OutrankingTools (version 1.0)

Electre_tri: ELECTRE TRI Method

Description

The Electre Tri is a multiple criteria decision aiding method, designed to deal with sorting problems. Electre Tri method has been developed by LAMSADE (Paris-Dauphine University, Paris, France).

Usage

Electre_tri(performanceMatrix,
				alternatives,
				profiles,
				profiles_names,
				criteria,
				minmaxcriteria,
				criteriaWeights,
				IndifferenceThresholds,
				PreferenceThresholds,
				VetoThresholds,
				lambda = NULL)

Arguments

performanceMatrix

Matrix or data frame containing the performance 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).

alternatives

Vector containing names of alternatives, according to which the data should be filtered.

profiles

Matrix containing, in each row, the lower profiles of the categories. The columns are named according to the criteria, and the rows are named according to the categories. The index of the row in the matrix corresponds to the rank of the category.

profiles_names

Vector containing profiles'names

criteria

Vector containing names of criteria, according to which the data should be filtered.

minmaxcriteria

criteriaMinMax Vector containing the preference direction on each of the criteria. "min" (resp."max") indicates that the criterion has to be minimized (maximized).

criteriaWeights

Vector containing the weights of the criteria.

IndifferenceThresholds

Vector containing the indifference thresholds constraints defined for each criterion.

PreferenceThresholds

Vector containing the preference thresholds constraints defined for each criterion.

VetoThresholds

Vector containing the veto thresholds constraints defined for each criterion

lambda

The lambda-cutting lambda- should be in the range 0.5 and 1.0) level indicates how many of the criteria have to be fulfilled in order to assign an alternative to a specific category. Default value=0.75

References

Mousseau V., Slowinski R., "Inferring an ELECTRE TRI Model from Assignment Examples", Journal of Global Optimization, vol. 12, 1998, 157-174. Mousseau V., Figueira J., NAUX J.P, "Using assignment examples to infer weights for ELECTRE TRI method : Some experimental results", Universite de Paris Dauphine, cahier du Lamsade n 150, 1997, Mousseau V., Slowinski R., Zielniewicz P. : "ELECTRE TRI 2.0a, User documentation", Universite de Paris-Dauphine, Document du LAMSADE no 111

Examples

# the performance table

performanceMatrix <- cbind(
c(-120.0,-150.0,-100.0,-60,-30.0,-80,-45.0),
c(-284.0,-269.0,-413.0,-596,-1321.0,-734,-982.0),				
c(5.0,2.0,4.0,6,8.0,5,7.0),					
c(3.5,4.5,5.5,8,7.5,4,8.5),		
c(18.0,24.0,17.0,20,16.0,21,13.0)
)
# Vector containing names of alternatives

alternatives <- c("a1","a2","a3","a4","a5","a6","a7")

# Vector containing names of criteria

criteria <- c( "g1","g2","g3","g4","g5")
criteriaWeights <- c(0.25,0.45,0.10,0.12,0.08)

# vector indicating the direction of the criteria evaluation .

minmaxcriteria <- c("max","max","max","max","max")

# Matrix containing the profiles.

profiles <- cbind(c(-100,-50),c(-1000,-500),c(4,7),c(4,7),c(15,20))

#  vector defining profiles' names

profiles_names <-c("b1","b2")

# thresholds vector
IndifferenceThresholds <- c(15,80,1,0.5,1)
PreferenceThresholds <- c(40,350,3,3.5,5)
VetoThresholds <- c(100,850,5,4.5,8)

# Testing

Electre_tri(performanceMatrix,
			alternatives,
			profiles,
			profiles_names,
			criteria,
			minmaxcriteria,
			criteriaWeights,
			IndifferenceThresholds,
			PreferenceThresholds,
			VetoThresholds,
			lambda=NULL)