))
{
# cat(strrep("-", 30),a,strrep("-", 30),"\n")
AHP_base_results[[a]] = AHP(dataList = PRM_list,alternativeNo=4,PO = POs[[a]])
}final_AHP_base_results = final_AHP_PO_results(AHP_base_results,3)
final_AHP_base_results## T1 T2 T3 T4
## NRS 0.221:(3) 0.304:(1) 0.195:(4) 0.28:(2)
## NRCS 0.205:(3) 0.277:(2) 0.19:(4) 0.328:(1)
## AMNC 0.23:(3) 0.291:(1) 0.199:(4) 0.281:(2)
## NGMR 0.219:(3) 0.289:(2) 0.19:(4) 0.302:(1)
## EV 0.217:(3) 0.287:(2) 0.196:(4) 0.3:(1)
## SVD 0.198:(3) 0.274:(2) 0.197:(4) 0.331:(1)
## CosMax 0.231:(3) 0.293:(1) 0.197:(4) 0.279:(2)
## PIGM 0.193:(3) 0.278:(2) 0.183:(4) 0.345:(1)
## DLS 0.238:(3) 0.346:(1) 0.163:(4) 0.254:(2)ardlsPOList = list()
regLambda = 1
for (a in names(POs)) {
# cat(strrep("-", 30), paste0("ardls_", a), strrep("-", 30), "\n")
ardlsPOList[[paste0("ardls_", a)]] <- function(PRM) {
solve_ARDLS(PRM, W_anchor = POs[[a]](PRM), reg_lambda = regLambda)$weights
}
}AHP_ardls_results = list()
for (a in names(POs))
{
# cat(strrep("-", 30),a,strrep("-", 30),"\n")
AHP_ardls_results[[paste0("ardls_", a)]] = AHP(dataList = PRM_list,alternativeNo=4,
PO = ardlsPOList[[paste0("ardls_", a)]])
}
AHP_ardls_results ## $ardls_NRS
## $ardls_NRS$Priority_Vectors
## $ardls_NRS$Priority_Vectors$C0
## C1 C2 C3 C4 C5
## 0.1861848 0.1193869 0.2032170 0.3669536 0.1242575
##
## $ardls_NRS$Priority_Vectors$C1
## T1 T2 T3 T4
## 0.11998624 0.40039568 0.42619976 0.05341832
##
## $ardls_NRS$Priority_Vectors$C2
## T1 T2 T3 T4
## 0.07172784 0.29541540 0.11145749 0.52139927
##
## $ardls_NRS$Priority_Vectors$C3
## T1 T2 T3 T4
## 0.06746832 0.27806789 0.09845011 0.55601367
##
## $ardls_NRS$Priority_Vectors$C4
## T1 T2 T3 T4
## 0.41909877 0.40712858 0.12046937 0.05330327
##
## $ardls_NRS$Priority_Vectors$C5
## T1 T2 T3 T4
## 0.31531944 0.24064920 0.04777072 0.39626064
##
##
## $ardls_NRS$Weighted_Decision_Matrix
## C1 C2 C3 C4 C5
## C0 0.18618485 0.11938694 0.20321704 0.36695364 0.12425753
## T1 0.11998624 0.07172784 0.06746832 0.41909877 0.31531944
## T2 0.40039568 0.29541540 0.27806789 0.40712858 0.24064920
## T3 0.42619976 0.11145749 0.09845011 0.12046937 0.04777072
## T4 0.05341832 0.52139927 0.55601367 0.05330327 0.39626064
##
## $ardls_NRS$CR
## $ardls_NRS$CR$C0
## [1] 0.8523963
##
## $ardls_NRS$CR$C1
## [1] 0.07417222
##
## $ardls_NRS$CR$C2
## [1] 0.03021444
##
## $ardls_NRS$CR$C3
## [1] 0.03085185
##
## $ardls_NRS$CR$C4
## [1] 0.04671233
##
## $ardls_NRS$CR$C5
## [1] 0.4323662
##
##
## $ardls_NRS$Final_Result
## T1 T2 T3 T4
## 0.2375843 0.3456243 0.1628078 0.2539836
##
## $ardls_NRS$Rank
## T1 T2 T3 T4
## 3 1 4 2
##
##
## $ardls_NRCS
## $ardls_NRCS$Priority_Vectors
## $ardls_NRCS$Priority_Vectors$C0
## C1 C2 C3 C4 C5
## 0.1860557 0.1194571 0.2033390 0.3668626 0.1242856
##
## $ardls_NRCS$Priority_Vectors$C1
## T1 T2 T3 T4
## 0.11992890 0.40008321 0.42656152 0.05342637
##
## $ardls_NRCS$Priority_Vectors$C2
## T1 T2 T3 T4
## 0.07173174 0.29535145 0.11143770 0.52147911
##
## $ardls_NRCS$Priority_Vectors$C3
## T1 T2 T3 T4
## 0.06746949 0.27806072 0.09843757 0.55603222
##
## $ardls_NRCS$Priority_Vectors$C4
## T1 T2 T3 T4
## 0.41934311 0.40693412 0.12041422 0.05330855
##
## $ardls_NRCS$Priority_Vectors$C5
## T1 T2 T3 T4
## 0.31509797 0.24079592 0.04777138 0.39633474
##
##
## $ardls_NRCS$Weighted_Decision_Matrix
## C1 C2 C3 C4 C5
## C0 0.18605565 0.11945714 0.20333905 0.36686259 0.12428556
## T1 0.11992890 0.07173174 0.06746949 0.41934311 0.31509797
## T2 0.40008321 0.29535145 0.27806072 0.40693412 0.24079592
## T3 0.42656152 0.11143770 0.09843757 0.12041422 0.04777138
## T4 0.05342637 0.52147911 0.55603222 0.05330855 0.39633474
##
