version 1.0

DESCRIPTION

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+Package: MCDM
+Title: Multi-Criteria Decision Making Methods
+Version: 1.0
+Date: 2015-09-10
+Author: Blanca A. Ceballos Martin <[email protected]>
+Maintainer: Blanca A. Ceballos Martin <[email protected]>
+Description: An R implementation of Four Multi-Criteria Decision Making (MCDM) Methods: Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), "VIseKriterijumska Optimizacija I Kompromisno Resenje" (VIKOR), both Multi-Objective Optimization by Ratio Analysis and Full Multiplicative Form (Multi-MOORA) and Weighted Aggregated Sum Product ASsessment (WASPAS). In addition, this package provides a MetaRanking function which combines the output of the previous methods. 
+License: LGPL (>= 3)
+URL: http://decsai.ugr.es/index.php?p=miembros&id=19909
+NeedsCompilation: no
+Packaged: 2015-11-18 16:00:54 UTC; Blanky
+Repository: CRAN
+Date/Publication: 2015-11-19 11:02:12

MD5

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+b301612e520e87ecf367a63d632b0645 *DESCRIPTION
+0f714634d9b6e945d6b30e5d6276b22e *NAMESPACE
+a6d7468cec7f23a7d52226beb220a609 *R/MMOORA.R
+916b563fb195602c830dd3c55b3f1f7e *R/MetaRanking.R
+5b246b44eab588a3641bf7288c90f566 *R/TOPSIS.R
+6f0bdad34dcfb7883f3dc08ebdecb72e *R/VIKOR.R
+f80bef4b19a66218360122eb29b1f0b0 *R/WASPAS.R
+e91d631037e23f00c7fd70739a1278c3 *man/MMOORA.Rd
+c3d685827adbeb13256720e443d2687a *man/MetaRanking.Rd
+a263ae3ec5866104e5736868d3ebbd8e *man/TOPSIS.Rd
+73dae3c80f82ad4dd9119924e75ce00d *man/VIKOR.Rd
+244851b5223807a97aaceba704f70a8e *man/WASPAS.Rd
+9120b7e76ff718096df3feea7dce908d *vignettes/MCDM.pdf

NAMESPACE

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+exportPattern("^[[:alpha:]]+")
+

R/MMOORA.R

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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(rpois(12, 5), nrow = 4)
+#'  w <- c(0.2, 0.2, 0.6)
+#'  cb <- c('max','min','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
+  NEW <- matrix(nrow = nrow(decision), ncol = ncol(decision))
+  for(j in 1:ncol(decision)){
+    NEW[,j] <- (decision[,j] / d[j]) ^ weights[j]
+  }
+
+  max <- NEW
+  min <- NEW
+  for (j in 1:ncol(NEW)){
+    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)
+  Rrp <- rank(RP)
+  Rm <- rank(-M)
+  R <- Rrs + Rrp + Rm
+  return(data.frame(Alternatives = 1:nrow(decision), RatioSystem = RS, Ranking = rank(-RS, ties.method= "random"), ReferencePoint = RP, Ranking = rank(RP, ties.method= "random"), MultiplicativeForm = M, Ranking = rank(-M, ties.method= "random"), MultiMooraRanking = rank(R, ties.method= "random")))
+
+}

R/MetaRanking.R

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+#' Implementation of MetaRanking function for Multi-Criteria Decision Making Problems.
+#'
+#' @description The \code{MetaRanking} function internally calls functions  \code{MMOORA}, \code{TOPSIS}, \code{VIKOR} and \code{WASPAS} and then calculates a sum of the their rankings.
+#' @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.
+#' @param lambda A value in [0,1]. It is used in the calculation of the W index for WASPAS method.
+#' @param v A value in [0,1]. It is used in the calculation of the Q index for VIKOR method.
+#' @return \code{MetaRanking} returns a data frame which contains the rankings of the Multi-MOORA, TOPSIS, VIKOR, WASPAS Methods and the MetaRanking of the alternatives. 
+#' @examples
+#' 
+#'  d <- matrix(rpois(12, 5), nrow = 4)
+#'  w <- c(0.2, 0.2, 0.6)
+#'  cb <- c('max','min','max')
+#'  lambda <- 0.5
+#'  v <- 0.5
+#'  MetaRanking(d,w,cb,lambda,v)
+
+MetaRanking <- 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")
+                        lambda,   #value with the real number of the 'lambda' parameter to calculate W
+                        v         #value with the real number of the 'v' parameter to calculate Q
+)
+{
+  #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")
+  if(missing(lambda))
+    stop("a value for 'lambda' in [0,1] should be provided")
+  if(missing(v))
+    stop("a value for 'v' in [0,1] should be provided")
+
+
+  #Multi-MOORA method 
+  MMoora = MMOORA(decision,weights,cb)
+
+  #TOPSIS method 
+  Topsis = TOPSIS(decision,weights,cb)
+
+  #VIKOR method  
+  Vikor = VIKOR(decision,weights,cb,v)
+
+  #WASPAS method  
+  Waspas = WASPAS(decision,weights,cb,lambda)
+
+  #Meta-Ranking
+  MetaR = MMoora[,8]+Topsis[,3]+Vikor[,5]+Waspas[,3]
+  return(data.frame(Alternatives = 1:nrow(decision), MMOORA = MMoora[,8], TOPSIS = Topsis[,3], VIKOR = Vikor[,5], WASPAS = Waspas[,3], METARANKING = rank(MetaR, ties.method= "random")))
+
+}

