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Electre_tri.R
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Electre_tri.R
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Electre_tri <-
function(performanceMatrix,alternatives,profiles,profiles_names,criteria,minmaxcriteria,criteriaWeights,IndifferenceThresholds,PreferenceThresholds,VetoThresholds,lambda=NULL){
cat("\014")
####################################################################################################################################################
# #
# Copyright Michel Prombo, 2014 #
# Module : electre tri #
# ELECTRE TRI assigns alternatives to predefined categories. The assignment of an alternative results from the comparison with the profiles #
#defining the limits of the categories. #
# Version 1.0 #
# #
# Contributors: #
# Michel Prombo <michel.prombo@statec.etat.lu> #
# Kevin Prombo-Rosamont <kevinrosamont@ymail.com> #
# #
# This software, ELECTRE III , is a package for the R OR software which allows to use MCDA algorithms and methods. #
# #
# This software is governed by the terms and conditions of the Free and open-source licenses. You can #
# use, modify and/ or redistribute the software under the terms of ....... #
# #
# #
# As a counterpart to the access to the source code and rights to copy,modify and redistribute granted by the license, users are provided only #
# with a limited warranty and the software's author, the holder of the economic rights, and the successive licensors have only limited liability. #
# #
# In this respect, the user's attention is drawn to the risks associated with loading, using, modifying and/or developing or reproducing the #
# software by the user in light of its specific status of free software, that may mean that it is complicated to manipulate, and that also #
# therefore means that it is reserved for developers and experienced professionals having in-depth computer knowledge. Users are therefore #
# encouraged to load and test the software's suitability as regards their requirements in conditions enabling the security of their systems and/or #
# data to be ensured and, more generally, to use and operate it in the # same conditions as regards security. #
# #
# The fact that you are presently reading this means that you have had knowledge of the terms and conditions of the Free and open-source licenses #
# and that you accept its terms. #
# #
####################################################################################################################################################
## ******************************************************* checking the input data *****************************************************************#
# data is filtered, check for some data consistency
# if there are less than 2 criteria or 2 alternatives, there is no problem to resolve here
if (is.null(dim(performanceMatrix)))
stop("less than 2 criteria or 2 alternatives")
if (!((is.matrix(performanceMatrix) || (is.data.frame(performanceMatrix)))))
stop("wrong performanceMatrix, should be a matrix or a data frame")
if (!((is.matrix(profiles) || (is.data.frame(profiles)))))
stop("wrong profiles, should be a matrix or a data frame")
if (is.null(dim(profiles)))
stop("less than 2 criteria or 2 profiles")
if (!(is.vector(profiles_names)))
stop("profiles_names should be a vector")
if (!(is.vector(alternatives)))
stop("alternatives should be a vector")
if (!is.character(alternatives))
stop("alternatives should be a character vector")
if(!(nrow(performanceMatrix)==length(alternatives)))
stop("length of alternatives should be checked")
if (!(is.vector(criteria)))
stop("criteria should be a vector")
if (!is.character(criteria))
stop("criteria should be a character vector")
if(!(ncol(performanceMatrix)==length(criteria)))
stop("length of criteria should be checked")
if (!(is.vector(minmaxcriteria)))
stop("minmaxcriteria should be a vector")
minmaxcriteria=tolower(minmaxcriteria)
if(!(ncol(performanceMatrix)==length(minmaxcriteria)))
stop("length of minmaxcriteria should be checked")
n=length(minmaxcriteria)
for (i in 1:n){
if(!((minmaxcriteria[i]=='min') ||(minmaxcriteria[i]=='max'))){
stop(" Vector minmaxcriteria must contain 'max' or 'min' ")