## $ardls_NRCS$CR
## $ardls_NRCS$CR$C0
## [1] 0.8523963
##
## $ardls_NRCS$CR$C1
## [1] 0.07417222
##
## $ardls_NRCS$CR$C2
## [1] 0.03021444
##
## $ardls_NRCS$CR$C3
## [1] 0.03085185
##
## $ardls_NRCS$CR$C4
## [1] 0.04671233
##
## $ardls_NRCS$CR$C5
## [1] 0.4323662
##
##
## $ardls_NRCS$Final_Result
## T1 T2 T3 T4
## 0.2376049 0.3454765 0.1628052 0.2541133
##
## $ardls_NRCS$Rank
## T1 T2 T3 T4
## 3 1 4 2
##
##
## $ardls_AMNC
## $ardls_AMNC$Priority_Vectors
## $ardls_AMNC$Priority_Vectors$C0
## [1] 0.1862051 0.1193856 0.2031889 0.3669686 0.1242517
##
## $ardls_AMNC$Priority_Vectors$C1
## [1] 0.11995071 0.40022827 0.42639810 0.05342292
##
## $ardls_AMNC$Priority_Vectors$C2
## [1] 0.07172979 0.29538518 0.11144610 0.52143894
##
## $ardls_AMNC$Priority_Vectors$C3
## [1] 0.06746895 0.27806396 0.09844329 0.55602379
##
## $ardls_AMNC$Priority_Vectors$C4
## [1] 0.41924498 0.40701330 0.12043524 0.05330647
##
## $ardls_AMNC$Priority_Vectors$C5
## [1] 0.31527512 0.24072696 0.04776958 0.39622835
##
##
## $ardls_AMNC$Weighted_Decision_Matrix
## C1 C2 C3 C4 C5
## C0 0.18620514 0.11938560 0.20318894 0.36696859 0.12425172
## T1 0.11995071 0.07172979 0.06746895 0.41924498 0.31527512
## T2 0.40022827 0.29538518 0.27806396 0.40701330 0.24072696
## T3 0.42639810 0.11144610 0.09844329 0.12043524 0.04776958
## T4 0.05342292 0.52143894 0.55602379 0.05330647 0.39622835
##
## $ardls_AMNC$CR
## $ardls_AMNC$CR$C0
## [1] 0.8523963
##
## $ardls_AMNC$CR$C1
## [1] 0.07417222
##
## $ardls_AMNC$CR$C2
## [1] 0.03021444
##
## $ardls_AMNC$CR$C3
## [1] 0.03085185
##
## $ardls_AMNC$CR$C4
## [1] 0.04671233
##
## $ardls_AMNC$CR$C5
## [1] 0.4323662
##
##
## $ardls_AMNC$Final_Result
## T1 T2 T3 T4
## 0.2376311 0.3455607 0.1628366 0.2539717
##
## $ardls_AMNC$Rank
## T1 T2 T3 T4
## 3 1 4 2
##
##
## $ardls_NGMR
## $ardls_NGMR$Priority_Vectors
## $ardls_NGMR$Priority_Vectors$C0
## C1 C2 C3 C4 C5
## 0.1861251 0.1194199 0.2032567 0.3669215 0.1242769
##
## $ardls_NGMR$Priority_Vectors$C1
## T1 T2 T3 T4
## 0.11994716 0.40022225 0.42640751 0.05342308
##
## $ardls_NGMR$Priority_Vectors$C2
## T1 T2 T3 T4
## 0.07172981 0.29538375 0.11144351 0.52144293
##
## $ardls_NGMR$Priority_Vectors$C3
## T1 T2 T3 T4
## 0.06746893 0.27806235 0.09844182 0.55602690
##
## $ardls_NGMR$Priority_Vectors$C4
## T1 T2 T3 T4
## 0.41924468 0.40701622 0.12043259 0.05330651
##
## $ardls_NGMR$Priority_Vectors$C5
## T1 T2 T3 T4
## 0.31523510 0.24071075 0.04777081 0.39628334
##
##
## $ardls_NGMR$Weighted_Decision_Matrix
## C1 C2 C3 C4 C5
## C0 0.18612510 0.11941988 0.20325669 0.36692148 0.12427685
## T1 0.11994716 0.07172981 0.06746893 0.41924468 0.31523510
## T2 0.40022225 0.29538375 0.27806235 0.40701622 0.24071075
## T3 0.42640751 0.11144351 0.09844182 0.12043259 0.04777081
## T4 0.05342308 0.52144293 0.55602690 0.05330651 0.39628334
##
## $ardls_NGMR$CR
## $ardls_NGMR$CR$C0
## [1] 0.8523963
##
## $ardls_NGMR$CR$C1
## [1] 0.07417222
##
## $ardls_NGMR$CR$C2
## [1] 0.03021444
##
## $ardls_NGMR$CR$C3
## [1] 0.03085185
##
## $ardls_NGMR$CR$C4
## [1] 0.04671233
##
## $ardls_NGMR$CR$C5
## [1] 0.4323662
##
##
## $ardls_NGMR$Final_Result
## T1 T2 T3 T4
## 0.2376110 0.3455419 0.1628088 0.2540384
##
## $ardls_NGMR$Rank
## T1 T2 T3 T4
## 3 1 4 2
##
##
## $ardls_EV
## $ardls_EV$Priority_Vectors
## $ardls_EV$Priority_Vectors$C0
## [1] 0.1861696 0.1193909 0.2032756 0.3668887 0.1242752
##
## $ardls_EV$Priority_Vectors$C1
## [1] 0.1199447 0.4002116 0.4264203 0.0534234
##
## $ardls_EV$Priority_Vectors$C2
## [1] 0.0717297 0.2953867 0.1114447 0.5214389
##
## $ardls_EV$Priority_Vectors$C3
## [1] 0.06746894 0.27806305 0.09844250 0.55602551
##
