R/modelfuzzy_possibilistic.R

In deaR: Conventional and Fuzzy Data Envelopment Analysis

#' @title Possibilistic Fuzzy DEA model.
#'   
#' @description Solve the possibilistic fuzzy DEA model proposed by León et. al (2003).
#' 
#' @usage modelfuzzy_possibilistic(datadea,
#'                          dmu_eval = NULL,
#'                          poss_modelname = c("basic"),
#'                          h = 1,
#'                          ...)
#' 
#' @param datadea A \code{deadata_fuzzy} object, including DMUs, inputs and outputs.
#' @param dmu_eval A numeric vector containing which DMUs have to be evaluated.
#' If \code{NULL} (default), all DMUs are considered.
#' @param poss_modelname a string containing the name of the model.
#' @param h A numeric vector with the h-levels (in [0,1]).
#' @param ... \code{dmu_ref}, \code{orientation}, \code{rts} and other model parameters.
#'   
#' @return An object of class \code{deadata_fuzzy}.
#' 
#' @author 
#' \strong{Vicente Coll-Serrano} (\email{vicente.coll@@uv.es}).
#' \emph{Quantitative Methods for Measuring Culture (MC2). Applied Economics.}
#' 
#' \strong{Vicente Bolós} (\email{vicente.bolos@@uv.es}).
#' \emph{Department of Business Mathematics}
#'
#' \strong{Rafael Benítez} (\email{rafael.suarez@@uv.es}).
#' \emph{Department of Business Mathematics}
#'
#' University of Valencia (Spain)
#'  
#' @examples 
#' # Replication of results in Leon et. al (2003, p. 416)
#' data("Leon2003")
#' data_example <- make_deadata_fuzzy(Leon2003,
#'                                    inputs.mL = 2, 
#'                                    inputs.dL = 3, 
#'                                    outputs.mL = 4, 
#'                                    outputs.dL = 5)
#' result <- modelfuzzy_possibilistic(data_example, 
#'                                    h = seq(0, 1, by = 0.1), 
#'                                    orientation = "io", 
#'                                    rts = "vrs")
#' efficiencies(result)
#'  
#' @references
#' Emrouznejad, A.; Tavana, M.; Hatami-Marbini, A. (2014). “The State of the Art
#' in Fuzzy Data Envelopment Analysis”, in A. Emrouznejad and M. Tavana (eds.),
#' Performance Measurement with Fuzzy Data Envelopment Analysis. Studies in Fuzziness
#' and Soft Computing 309. Springer, Berlin. \doi{10.1007/978-3-642-41372-8_1}
#' 
#' Hatami-Marbini, A.; Emrouznejad, A.; Tavana, M. (2011). "A Taxonomy and Review
#' of the Fuzzy Data Envelopment Analysis Literature: Two Decades in the Making",
#' European Journal of Operational Research, 214, 457–472.
#' \doi{10.1016/j.ejor.2011.02.001}
#' 
#' Leon, T.; Liern, V. Ruiz, J.; Sirvent, I. (2003). "A Possibilistic Programming
#' Approach to the Assessment of Efficiency with DEA Models", Fuzzy Sets and Systems,
#' 139, 407–419. \doi{10.1016/S0165-0114(02)00608-5}
#' 
#' @seealso \code{\link{model_basic}}, \code{\link{modelfuzzy_kaoliu}},
#' \code{\link{modelfuzzy_guotanaka}}

#' 
#' @import lpSolve
#' 
#' @export
  
modelfuzzy_possibilistic <-
  function(datadea,
           dmu_eval = NULL,
           poss_modelname = c("basic"),
           h = 1,
           ...) {
 
  # Cheking whether datadea is of class "deadata_fuzzy" or not...  
  if (!is.deadata_fuzzy(datadea)) {
    stop("Data should be of class deadata_fuzzy. Run make_deadata_fuzzy function first!")
  }
    
  if (!is.null(datadea$ud_inputs) || !is.null(datadea$ud_outputs)) {
    warning("This model does not take into account the undesirable feature for inputs/outputs.")
  }
  if (!is.null(datadea$nc_inputs) || !is.null(datadea$nc_outputs)) {
    warning("This model does not take into account the non-controllable feature for inputs/outputs.")
  }
  if (!is.null(datadea$nd_inputs) || !is.null(datadea$nd_outputs)) {
    warning("This model does not take into account the non-discretionary feature for inputs/outputs.")
  }
    