}
}
if (!(is.vector(criteriaWeights)))
stop("criteriaWeights should be a vector")
if (!is.numeric(criteriaWeights))
stop("criteriaWeights should be a numeric vector")
if(!(ncol(performanceMatrix)==length(criteriaWeights)))
stop("length of criteriaWeights should be checked")
if (!(is.vector(IndifferenceThresholds)))
stop("IndifferenceThresholds should be a vector")
if(!(ncol(performanceMatrix)==length(IndifferenceThresholds)))
stop("length of IndifferenceThresholds should be checked")
if (!(is.vector(PreferenceThresholds)))
stop("PreferenceThresholds should be a vector")
if(!(ncol(performanceMatrix)==length(PreferenceThresholds)))
stop("length of PreferenceThresholds should be checked")
if (!(is.vector(VetoThresholds)))
stop("VetoThresholds should be a vector")
if(!(ncol(performanceMatrix)==length(VetoThresholds)))
stop("length of VetoThresholds should be checked")
## ************************************* End of checking the validity of the "inputs" **********************************************************####
pm=performanceMatrix
pr_names=profiles_names
nrow_pm=nrow(pm)
al <- alternatives
pr <- profiles
nrow_pr=nrow(pr)
cr <- criteria
length_cr=length(cr)
vp <- criteriaWeights
if (sum(vp)>1){
vp <- vp/sum(vp)
}
mmv <- minmaxcriteria
p_t=PreferenceThresholds
q_t=IndifferenceThresholds
v_t=VetoThresholds
if (is.null(lambda)){
lambda <-0.75
}
partialConcordance_al_pr_gj <- matrix (rep(0, nrow_pm*length_cr), nrow_pm, length_cr)
partialConcordance_pr_al_gj <- matrix (rep(0, nrow_pm*length_cr), nrow_pm, length_cr)
partialDiscordance_al_pr_gj <- matrix (rep(0, nrow_pm*length_cr), nrow_pm, length_cr)
partialDiscordance_pr_al_gj <- matrix (rep(0, nrow_pm*length_cr), nrow_pm, length_cr)
globalconcordance <- matrix (rep(0, nrow_pm*nrow_pr*2), nrow_pm, nrow_pr*2)
credibility <- matrix (rep(0, nrow_pm*nrow_pr*2), nrow_pm, nrow_pr*2)
relations <- matrix (rep(0, nrow_pm*nrow_pr*2), nrow_pm, nrow_pr*2)
Pessimistic <- matrix (rep(0, nrow_pm*(nrow_pr+1)), nrow_pm, nrow_pr+1)
Optimistic <- matrix (rep(0, nrow_pm*(nrow_pr+1)), nrow_pm, nrow_pr+1)
names_glo_con=list()
for (i in 1:nrow_pr){
v1=paste("c(","ai",",","b",i,")",sep="")
names_glo_con <-union(names_glo_con,v1)
v2=paste("c(","b",i,",","ai",")",sep="")
names_glo_con <-union(names_glo_con,v2)
}
names_relations=list()
for (i in 0:(2*nrow_pr-1)){
v1=paste("b",i,sep="")
names_relations <-union(names_relations,v1)
}
names_categories=list()
for (i in 1:(nrow_pr+1)){
v1=paste("C",i,sep="")
names_categories <-union(names_categories,v1)
}
colnames(globalconcordance)=names_glo_con
rownames(globalconcordance)=al
colnames(credibility)=names_glo_con
rownames(credibility)=al
# colnames(relations)=names_glo_con
rownames(relations)=al
colnames(Pessimistic)=names_categories
rownames(Pessimistic)=al
colnames(Optimistic)=names_categories
rownames(Optimistic)=al
rownames(partialConcordance_al_pr_gj)=al
colnames(partialConcordance_al_pr_gj)=cr
rownames(partialConcordance_pr_al_gj)=al
colnames(partialConcordance_pr_al_gj)=cr
rownames(partialDiscordance_al_pr_gj)=al
colnames(partialDiscordance_al_pr_gj)=cr
rownames(partialDiscordance_pr_al_gj)=al
colnames(partialDiscordance_pr_al_gj)=cr
credibility_al_pr <- matrix (rep(0, nrow_pm%*%nrow_pr), nrow_pm, nrow_pr)
credibility_pr_al <- matrix (rep(0, nrow_pr*nrow_pm), nrow_pr, nrow_pm)
# globalconcordance_al_pr=0
# globalconcordance_pr_al=0
# 1. Computation of partial concordance indices cj(a,b) and cj(b,a)
h=0
k=1
while (k<=nrow_pr){
for (i in 1: nrow_pm){
# Columns' iterations
for (j in 1:length_cr){
if (mmv[j]=="max"){
c_a_b = (pm[i,j]-pr[k,j]+p_t[j])/(p_t[j]-q_t[j])
}
if (mmv[j]=="min"){
c_a_b = (pr[k,j]-pm[i,j]+p_t[j])/(p_t[j]-q_t[j])
}
c_a_b=round(c_a_b,digits=4)
if ( c_a_b < 0){
c_a_b <- 0
}
if ( c_a_b < 0){
partialConcordance_al_pr_gj[i,j]=0
}
if ( c_a_b >= 1 ){
partialConcordance_al_pr_gj[i,j]=1
} else {
partialConcordance_al_pr_gj[i,j]= c_a_b
}
}
}
h=h+1
globalconcordance[,h]=partialConcordance_al_pr_gj%*%vp
for (i in 1: nrow_pm){
# Columns' iterations
for (j in 1:length_cr){
if (mmv[j]=="max"){
c_a_b = (pr[k,j]-pm[i,j]+p_t[j])/(p_t[j]-q_t[j])
}
if (mmv[j]=="min"){
c_a_b = (pm[i,j]-pr[k,j]+p_t[j])/(p_t[j]-q_t[j])
}
c_a_b=round(c_a_b,digits=4)