## $ardls_EV$Priority_Vectors$C4
## [1] 0.41925508 0.40700610 0.12043216 0.05330667
##
## $ardls_EV$Priority_Vectors$C5
## [1] 0.31520808 0.24071454 0.04777087 0.39630652
##
##
## $ardls_EV$Weighted_Decision_Matrix
## C1 C2 C3 C4 C5
## C0 0.1861696 0.1193909 0.20327561 0.36688868 0.12427517
## T1 0.1199447 0.0717297 0.06746894 0.41925508 0.31520808
## T2 0.4002116 0.2953867 0.27806305 0.40700610 0.24071454
## T3 0.4264203 0.1114447 0.09844250 0.12043216 0.04777087
## T4 0.0534234 0.5214389 0.55602551 0.05330667 0.39630652
##
## $ardls_EV$CR
## $ardls_EV$CR$C0
## [1] 0.8523963
##
## $ardls_EV$CR$C1
## [1] 0.07417222
##
## $ardls_EV$CR$C2
## [1] 0.03021444
##
## $ardls_EV$CR$C3
## [1] 0.03085185
##
## $ardls_EV$CR$C4
## [1] 0.04671233
##
## $ardls_EV$CR$C5
## [1] 0.4323662
##
##
## $ardls_EV$Final_Result
## T1 T2 T3 T4
## 0.2376012 0.3455379 0.1628249 0.2540360
##
## $ardls_EV$Rank
## T1 T2 T3 T4
## 3 1 4 2
##
##
## $ardls_SVD
## $ardls_SVD$Priority_Vectors
## $ardls_SVD$Priority_Vectors$C0
## [1] 0.1860756 0.1194323 0.2033906 0.3668307 0.1242709
##
## $ardls_SVD$Priority_Vectors$C1
## [1] 0.11993063 0.40008375 0.42655930 0.05342631
##
## $ardls_SVD$Priority_Vectors$C2
## [1] 0.07173202 0.29534886 0.11144009 0.52147903
##
## $ardls_SVD$Priority_Vectors$C3
## [1] 0.06746967 0.27806199 0.09843827 0.55603007
##
## $ardls_SVD$Priority_Vectors$C4
## [1] 0.41934015 0.40693491 0.12041646 0.05330848
##
## $ardls_SVD$Priority_Vectors$C5
## [1] 0.3150242 0.2407944 0.0477725 0.3964090
##
##
## $ardls_SVD$Weighted_Decision_Matrix
## C1 C2 C3 C4 C5
## C0 0.18607558 0.11943228 0.20339063 0.36683065 0.1242709
## T1 0.11993063 0.07173202 0.06746967 0.41934015 0.3150242
## T2 0.40008375 0.29534886 0.27806199 0.40693491 0.2407944
## T3 0.42655930 0.11144009 0.09843827 0.12041646 0.0477725
## T4 0.05342631 0.52147903 0.55603007 0.05330848 0.3964090
##
## $ardls_SVD$CR
## $ardls_SVD$CR$C0
## [1] 0.8523963
##
## $ardls_SVD$CR$C1
## [1] 0.07417222
##
## $ardls_SVD$CR$C2
## [1] 0.03021444
##
## $ardls_SVD$CR$C3
## [1] 0.03085185
##
## $ardls_SVD$CR$C4
## [1] 0.04671233
##
## $ardls_SVD$CR$C5
## [1] 0.4323662
##
##
## $ardls_SVD$Final_Result
## T1 T2 T3 T4
## 0.2375811 0.3454751 0.1628124 0.2541313
##
## $ardls_SVD$Rank
## T1 T2 T3 T4
## 3 1 4 2
##
##
## $ardls_CosMax
## $ardls_CosMax$Priority_Vectors
## $ardls_CosMax$Priority_Vectors$C0
## C1 C2 C3 C4 C5
## 0.1861986 0.1193885 0.2031866 0.3669708 0.1242555
##
## $ardls_CosMax$Priority_Vectors$C1
## T1 T2 T3 T4
## 0.11995479 0.40024432 0.42637845 0.05342244
##
## $ardls_CosMax$Priority_Vectors$C2
## T1 T2 T3 T4
## 0.07172974 0.29538596 0.11144698 0.52143731
##
## $ardls_CosMax$Priority_Vectors$C3
## T1 T2 T3 T4
## 0.06746894 0.27806435 0.09844373 0.55602298
##
## $ardls_CosMax$Priority_Vectors$C4
## T1 T2 T3 T4
## 0.41923571 0.40702040 0.12043762 0.05330628
##
## $ardls_CosMax$Priority_Vectors$C5
## T1 T2 T3 T4
## 0.31529290 0.24073794 0.04776907 0.39620009
##
##
## $ardls_CosMax$Weighted_Decision_Matrix
## C1 C2 C3 C4 C5
## C0 0.18619862 0.11938851 0.20318663 0.36697075 0.12425549
## T1 0.11995479 0.07172974 0.06746894 0.41923571 0.31529290
## T2 0.40024432 0.29538596 0.27806435 0.40702040 0.24073794
## T3 0.42637845 0.11144698 0.09844373 0.12043762 0.04776907
## T4 0.05342244 0.52143731 0.55602298 0.05330628 0.39620009
##
## $ardls_CosMax$CR
## $ardls_CosMax$CR$C0
## [1] 0.8523963
##
## $ardls_CosMax$CR$C1
## [1] 0.07417222
##
## $ardls_CosMax$CR$C2
## [1] 0.03021444
##
## $ardls_CosMax$CR$C3
## [1] 0.03085185
##
## $ardls_CosMax$CR$C4
## [1] 0.04671233
##
## $ardls_CosMax$CR$C5
## [1] 0.4323662
##
##
