PROMETHEEII {MCDA}

PROMETHEE II

Description

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.

Usage

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.

Value

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

# 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)