if ( c_a_b < 0){
c_a_b <- 0
}
if ( c_a_b < 0){
partialConcordance_pr_al_gj[i,j]=0
}
if ( c_a_b >= 1 ){
partialConcordance_pr_al_gj[i,j]=1
} else {
partialConcordance_pr_al_gj[i,j]= c_a_b
}
}
}
h=h+1
globalconcordance[,h]=partialConcordance_pr_al_gj%*%vp
k=k+1
}
# 2. Computation of the partial discordance indices dj(a,b) and dj(b,a).
l=0
k=1
while (k<=nrow_pr){
for (i in 1: nrow_pm){
# Columns' iterations
for (j in 1:length_cr){
if ((mmv[j]=="max")){
d_a_b = (pr[k,j]-pm[i,j]-p_t[j])/(v_t[j]-p_t[j])
}
if ((mmv[j]=="min")){
d_a_b = (pm[i,j]-pr[k,j]-p_t[j])/(v_t[j]-p_t[j])
}
d_a_b=round(d_a_b,digits=4)
if ( d_a_b < 0){
d_a_b <- 0
}
if ( d_a_b < 0){
partialDiscordance_al_pr_gj[i,j]=0
}
if ( d_a_b >= 1 ){
partialDiscordance_al_pr_gj[i,j]=1
} else {
partialDiscordance_al_pr_gj[i,j]= d_a_b
}
}
}
l=l+1
for (h in 1: nrow_pm){
if (max(partialDiscordance_al_pr_gj[h,]==1)){
credibility[h,l]=0
}else if (max(partialDiscordance_al_pr_gj[h,])<globalconcordance[h,l]){
credibility[h,l]=globalconcordance[h,l]
} else if (max(partialDiscordance_al_pr_gj[h,]) > globalconcordance[h,l]){
credibility[h,l]=((1-max(partialDiscordance_al_pr_gj[h,]))/(1-globalconcordance[h,l]))*globalconcordance[h,l]
}
}
for (i in 1: nrow_pm){
# Columns' iterations
for (j in 1:length_cr){
if ((mmv[j]=="max")){
d_b_a = (pm[i,j]-pr[k,j]-p_t[j])/(v_t[j]-p_t[j])
}
if ((mmv[j]=="min")){
d_b_a = (pr[k,j]-pm[i,j]-p_t[j])/(v_t[j]-p_t[j])
}
d_b_a = round(d_b_a,digits=4)
if ( d_b_a < 0){
d_b_a <- 0
}
if ( d_b_a < 0){
partialDiscordance_pr_al_gj[i,j]=0
}
if ( d_b_a >= 1 ){
partialDiscordance_pr_al_gj[i,j]=1
} else {
partialDiscordance_pr_al_gj[i,j]= d_b_a
}
}
}
l=l+1
for (h in 1: nrow_pm){
if (max(partialDiscordance_pr_al_gj[h,]==1)){
credibility[h,l]=0
}else if (max(partialDiscordance_pr_al_gj[h,])< globalconcordance[h,l]){
credibility[h,l]=globalconcordance[h,l]
} else if (max(partialDiscordance_pr_al_gj[h,]) > globalconcordance[h,l]){
credibility[h,l]=((1-max(partialDiscordance_pr_al_gj[h,]))/(1-globalconcordance[h,l]))*globalconcordance[h,l]
}
}
k=k+1
}
relations=data.frame(relations)
colnames(relations)=names_relations
for (i in 1:nrow_pm){
# Columns' iterations
for (j in 0:(nrow_pr+1)){
if (j==0) {
relations[i,1]=">"
} else if (j==nrow_pr+1) {
relations[i,nrow_pr+2]="<"
}else {
if (credibility[i,2*j-1]>= lambda){
if (credibility[i,2*j]>=lambda){
relations[i,j+1]="I"
} else {
relations[i,j+1]=">"
}
} else if (credibility[i,2*j] >=lambda){
relations[i,j+1]="<"
} else {
relations[i,j+1]="R"
}
}
}
}
# pessimistic assignment
# a) compare alternatives ("a") successively to "b(i)" , for i=p,p-1, ..., 0,
# b) let "b(h)" = the first profile such that "a" outranks "b(h).",
# affect "a" to the category C(h+1).
# Pessimistic decisions ...
for (i in 1:nrow_pm){
# Columns' iterations
ok=0
for (j in nrow_pr:1){
if ( (credibility[i,2*j-1]>=0.75) && (credibility[i,2*j]<0.75)) {
if (ok==0) {
Pessimistic[i,j+1]=1
ok=1
}
}
}
if (ok==0){
Pessimistic[i,j]=1
}
}
# optimistic assignment,
# a) compare alternatives ("a") successively to "b(i)" ,for i=1, 2, ..., p+1,
# b) let "b(h)" = the first profile such that "b(h)" outranks ("a"),
# affect "a" to the category C(h).
# Optimistic decisions ...
for (i in 1:nrow_pm){
# Columns' iterations
ok=0
for (j in 1:nrow_pr){
if ( (credibility[i,2*j-1]<0.75) && (credibility[i,2*j]>=0.75)) {
if (ok==0) {
Optimistic[i,j]=1
ok=1
}
}
}
if (ok==0){
Optimistic[i,j+1]=1
}
}
rest<- list(PartialConcordance_al_pr_gj=partialConcordance_al_pr_gj,partialConcordance_pr_al_gj=partialConcordance_pr_al_gj,partialDiscordance_al_pr_gj=partialDiscordance_al_pr_gj,
partialDiscordance_pr_al_gj=partialDiscordance_pr_al_gj,globalconcordance=globalconcordance,
credibility=credibility,relations=relations,Pessimistic=Pessimistic,Optimistic=Optimistic)
return(rest)
}