## $ardls_CosMax$Final_Result
## T1 T2 T3 T4
## 0.2376320 0.3455672 0.1628317 0.2539691
##
## $ardls_CosMax$Rank
## T1 T2 T3 T4
## 3 1 4 2
##
##
## $ardls_PIGM
## $ardls_PIGM$Priority_Vectors
## $ardls_PIGM$Priority_Vectors$C0
## [1] 0.1860156 0.1194692 0.2033960 0.3668447 0.1242745
##
## $ardls_PIGM$Priority_Vectors$C1
## [1] 0.11993414 0.40011184 0.42652837 0.05342565
##
## $ardls_PIGM$Priority_Vectors$C2
## [1] 0.07173162 0.29536317 0.11143782 0.52146739
##
## $ardls_PIGM$Priority_Vectors$C3
## [1] 0.06746961 0.27806283 0.09843734 0.55603022
##
## $ardls_PIGM$Priority_Vectors$C4
## [1] 0.41930829 0.40696623 0.12041742 0.05330806
##
## $ardls_PIGM$Priority_Vectors$C5
## [1] 0.31500045 0.24075990 0.04777357 0.39646608
##
##
## $ardls_PIGM$Weighted_Decision_Matrix
## C1 C2 C3 C4 C5
## C0 0.18601556 0.11946924 0.20339602 0.36684467 0.12427451
## T1 0.11993414 0.07173162 0.06746961 0.41930829 0.31500045
## T2 0.40011184 0.29536317 0.27806283 0.40696623 0.24075990
## T3 0.42652837 0.11143782 0.09843734 0.12041742 0.04777357
## T4 0.05342565 0.52146739 0.55603022 0.05330806 0.39646608
##
## $ardls_PIGM$CR
## $ardls_PIGM$CR$C0
## [1] 0.8523963
##
## $ardls_PIGM$CR$C1
## [1] 0.07417222
##
## $ardls_PIGM$CR$C2
## [1] 0.03021444
##
## $ardls_PIGM$CR$C3
## [1] 0.03085185
##
## $ardls_PIGM$CR$C4
## [1] 0.04671233
##
## $ardls_PIGM$CR$C5
## [1] 0.4323662
##
##
## $ardls_PIGM$Final_Result
## T1 T2 T3 T4
## 0.2375699 0.3454844 0.1627876 0.2541581
##
## $ardls_PIGM$Rank
## T1 T2 T3 T4
## 3 1 4 2
##
##
## $ardls_DLS
## $ardls_DLS$Priority_Vectors
## $ardls_DLS$Priority_Vectors$C0
## [1] 0.1859740 0.1193621 0.2031893 0.3673751 0.1240995
##
## $ardls_DLS$Priority_Vectors$C1
## [1] 0.11996687 0.40049484 0.42612012 0.05341817
##
## $ardls_DLS$Priority_Vectors$C2
## [1] 0.07172988 0.29541470 0.11143816 0.52141726
##
## $ardls_DLS$Priority_Vectors$C3
## [1] 0.06746969 0.27806251 0.09843827 0.55602953
##
## $ardls_DLS$Priority_Vectors$C4
## [1] 0.41904499 0.40720562 0.12044547 0.05330392
##
## $ardls_DLS$Priority_Vectors$C5
## [1] 0.31532594 0.24066366 0.04777042 0.39623998
##
##
## $ardls_DLS$Weighted_Decision_Matrix
## C1 C2 C3 C4 C5
## C0 0.18597398 0.11936207 0.20318933 0.36737513 0.12409948
## T1 0.11996687 0.07172988 0.06746969 0.41904499 0.31532594
## T2 0.40049484 0.29541470 0.27806251 0.40720562 0.24066366
## T3 0.42612012 0.11143816 0.09843827 0.12044547 0.04777042
## T4 0.05341817 0.52141726 0.55602953 0.05330392 0.39623998
##
## $ardls_DLS$CR
## $ardls_DLS$CR$C0
## [1] 0.8523963
##
## $ardls_DLS$CR$C1
## [1] 0.07417222
##
## $ardls_DLS$CR$C2
## [1] 0.03021444
##
## $ardls_DLS$CR$C3
## [1] 0.03085185
##
## $ardls_DLS$CR$C4
## [1] 0.04671233
##
## $ardls_DLS$CR$C5
## [1] 0.4323662
##
##
## $ardls_DLS$Final_Result
## T1 T2 T3 T4
## 0.2376602 0.3457057 0.1627273 0.2539068
##
## $ardls_DLS$Rank
## T1 T2 T3 T4
## 3 1 4 2final_AHP_ardls_results = final_AHP_PO_results(AHP_ardls_results,4)
final_AHP_ardls_results ## T1 T2 T3 T4
## ardls_NRS 0.2376:(3) 0.3456:(1) 0.1628:(4) 0.254:(2)
## ardls_NRCS 0.2376:(3) 0.3455:(1) 0.1628:(4) 0.2541:(2)
## ardls_AMNC 0.2376:(3) 0.3456:(1) 0.1628:(4) 0.254:(2)
## ardls_NGMR 0.2376:(3) 0.3455:(1) 0.1628:(4) 0.254:(2)
## ardls_EV 0.2376:(3) 0.3455:(1) 0.1628:(4) 0.254:(2)
## ardls_SVD 0.2376:(3) 0.3455:(1) 0.1628:(4) 0.2541:(2)
## ardls_CosMax 0.2376:(3) 0.3456:(1) 0.1628:(4) 0.254:(2)
## ardls_PIGM 0.2376:(3) 0.3455:(1) 0.1628:(4) 0.2542:(2)
## ardls_DLS 0.2377:(3) 0.3457:(1) 0.1627:(4) 0.2539:(2)safe_Reg = list()
for (a in names(PRM_list))
{
cat(strrep("-", 30),a,strrep("-", 30),"\n")
safe_Reg[[a]] = safeRegularizer(PRM_list[[a]])
