# PROMETHEE II The PROMETHEE II constructs preference indices from the criteria evaluations of alternatives and outputs a pre-order based on the outranking flows between the alternatives. ```r PROMETHEEII( performanceTable, preferenceFunction, preferenceThreshold, indifferenceThreshold, gaussParameter, criteriaWeights, criteriaMinMax ) ``` ## Arguments - `performanceTable`: Matrix containing the evaluation table. Each row corresponds to an alternative, and each column to a criterion. Rows (resp. columns) must be named according to the IDs of the alternatives (resp. criteria). - `preferenceFunction`: A vector with preference functions.preferenceFunction should be equal to Usual,U-shape,V-shape, Level,V-shape-Indiff or Gaussian. The elements are named according to the IDs of the criteria. - `preferenceThreshold`: A vector containing threshold of strict preference. The elements are named according to the IDs of the criteria. - `indifferenceThreshold`: A vector containing threshold of indifference. The elements are named according to the IDs of the criteria. - `gaussParameter`: A vector containing parameter of the Gaussian preference function. The elements are named according to the IDs of the criteria. - `criteriaWeights`: Vector containing the weights of the criteria. The elements are named according to the IDs of the criteria. - `criteriaMinMax`: Vector containing the preference direction on each of the criteria. "min" (resp. "max") indicates that the criterion has to be minimized (maximized). The elements are named according to the IDs of the criteria. ## Returns The function returns a list containing the alternatives IDs in decreasing order of preference. Each elements of the list can be a vector of alternatives IDs. ## Examples ```r # The evaluation table performanceTable <- rbind( c(1,10,1), c(4,20,2), c(2,20,0), c(6,40,0), c(30,30,3)) rownames(performanceTable) <- c("RER","METRO1","METRO2","BUS","TAXI") colnames(performanceTable) <- c("Price","Time","Comfort") # The preference functions preferenceFunction<-c("Gaussian","Level","V-shape-Indiff") #Preference threshold preferenceThreshold<-c(5,15,3) names(preferenceThreshold)<-colnames(performanceTable) #Indifference threshold indifferenceThreshold<-c(3,11,1) names(indifferenceThreshold)<-colnames(performanceTable) #Parameter of the Gaussian preference function gaussParameter<-c(4,0,0) names(gaussParameter)<-colnames(performanceTable) #weights criteriaWeights<-c(0.2,0.3,0.5) names(criteriaWeights)<-colnames(performanceTable) # criteria to minimize or maximize criteriaMinMax<-c("min","min","max") names(criteriaMinMax)<-colnames(performanceTable) PROMETHEEII(performanceTable, preferenceFunction,preferenceThreshold, indifferenceThreshold,gaussParameter,criteriaWeights, criteriaMinMax) ```

PROMETHEEII function