# PROMETHEE I The PROMETHEE I constructs preference indices from the criteria evaluations of alternatives and outputs three preference relations (P - preference, I - indifference, R - incomparability) based on the outranking flows between the alternatives. ```r PROMETHEEI( 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 three matrices: The first one contains the preference relations between the alternatives, the second one contains the indifference relations between the alternatives and the third one contains the incomparability relations between the alternatives. ## 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) PROMETHEEI(performanceTable, preferenceFunction,preferenceThreshold, indifferenceThreshold,gaussParameter,criteriaWeights,criteriaMinMax) ```

PROMETHEEI function