}## ------------------------------ A0 ------------------------------
## Running DLS optimization from 300 random starting points...
##
## === DLS Optimization Results ===
## Global Minimum Objective Value: 79.41438729
## Number of Unique Optimal Solutions Found: 1
## Optimal Weight Vectors:
## w1 w2 w3 w4 w5
## [1,] 0.186 0.119 0.203 0.367 0.124
## ------------------------------ A1 ------------------------------
## Running DLS optimization from 300 random starting points...
##
## === DLS Optimization Results ===
## Global Minimum Objective Value: 10.65809414
## Number of Unique Optimal Solutions Found: 1
## Optimal Weight Vectors:
## w1 w2 w3 w4
## [1,] 0.12 0.4 0.426 0.053
## ------------------------------ A2 ------------------------------
## Running DLS optimization from 300 random starting points...
##
## === DLS Optimization Results ===
## Global Minimum Objective Value: 2.56165895
## Number of Unique Optimal Solutions Found: 1
## Optimal Weight Vectors:
## w1 w2 w3 w4
## [1,] 0.072 0.295 0.111 0.521
## ------------------------------ A3 ------------------------------
## Running DLS optimization from 300 random starting points...
##
## === DLS Optimization Results ===
## Global Minimum Objective Value: 2.72637538
## Number of Unique Optimal Solutions Found: 1
## Optimal Weight Vectors:
## w1 w2 w3 w4
## [1,] 0.067 0.278 0.098 0.556
## ------------------------------ A4 ------------------------------
## Running DLS optimization from 300 random starting points...
##
## === DLS Optimization Results ===
## Global Minimum Objective Value: 7.57088875
## Number of Unique Optimal Solutions Found: 1
## Optimal Weight Vectors:
## w1 w2 w3 w4
## [1,] 0.419 0.407 0.12 0.053
## ------------------------------ A5 ------------------------------
## Running DLS optimization from 300 random starting points...
##
## === DLS Optimization Results ===
## Global Minimum Objective Value: 20.90953376
## Number of Unique Optimal Solutions Found: 1
## Optimal Weight Vectors:
## w1 w2 w3 w4
## [1,] 0.315 0.241 0.048 0.396safe_Reg ## $A0
## $A0$lambda_star
## [1] 1
##
## $A0$case
## [1] "Case 1: Unique Convex Minimum (|W*| = 1, Delta_min > 0)"
##
## $A0$delta_min
## [1] 299.965
##
## $A0$delta_max
## [1] 299.965
##
## $A0$lambda_tilde
## [1] -149.9825
##
## $A0$num_solutions
## [1] 1
##
## $A0$W_star
## w1 w2 w3 w4 w5
## [1,] 0.186 0.119 0.203 0.367 0.124
##
##
## $A1
## $A1$lambda_star
## [1] 1
##
## $A1$case
## [1] "Case 1: Unique Convex Minimum (|W*| = 1, Delta_min > 0)"
##
## $A1$delta_min
## [1] 825.6845
##
## $A1$delta_max
## [1] 825.6845
##
## $A1$lambda_tilde
## [1] -412.8423
##
## $A1$num_solutions
## [1] 1
##
## $A1$W_star
## w1 w2 w3 w4
## [1,] 0.12 0.4 0.426 0.053
##
##
## $A2
## $A2$lambda_star
## [1] 1
##
## $A2$case
## [1] "Case 1: Unique Convex Minimum (|W*| = 1, Delta_min > 0)"
##
## $A2$delta_min
## [1] 574.5303
##
## $A2$delta_max
## [1] 574.5303
##
## $A2$lambda_tilde
## [1] -287.2651
##
## $A2$num_solutions
## [1] 1
##
## $A2$W_star
## w1 w2 w3 w4
## [1,] 0.072 0.295 0.111 0.521
##
##
## $A3
## $A3$lambda_star
## [1] 1
##
## $A3$case
## [1] "Case 1: Unique Convex Minimum (|W*| = 1, Delta_min > 0)"
##
## $A3$delta_min
## [1] 681.5859
##
## $A3$delta_max
## [1] 681.5859
##
## $A3$lambda_tilde
## [1] -340.7929
##
## $A3$num_solutions
## [1] 1
##
## $A3$W_star
## w1 w2 w3 w4
## [1,] 0.067 0.278 0.098 0.556
##
##
## $A4
## $A4$lambda_star
## [1] 1
##
## $A4$case
## [1] "Case 1: Unique Convex Minimum (|W*| = 1, Delta_min > 0)"
##
## $A4$delta_min
## [1] 851.9445
##
## $A4$delta_max
## [1] 851.9445
##
## $A4$lambda_tilde
## [1] -425.9723
##
## $A4$num_solutions
## [1] 1
##
## $A4$W_star
## w1 w2 w3 w4
## [1,] 0.419 0.407 0.12 0.053
##
##
## $A5
## $A5$lambda_star
## [1] 1
##
## $A5$case
## [1] "Case 1: Unique Convex Minimum (|W*| = 1, Delta_min > 0)"
##
## $A5$delta_min
## [1] 783.0577
##
## $A5$delta_max
## [1] 783.0577
##
## $A5$lambda_tilde
## [1] -391.5288
##
## $A5$num_solutions
## [1] 1
##
## $A5$W_star
## w1 w2 w3 w4
## [1,] 0.315 0.241 0.048 0.396Conclusion on Safe Regularizer:
Across all evaluated PRMs, since \(\min(\text{DLS}) > 0\) and \(\Vert{}W\Vert{}_1 = 1\), the optimal
regularizer scaling parameter is \(\lambda^* =
1\).