  # Checking modelname
  poss_modelname <- tolower(poss_modelname)
  poss_modelname <- match.arg(poss_modelname)
  model_modelname <- paste("model", poss_modelname, sep = "_")
  
  dmunames <- datadea$dmunames
  nd <- length(dmunames) # number of dmus
  
  if (is.null(dmu_eval)) {
    dmu_eval <- 1:nd
  } else if (!all(dmu_eval %in% (1:nd))) {
    stop("Invalid set of DMUs to be evaluated (dmu_eval).")
  }
  names(dmu_eval) <- dmunames[dmu_eval]
  nde <- length(dmu_eval)
  
  input.mL <- datadea$input$mL
  output.mL <- datadea$output$mL
  input.mR <- datadea$input$mR
  output.mR <- datadea$output$mR
  input.dL <- datadea$input$dL
  output.dL <- datadea$output$dL
  input.dR <- datadea$input$dR
  output.dR <- datadea$output$dR
  inputnames <- rownames(input.mL)
  outputnames <- rownames(output.mL)
  ni <- length(inputnames) # number of inputs
  no <- length(outputnames) # number of outputs
  
  datadea.mL <- structure(list(input = input.mL, output = output.mL, dmunames = dmunames), class = "deadata")
  datadea.mR <- structure(list(input = input.mR, output = output.mR, dmunames = dmunames), class = "deadata")
  
  # Checking h
  if ((length(h) == 1) && (h > 1)){
    h <- seq(from = 0, to = 1, length.out = h)
  } else if (any(h > 1) || any(h < 0)){
    stop("Invalid h vector.")
  }
  h <- sort(unique(h))
  nh <- length(h) # number of h-levels
  hlevel <- vector(mode = "list", length = nh)
  names(hlevel) <- as.character(h)

  for (i in 1:nh) {

    # h-level
    
    a <- h[i]
    input.L <- input.mL - input.dL * (1 - a)
    input.U <- input.mR + input.dR * (1 - a)
    output.L <- output.mL - output.dL * (1 - a)
    output.U <- output.mR + output.dR * (1 - a)
    
    datadea.L <- structure(list(input = input.L, output = output.L, dmunames = dmunames), class = "deadata")
    datadea.U <- structure(list(input = input.U, output = output.U, dmunames = dmunames), class = "deadata")
    
    DMU <- vector(mode = "list", length = nde)
    names(DMU) <- dmunames[dmu_eval]
    
    for (j in 1:nde) {
      
      jj <- dmu_eval[j]
      
      lp.mL <- do.call(model_modelname, list(datadea = datadea.mL, dmu_eval = jj, returnlp = TRUE, ...))
      lp.mR <- do.call(model_modelname, list(datadea = datadea.mR, dmu_eval = jj, returnlp = TRUE, ...))
      lp.L <- do.call(model_modelname, list(datadea = datadea.L, dmu_eval = jj, returnlp = TRUE, ...))
      lp.U <- do.call(model_modelname, list(datadea = datadea.U, dmu_eval = jj, returnlp = TRUE, ...))
      
      obj <- lp.mL$DMU[[1]]$direction
      f.obj <- lp.mL$DMU[[1]]$objective.in
      
      f.con <- rbind(lp.mL$DMU[[1]]$const.mat,
                     lp.mR$DMU[[1]]$const.mat,
                     lp.L$DMU[[1]]$const.mat,
                     lp.U$DMU[[1]]$const.mat)
      
      f.dir <- c(lp.mL$DMU[[1]]$const.dir,
                 lp.mR$DMU[[1]]$const.dir,
                 lp.L$DMU[[1]]$const.dir,
                 lp.U$DMU[[1]]$const.dir)
      
      f.rhs <- c(lp.mL$DMU[[1]]$const.rhs,
                 lp.mR$DMU[[1]]$const.rhs,
                 lp.L$DMU[[1]]$const.rhs,
                 lp.U$DMU[[1]]$const.rhs)
      
      res <- lp(obj, f.obj, f.con, f.dir, f.rhs)
      objval <- res$objval
      names(objval) <- "objval"
      res <- res$solution
      
      DMU[[j]] <- lp.mL$DMU[[1]]$var
      nv <- length(DMU[[j]])
      
      icontador <- 1
      for (iv in 1:nv) {
        nv2 <- length(DMU[[j]][[iv]])
        for (iv2 in 1:nv2) {
          DMU[[j]][[iv]][iv2] <- res[icontador]
          icontador <- icontador + 1
        }
      }
      
    }
    
    hlevel[[i]] <- list(input = list(Lower = input.L, Upper = input.U),
                        output = list(Lower = output.L, Upper = output.U),
                        DMU = DMU)
    
  }
    deaOutput <- list(modelname = paste("fuzzy_possibilistic", poss_modelname, sep = "_"),
                      orientation = lp.mL$orientation,
                      rts = lp.mL$rts,
                      L = lp.mL$L,
                      U = lp.mL$U,
                      h = h,
                      hlevel = hlevel,
                      data = datadea,
                      dmu_eval = dmu_eval,
                      dmu_ref = lp.mL$dmu_ref)
  
  return(structure(deaOutput, class = "dea_fuzzy"))
  
}