R/TOPSIS.R

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+#' Implementation of TOPSIS Method for Multi-Criteria Decision Making Problems.
+#'
+#' @description The \code{TOPSIS} function implements the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) Method.
+#' @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{TOPSIS} returns a data frame which contains the score of the R index and the ranking of the alternatives.
+#' @references Hwang, C.L.; Yoon, K. Multiple Attribute Decision Making. In: Lecture Notes in Economics and Mathematical Systems 186. Springer-Verlag, Berlin, 1981.
+#' @examples
+#' 
+#'  d <- matrix(rpois(12, 5), nrow = 4)
+#'  w <- c(0.2, 0.2, 0.6)
+#'  cb <- c('max','min','max')
+#'  TOPSIS(d,w,cb)
+
+TOPSIS <- 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")
+
+
+  #TOPSIS 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. Ideal solutions
+  posI <- as.integer(cb == "max") * apply(NW, 2, max) + 
+    as.integer(cb == "min") * apply(NW, 2, min)
+  negI <- as.integer(cb == "min") * apply(NW, 2, max) + 
+    as.integer(cb == "max") * apply(NW, 2, min)
+
+  #3. Distances to the ideal solutions
+  distance =function(x,y){
+    sqrt(sum((x - y) ^ 2))
+  }
+  posDis <- apply(NW, 1, distance, posI)
+  negDis <- apply(NW, 1, distance, negI)
+
+  #4. R index
+  R <- negDis/(negDis+posDis)
+
+  #5. Rank the alternatives
+  return(data.frame(Alternatives = 1:nrow(decision), R = R, Ranking = rank(-R, ties.method= "random")))
+
+}

R/VIKOR.R

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+#' Implementation of VIKOR Method for Multi-Criteria Decision Making Problems.
+#'
+#' @description The \code{VIKOR} function implements the "VIseKriterijumska Optimizacija I Kompromisno Resenje" (VIKOR) Method.
+#' @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.
+#' @param v A value in [0,1]. It is used in the calculation of the Q index.
+#' @return \code{VIKOR} returns a data frame which contains the score of the S, R and Q indixes and the ranking of the alternatives according to Q index. 
+#' @references Opricovic, S.; Tzeng, G.H. Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS. European Journal of Operational Research, 156(2), 445-455, 2004.
+#' @examples
+#' 
+#'  d <- matrix(rpois(12, 5), nrow = 4)
+#'  w <- c(0.2, 0.2, 0.6)
+#'  cb <- c('max','min','max')
+#'  v <- 0.5
+#'  VIKOR(d,w,cb,v)
+
+VIKOR <- 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")
+                  v         #value with the real number of the 'v' parameter to calculate Q
+)
+{
+  #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")
+  if(missing(v))
+    stop("a value for 'v' in [0,1] should be provided")
+
+
+  #VIKOR method
+
+  #1. Ideal solutions
+  posI <- as.integer(cb == "max") * apply(decision, 2, max) + 
+    as.integer(cb == "min") * apply(decision, 2, min)
+  negI <- as.integer(cb == "min") * apply(decision, 2, max) + 
+    as.integer(cb == "max") * apply(decision, 2, min)
+
+  #2. S and R index
+  norm =function(x,w,p,n){
+    w*((p-x)/(p-n))
+  }
+  SAux <- apply(decision, 1, norm, weights, posI, negI)
+  S <- apply(SAux, 2, sum)
+  R <- apply(SAux, 2, max)
+
+
+  #3. Q index
+  Q <- v*(S-min(S))/(max(S)-min(S))+(1-v)*(R-min(R))/(max(R)-min(R))
+
+  #4. Ranking the alternatives
+  return(data.frame(Alternatives = 1:nrow(decision), S = S, R = R, Q = Q, Ranking = rank(Q, ties.method= "random")))
+
+}