ARDLS_anchor_results = list()
for (a in names(PRM_list))
{
# cat(strrep("-", 30),a,strrep("-", 30),"\n")
ARDLS_anchor_results[[a]] = compare_ARDLS_anchors(PRM_list[[a]], POs, reg_lambda = 1)
}ARDLS_anchor_results## $A0
## NRS NRCS AMNC NGMR EV SVD
## Base_w1 0.216200 0.184700 0.219600 0.199200 0.214800 0.198700
## Base_w2 0.149300 0.199300 0.151100 0.173400 0.148300 0.175400
## Base_w3 0.194600 0.202400 0.188600 0.192000 0.207800 0.227500
## Base_w4 0.242600 0.208400 0.246400 0.228800 0.225100 0.205500
## Base_w5 0.197300 0.205200 0.194200 0.206600 0.204000 0.192900
## ARDLS_w1 0.186200 0.186100 0.186200 0.186100 0.186200 0.186100
## ARDLS_w2 0.119400 0.119500 0.119400 0.119400 0.119400 0.119400
## ARDLS_w3 0.203200 0.203300 0.203200 0.203300 0.203300 0.203400
## ARDLS_w4 0.367000 0.366900 0.367000 0.366900 0.366900 0.366800
## ARDLS_w5 0.124300 0.124300 0.124300 0.124300 0.124300 0.124300
## Objective_Val 79.437113 79.452529 79.436220 79.443530 79.442616 79.449120
## ARDSE 79.437113 79.452529 79.436220 79.443530 79.442616 79.449120
## DSE_ARDLS 79.414458 79.414491 79.414455 79.414469 79.414477 79.414497
## DSE_Base 82.810408 84.662376 82.753702 83.656827 83.266023 84.266456
## ARP 0.022655 0.038038 0.021765 0.029061 0.028139 0.034623
## RMSV_Base 1.820004 1.840243 1.819381 1.829282 1.825004 1.835935
## RMSV_ARDLS 1.782296 1.782296 1.782296 1.782296 1.782296 1.782296
## CosMax PIGM DLS
## Base_w1 0.217000 0.180400 0.186000
## Base_w2 0.153300 0.205700 0.119400
## Base_w3 0.186200 0.216000 0.203200
## Base_w4 0.246400 0.203300 0.367400
## Base_w5 0.197100 0.194700 0.124100
## ARDLS_w1 0.186200 0.186000 0.186000
## ARDLS_w2 0.119400 0.119500 0.119400
## ARDLS_w3 0.203200 0.203400 0.203200
## ARDLS_w4 0.367000 0.366800 0.367400
## ARDLS_w5 0.124300 0.124300 0.124100
## Objective_Val 79.436683 79.453807 79.414387
## ARDSE 79.436683 79.453807 79.414387
## DSE_ARDLS 79.414455 79.414498 79.414387
## DSE_Base 82.816596 84.917553 79.414387
## ARP 0.022227 0.039309 0.000000
## RMSV_Base 1.820072 1.843014 1.782295
## RMSV_ARDLS 1.782296 1.782296 1.782295
##
## $A1
## NRS NRCS AMNC NGMR EV SVD
## Base_w1 0.156400 0.110400 0.125500 0.122600 0.120300 0.111900
## Base_w2 0.348600 0.229100 0.286900 0.287000 0.282900 0.227800
## Base_w3 0.452200 0.609400 0.540000 0.546300 0.551700 0.607100
## Base_w4 0.042900 0.051100 0.047600 0.044100 0.045100 0.053200
## ARDLS_w1 0.120000 0.119900 0.120000 0.119900 0.119900 0.119900
## ARDLS_w2 0.400400 0.400100 0.400200 0.400200 0.400200 0.400100
## ARDLS_w3 0.426200 0.426600 0.426400 0.426400 0.426400 0.426600
## ARDLS_w4 0.053400 0.053400 0.053400 0.053400 0.053400 0.053400
## Objective_Val 10.662900 10.720999 10.683978 10.685439 10.687698 10.720587
## ARDSE 10.662900 10.720999 10.683978 10.685439 10.687698 10.720587
## DSE_ARDLS 10.658102 10.658246 10.658156 10.658159 10.658165 10.658245
## DSE_Base 20.849485 41.371903 26.985963 34.704585 33.957088 38.204952
## ARP 0.004798 0.062753 0.025822 0.027279 0.029533 0.062342
## RMSV_Base 1.141531 1.608025 1.298700 1.472765 1.456818 1.545254
## RMSV_ARDLS 0.816169 0.816174 0.816171 0.816171 0.816171 0.816174
## CosMax PIGM DLS
## Base_w1 0.129100 0.114200 0.120000
## Base_w2 0.292100 0.239600 0.400500
## Base_w3 0.530600 0.594600 0.426100
## Base_w4 0.048100 0.051500 0.053400
## ARDLS_w1 0.120000 0.119900 0.120000
## ARDLS_w2 0.400200 0.400100 0.400500
## ARDLS_w3 0.426400 0.426500 0.426100
## ARDLS_w4 0.053400 0.053400 0.053400
## Objective_Val 10.680820 10.712246 10.658094
## ARDSE 10.680820 10.712246 10.658094
## DSE_ARDLS 10.658148 10.658224 10.658094
## DSE_Base 24.556890 36.174463 10.658094
## ARP 0.022672 0.054022 0.000000
## RMSV_Base 1.238873 1.503630 0.816168
## RMSV_ARDLS 0.816170 0.816173 0.816168
##
## $A2
## NRS NRCS AMNC NGMR EV SVD CosMax
## Base_w1 0.058000 0.067000 0.062400 0.060500 0.061200 0.070600 0.062600
## Base_w2 0.285600 0.280300 0.284600 0.286800 0.286500 0.276600 0.284100
## Base_w3 0.152300 0.107600 0.127200 0.122600 0.124800 0.111200 0.128800
## Base_w4 0.504000 0.545100 0.525800 0.530100 0.527500 0.541600 0.524500
## ARDLS_w1 0.071700 0.071700 0.071700 0.071700 0.071700 0.071700 0.071700
## ARDLS_w2 0.295400 0.295400 0.295400 0.295400 0.295400 0.295300 0.295400
## ARDLS_w3 0.111500 0.111400 0.111400 0.111400 0.111400 