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#' Implementation of MULTIMOORA Method for Multi-Criteria Decision Making Problems.
#'
#' @description The \code{MMOORA} function implements both the Multi-Objetive Optimization by Ration Analysis (MOORA) and the "Full Multiplicative Form" (MULTIMOORA).
#' @param decision The decision matrix (\emph{m} x \emph{n}) with the values of the \emph{m} alternatives, for the \emph{n} criteria.
#' @param weights A vector of length \emph{n}, containing the weights for the criteria. The sum of the weights has to be 1.
#' @param cb A vector of length \emph{n}. Each component is either \code{cb(i)='max'} if the \emph{i-th} criterion is benefit or \code{cb(i)='min'} if the \emph{i-th} criterion is a cost.
#' @return \code{MMOORA} returns a data frame which contains the scores and the four rankings calculated (Ratio System, Reference Point, Multiplicative Form and Multi-MOORA ranking).
#' @references Brauers, W. K. M.; Zavadskas, E. K. Project management by MULTIMOORA as an instrument for transition economies. Technological and Economic Development of Economy, 16(1), 5-24, 2010.
#' @examples
#'
#' d <- matrix(c(60,6.35,6.8,10,2.5,4.5,3,0.4,0.15,0.1,0.2,0.1,0.08,0.1,2540,1016,1727.2,
#' 1000,560,1016,1778,500,3000,1500,2000,500,350,1000,990,1041,1676,965,915,508,920),
#' nrow=7,ncol=5)
#' w <- c(0.036,0.192,0.326,0.326,0.12)
#' cb <- c('max','min','max','max','max')
#' MMOORA(d,w,cb)
MMOORA <- function(decision, #matrix with all the alternatives
weights, #vector with the numeric values of the weights
cb #vector with the "type" of the criteria (benefit = "max", cost = "min")
)
{
#Checking the arguments
if(! is.matrix(decision))
stop("'decision' must be a matrix with the values of the alternatives")
if(missing(weights))
stop("a vector containing n weigths, adding up to 1, should be provided")
if(sum(weights) != 1)
stop("The sum of 'weights' is not equal to 1")
if(! is.character(cb))
stop("'cb' must be a character vector with the type of the criteria")
if(! all(cb == "max" | cb == "min"))
stop("'cb' should contain only 'max' or 'min'")
if(length(weights) != ncol(decision))
stop("length of 'weights' does not match the number of the criteria")
if(length(cb) != ncol(decision))
stop("length of 'cb' does not match the number of the criteria")
#MMOORA method
#1. Normalization and weighting
d = sqrt(colSums(decision^2))
NW <- matrix(nrow = nrow(decision), ncol = ncol(decision))
for(j in 1:ncol(decision)){
NW[,j] <- (decision[,j] / d[j]) * weights[j]
}
#2. Ration system
NR <- NW
for(j in 1:ncol(decision)){
if (cb[j] == 'min'){
NR[,j] <- NW[,j]*(-1)
}
}
RS <- apply(NR, 1, sum)
#3. Reference point
Ref <- as.integer(cb == "max") * apply(NW, 2, max) +
as.integer(cb == "min") * apply(NW, 2, min)
RefP <- matrix(nrow = nrow(decision), ncol = ncol(decision))
for(j in 1:ncol(decision)){
RefP[,j] <- abs(Ref[j]-NW[,j])
}
RP <- apply(RefP, 1, max)
#4. Multiplicative form
max <- NW
min <- NW
for (j in 1:ncol(NW)){
if (cb[j] == 'max'){
min[,j] <- 1
}else{
max[,j] <- 1
}
}
A <- apply(max, 1, prod)
B <- apply(min, 1, prod)
M <- A/B
#5. Ranking the alternatives
Rrs <- rank(-RS, ties.method= "first")
Rrp <- rank(RP, ties.method= "first")
Rm <- rank(-M, ties.method= "first")
MMRanking = TheoryOfDominance(Rrs,Rrp,Rm,decision)
return(data.frame(Alternatives = 1:nrow(decision), RatioSystem = RS, Ranking = Rrs, ReferencePoint = RP, Ranking = Rrp, MultiplicativeForm = M, Ranking = Rm, MultiMooraRanking = MMRanking))
}
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