0.111400 0.111400
## ARDLS_w4 0.521400 0.521500 0.521400 0.521400 0.521400 0.521500 0.521400
## Objective_Val 2.563916 2.562481 2.562128 2.562056 2.562064 2.562420 2.562181
## ARDSE 2.563916 2.562481 2.562128 2.562056 2.562064 2.562420 2.562181
## DSE_ARDLS 2.561660 2.561661 2.561659 2.561659 2.561659 2.561661 2.561659
## DSE_Base 8.089871 3.523515 4.663038 5.535659 5.169617 2.864735 4.637120
## ARP 0.002256 0.000820 0.000469 0.000397 0.000404 0.000759 0.000522
## RMSV_Base 0.711067 0.469276 0.539852 0.588200 0.568420 0.423138 0.538349
## RMSV_ARDLS 0.400130 0.400130 0.400130 0.400130 0.400130 0.400130 0.400130
## PIGM DLS
## Base_w1 0.070500 0.071700
## Base_w2 0.282200 0.295400
## Base_w3 0.107700 0.111400
## Base_w4 0.539600 0.521400
## ARDLS_w1 0.071700 0.071700
## ARDLS_w2 0.295400 0.295400
## ARDLS_w3 0.111400 0.111400
## ARDLS_w4 0.521500 0.521400
## Objective_Val 2.562176 2.561659
## ARDSE 2.562176 2.561659
## DSE_ARDLS 2.561661 2.561659
## DSE_Base 2.851137 2.561659
## ARP 0.000515 0.000000
## RMSV_Base 0.422133 0.400130
## RMSV_ARDLS 0.400130 0.400130
##
## $A3
## NRS NRCS AMNC NGMR EV SVD CosMax
## Base_w1 0.053900 0.062700 0.058600 0.056500 0.057200 0.065800 0.058900
## Base_w2 0.268100 0.280100 0.274600 0.276800 0.275800 0.278500 0.274100
## Base_w3 0.141900 0.097100 0.117600 0.113000 0.115300 0.098800 0.119000
## Base_w4 0.536100 0.560100 0.549200 0.553700 0.551700 0.557000 0.548100
## ARDLS_w1 0.067500 0.067500 0.067500 0.067500 0.067500 0.067500 0.067500
## ARDLS_w2 0.278100 0.278100 0.278100 0.278100 0.278100 0.278100 0.278100
## ARDLS_w3 0.098500 0.098400 0.098400 0.098400 0.098400 0.098400 0.098400
## ARDLS_w4 0.556000 0.556000 0.556000 0.556000 0.556000 0.556000 0.556000
## Objective_Val 2.728945 2.726420 2.726879 2.726715 2.726789 2.726380 2.726950
## ARDSE 2.728945 2.726420 2.726879 2.726715 2.726789 2.726380 2.726950
## DSE_ARDLS 2.726376 2.726375 2.726376 2.726375 2.726375 2.726375 2.726376
## DSE_Base 11.118966 3.355180 5.602304 6.593552 6.236224 2.794087 5.574289
## ARP 0.002569 0.000045 0.000503 0.000340 0.000413 0.000004 0.000574
## RMSV_Base 0.833628 0.457929 0.591730 0.641948 0.624311 0.417888 0.590248
## RMSV_ARDLS 0.412794 0.412793 0.412793 0.412793 0.412793 0.412793 0.412793
## PIGM DLS
## Base_w1 0.065900 0.067500
## Base_w2 0.280000 0.278100
## Base_w3 0.095800 0.098400
## Base_w4 0.558400 0.556000
## ARDLS_w1 0.067500 0.067500
## ARDLS_w2 0.278100 0.278100
## ARDLS_w3 0.098400 0.098400
## ARDLS_w4 0.556000 0.556000
## Objective_Val 2.726394 2.726375
## ARDSE 2.726394 2.726375
## DSE_ARDLS 2.726375 2.726375
## DSE_Base 2.841026 2.726375
## ARP 0.000019 0.000000
## RMSV_Base 0.421384 0.412793
## RMSV_ARDLS 0.412793 0.412793
##
## $A4
## NRS NRCS AMNC NGMR EV SVD
## Base_w1 0.434100 0.548200 0.502900 0.504700 0.508600 0.545400
## Base_w2 0.361800 0.292100 0.321200 0.324800 0.319800 0.290700
## Base_w3 0.160100 0.109200 0.128300 0.125400 0.125600 0.111300
## Base_w4 0.043900 0.050500 0.047700 0.045100 0.046100 0.052600
## ARDLS_w1 0.419100 0.419300 0.419200 0.419200 0.419300 0.419300
## ARDLS_w2 0.407100 0.406900 0.407000 0.407000 0.407000 0.406900
## ARDLS_w3 0.120500 0.120400 0.120400 0.120400 0.120400 0.120400
## ARDLS_w4 0.053300 0.053300 0.053300 0.053300 0.053300 0.053300
## Objective_Val 7.574839 7.600874 7.585372 7.585085 7.586597 7.600447
## ARDSE 7.574839 7.600874 7.585372 7.585085 7.586597 7.600447
## DSE_ARDLS 7.570894 7.570959 7.570922 7.570921 7.570925 7.570958
## DSE_Base 15.072193 23.309717 17.543377 21.043121 20.378298 21.270599
## ARP 0.003945 0.029916 0.014450 0.014164 0.015672 0.029490
## RMSV_Base 0.970573 1.207003 1.047120 1.146820 1.128558 1.153001
## RMSV_ARDLS 0.687881 0.687884 0.687883 0.687883 0.687883 0.687884
## CosMax PIGM DLS
## Base_w1 0.498200 0.532900 0.419000
## Base_w2 0.323300 0.305600 0.407200
## Base_w3 0.130400 0.109800 0.120400
## Base_w4 0.048000 0.051600 0.053300
## ARDLS_w1 0.419200 0.419300 0.419000
## ARDLS_w2 0.407000 0.407000 0.407200
## ARDLS_w3 0.120400 0.120400 0.120400
## ARDLS_w4 0.053300 0.053300 0.053300
## Objective_Val 7.584285 7.594235 7.570889
## ARDSE 7.584285 7.594235 7.570889
## DSE_ARDLS 7.570919 7.570943 7.570889
## DSE_Base 16.561011 19.056371 7.570889
## ARP 0.013366 0.023292 0.000000
## RMSV_Base 1.017381 1.091340 0.687881
## RMSV_ARDLS 0.687883 0.687884 0.687881
##
## $A5
## NRS NRCS AMNC NGMR EV SVD
## Base_w1 0.315500 0.215800 0.296500 0.278400 0.271900 0.188800
## Base_w2 0.234700 0.297300 0.276000 0.262800 0.267800 0.295300
## Base_w3 0.041300 0.066500 0.037500 0.047500 0.034900 0.062000
## Base_w4 0.408400 0.420300 0.390000 0.411300 0.425400 0.453900
## ARDLS_w1 0.315300 0.315100 0.315300 0.315200 0.315200 0.315000
## ARDLS_w2 0.240600 0.240800 0.240700 0.240700 0.240700 0.240800
## ARDLS_w3 0.047800 0.047800 0.047800 0.047800 0.047800 0.047800
## ARDLS_w4 0.396300 0.396300 0.396200 0.396300 0.396300 0.396400
## Objective_Val 20.909759 20.923553 20.911274 20.911607 20.913164 20.931997
## ARDSE 20.909759 20.923553 20.911274 20.911607 20.913164 20.931997
## DSE_ARDLS 20.909534 20.909566 20.909537 20.909539 20.909542 20.909589
## DSE_Base 24.922579 35.449548 32.734554 21.773938 44.604707 32.931713
## ARP 0.000225 0.013986 0.001737 0.002068 0.003622 0.022408
## RMSV_Base 1.248063 1.488488 1.430353 1.166564 1.669669 1.434654
## RMSV_ARDLS 1.143174 1.143174 1.143174 1.143174 1.143174 1.143175
## CosMax PIGM DLS
## Base_w1 0.302700 0.182800 0.315300
## Base_w2 0.282100 0.277700 0.240700
## Base_w3 0.038500 0.056600 0.047800
## Base_w4 0.376700 0.482900 0.396200
## ARDLS_w1 0.315300 0.315000 0.315300
## ARDLS_w2 0.240700 0.240800 0.240700
## ARDLS_w3 0.047800 0.047800 0.047800
## ARDLS_w4 0.396200 0.396500 0.396200
## Objective_Val 20.911877 20.935981 20.909534
## ARDSE 20.911877 20.935981 20.909534
## DSE_ARDLS 20.909538 20.909600 20.909534
## DSE_Base 30.149229 30.571146 20.909534
## ARP 0.002339 0.026381 0.000000
## RMSV_Base 1.372708 1.382280 1.143174
## RMSV_ARDLS 1.143174 1.143175 1.143174base_w = data.frame()
for (po in colnames(ARDLS_anchor_results[[1]]))
{
result = ARDLS_anchor_results[[1]][1:5,po] %*% rbind(
ARDLS_anchor_results[[2]][1:4,po],
ARDLS_anchor_results[[3]][1:4,po],
ARDLS_anchor_results[[4]][1:4,po],
ARDLS_anchor_results[[5]][1:4,po],
ARDLS_anchor_results[[6]][1:4,po])
base_w = rbind(base_w, result)
}
rownames(base_w) =colnames(ARDLS_anchor_results[[1]])
colnames(base_w) = paste0("t",1:4)base_w## t1 t2 t3 t4
## NRS 0.2205228 0.3042587 0.1951065 0.2800747
## NRCS 0.2049615 0.2767504 0.1900570 0.3282106
## AMNC 0.2295353 0.2905387 0.1988789 0.2809717
## NGMR 0.2187534 0.2886558 0.1902828 0.3023079
## EV 0.2167560 0.2871843 0.1963645 0.2997177
## SVD 0.1980865 0.2738405 0.1974442 0.3306516
## CosMax 0.2309971 0.2932387 0.1967619 0.2789745
## PIGM 0.1932677 0.2779491 0.1834549 0.3454116
## DLS 0.2376663 0.3457498 0.1627176 0.2539176base_r = t(apply(X = -base_w ,MARGIN = 1,FUN = rank))
base_r## t1 t2 t3 t4
## NRS 3 1 4 2
## NRCS 3 2 4 1
## AMNC 3 1 4 2
## NGMR 3 2 4 1
## EV 3 2 4 1
## SVD 3 2 4 1
## CosMax 3 1 4 2
## PIGM 3 2 4 1
## DLS 3 1 4 2ardls_s = data.frame()
for (po in colnames(ARDLS_anchor_results[[1]]))
{
result = ARDLS_anchor_results[[1]][6:10,po] %*% rbind(
ARDLS_anchor_results[[2]][5:8,po],
ARDLS_anchor_results[[3]][5:8,po],
ARDLS_anchor_results[[4]][5:8,po],
ARDLS_anchor_results[[5]][5:8,po],
ARDLS_anchor_results[[6]][5:8,po])
ardls_s = rbind(ardls_s, result)
}
rownames(ardls_s) =paste0("ardls_",colnames(ARDLS_anchor_results[[1]]))
colnames(ardls_s) = paste0("t",1:4)ardls_s ## t1 t2 t3 t4
## ardls_NRS 0.2376225 0.3456474 0.1628518 0.2539986
## ardls_NRCS 0.2376124 0.3455197 0.1628236 0.2541077
## ardls_AMNC 0.2376592 0.3455859 0.1628201 0.2539862
## ardls_NGMR 0.2375810 0.3455330 0.1627752 0.2540436
## ardls_EV 0.2376296 0.3455730 0.1628179 0.2540489
## ardls_SVD 0.2375576 0.3454653 0.1628102 0.2541182
## ardls_CosMax 0.2376592 0.3455859 0.1628201 0.2539862
## ardls_PIGM 0.2375528 0.3455035 0.1627601 0.2541774
## ardls_DLS 0.2376663 0.3457498 0.1627176 0.2539176ardls_s_rank = t(apply(X = -ardls_s ,MARGIN = 1,FUN = rank))
ardls_s_rank ## t1 t2 t3 t4
## ardls_NRS 3 1 4 2
## ardls_NRCS 3 1 4 2
## ardls_AMNC 3 1 4 2
## ardls_NGMR 3 1 4 2
## ardls_EV 3 1 4 2
## ardls_SVD 3 1 4 2
## ardls_CosMax 3 1 4 2
## ardls_PIGM 3 1 4 2
## ardls_DLS 3 1 4 2exportListtoCSV(listData = ARDLS_anchor_results ,path = ".//application/",digits=4)ExportResult = list(
final_AHP_base_results = final_AHP_base_results,
final_AHP_ardls_results = final_AHP_ardls_results
)exportListtoCSV(listData = ExportResult ,path = ".//application/")